Population Dynamics & Evolution (EVOP)

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Sub-group minisymposia

Non-equilibrium Thermodynamics in Biology: from Chemical Reaction Networks to Natural Selection

Organized by: John Baez (University of California, Riverside, USA), William Cannon (Pacific Northwest National Laboratory, USA), Larry Li (University of California, Riverside, USA)
Note: this minisymposia has multiple sessions. The second session is MS02-EVOP.

  • John Harte (University of California, Berkeley, USA)
    "Nonequilibrium dynamics of disturbed ecosystems"
  • The Maximum Entropy Theory of Ecology (METE) predicts the shapes of macroecological metrics in relatively static ecosystems, across spatial scales, taxonomic categories, and habitats, using constraints imposed by static state variables. In disturbed ecosystems, however, with time-varying state variables, its predictions often fail. We extend macroecological theory from static to dynamic, by combining the MaxEnt inference procedure with explicit mechanisms governing disturbance. In the static limit, the resulting theory, DynaMETE, reduces to METE but also predicts a new scaling relationship among static state variables. Under disturbances, expressed as shifts in demographic, ontogenic growth, or migration rates, DynaMETE predicts the time trajectories of the state variables as well as the time-varying shapes of macroecological metrics such as the species abundance distribution and the distribution of metabolic rates over individuals. An iterative procedure for solving the dynamic theory is presented. Characteristic signatures of the deviation from static predictions of macroecological patterns are shown to result from different kinds of disturbance. By combining MaxEnt inference with explicit dynamical mechanisms of disturbance, DynaMETE is a candidate theory of macroecology for ecosystems responding to anthropogenic or natural disturbances.
  • Hong Qian (University of Washington, USA)
    "Large deviations theory and emergent landscapes in biological dynamics"
  • The mathematical theory of large deviations provides a nonequilibrium thermodynamic description of complex biological systems that consist of heterogeneous individuals. In terms of the notions of stochastic elementary reactions and pure kinetic species, the continuous-time, integer-valued Markov process dictates a thermodynamic structure that generalizes (i) Gibbs’ macroscopic chemical thermodynamics of equilibrium matters to nonequilibrium small systems such as living cells and tissues; and (ii) Gibbs’ potential function to the landscapes for biological dynamics, such as that of C. H. Waddington’s and S. Wright’s.
  • Pierre Gaspard (Université libre de Bruxelles, Belgium)
    "Nonequilibrium biomolecular information processes"
  • Nearly 70 years have passed since the discovery of DNA structure and its role in coding genetic information. Yet, the kinetics and thermodynamics of genetic information processing in DNA replication, transcription, and translation remain poorly understood. These template-directed copolymerization processes are running away from equilibrium, being powered by extracellular energy sources. Recent advances show that their kinetic equations can be exactly solved in terms of so-called iterated function systems. Remarkably, iterated function systems can determine the effects of genome sequence on replication errors, up to a million times faster than kinetic Monte Carlo algorithms. With these new methods, fundamental links can be established between molecular information processing and the second law of thermodynamics, shedding a new light on genetic drift, mutations, and evolution.
  • Carsten Wiuf (University of Copenhagen, Denmark)
    "Reduction and the Quasi-Steady State Approximation"
  • Chemical reactions often occur at different time-scales. In applications of chemical reaction network theory it is often desirable to reduce a reaction network to a smaller reaction network by elimination of fast species or fast reactions. There exist various techniques for doing so, e.g. the Quasi-Steady-State Approximation or the Rapid Equilibrium Approximation. However, these methods are not always mathematically justifiable. Here, a method is presented for which (so-called) non-interacting species are eliminated by means of QSSA. It is argued that this method is mathematically sound. Various examples are given (Michaelis-Menten mechanism, two-substrate mechanism, ...) and older related techniques from the 50-60ies are briefly discussed.

Non-equilibrium Thermodynamics in Biology: from Chemical Reaction Networks to Natural Selection

Organized by: John Baez (University of California, Riverside, USA), William Cannon (Pacific Northwest National Laboratory, USA), Larry Li (University of California, Riverside, USA)
Note: this minisymposia has multiple sessions. The second session is MS01-EVOP.

  • Matteo Polettini (University of Luxembourg, Luxembourg)
    "Deficiency of chemical reaction networks and thermodynamics"
  • Deficiency is a topological property of a Chemical Reaction Network linked to important dynamical features, in particular of deterministic fixed points and of stochastic stationary states. Here we link it to thermodynamics: in particular we discuss the validity of a strong vs. weak zeroth law, the existence of time-reversed mass-action kinetics, and the possibility to formulate marginal fluctuation relations. Finally we illustrate some subtleties of the Python module we created for MCMC stochastic simulation of CRNs, soon to be made public.
  • Ken Dill (Stony Brook University, USA)
    "The principle of maximum caliber of nonequilibria"
  • Maximum Caliber is a principle for inferring pathways and rate distributions of kinetic processes. The structure and foundations of MaxCal are much like those of Maximum Entropy for static distributions. We have explored how MaxCal may serve as a general variational principle for nonequilibrium statistical physics - giving well-known results, such as the Green-Kubo relations, Onsager's reciprocal relations and Prigogine's Minimum Entropy Production principle near equilibrium, but is also applicable far from equilibrium. I will also discuss some applications, such as finding reaction coordinates in molecular simulations non-linear dynamics in gene circuits, power-law-tail distributions in 'social-physics' networks, and others.
  • Joseph Vallino (Marine Biological Laboratory, Woods Hole, USA)
    "Using the maximum entropy production principle to understand and predict microbial biogeochemistry"
  • Natural microbial communities contain billions of individuals per liter and can exceed a trillion cells per liter in sediments, as well as harbor thousands of species in the same volume. The high species diversity contributes to extensive metabolic functional capabilities to extract chemical energy from the environment, such as methanogenesis, sulfate reduction, anaerobic photosynthesis, chemoautotrophy, and many others, most of which are only expressed by bacteria and archaea. Reductionist modeling of natural communities is problematic, as we lack knowledge on growth kinetics for most organisms and have even less understanding on the mechanisms governing predation, viral lysis, and predator avoidance in these systems. As a result, existing models that describe microbial communities contain dozens to hundreds of parameters, and state variables are extensively aggregated. Overall, the models are little more than non-linear parameter fitting exercises that have limited, to no, extrapolation potential, as there are few principles governing organization and function of complex self-assembling systems. Over the last decade, we have been developing a systems approach that models microbial communities as a distributed metabolic network that focuses on metabolic function rather than describing individuals or species. We use an optimization approach to determine which metabolic functions in the network should be up regulated versus those that should be down regulated based on the non-equilibrium thermodynamics principle of maximum entropy production (MEP). Derived from statistical mechanics, MEP proposes that steady state systems will likely organize to maximize free energy dissipation rate. We have extended this conjecture to apply to non-steady state systems and have proposed that living systems maximize entropy production integrated over time and space, while non-living systems maximize instantaneous entropy production. Our presentation will provide a brief overview of the theory and approach, as well as present several examples of applying MEP to describe the biogeochemistry of microbial systems in laboratory experiments and natural ecosystems.
  • Gheorghe Craciun (University of Wisconsin-Madison, USA)
    "Persistence, permanence, and global stability in reaction network models: some results inspired by thermodynamic principles"
  • The standard mathematical model for the dynamics of concentrations in biochemical networks is called mass-action kinetics. We describe mass-action kinetics and discuss the connection between special classes of mass-action systems (such as detailed balanced and complex balanced systems) and the Boltzmann equation. We also discuss the connection between the 'global attractor conjecture' for complex balanced mass-action systems and Boltzmann's H-theorem. We also describe some implications for biochemical mechanisms that implement noise filtering and cellular homeostasis.

Modeling and Simulations of COVID-19 impact and mitigation strategies

Organized by: Preeti Dubey and Christopher Hoover (Francis I. Proctor Foundation, UCSF, USA)

  • Ranjit Upadhyay (Indian Institute of Technology (ISM) Dhanbad, India)
    "Modeling the recent outbreak of COVID-19 in India and its Control strategies using NPIs and vaccination"
  • Robust testing and tracing are key to fighting the menace of coronavirus disease 2019 (COVID19). This outbreak has progressed with tremendous impact on human life, society and economy. In this work, we propose few models (an age-structured SIQR model, SEQIR model and an SEICR model with comorbidity) to track the progression of the pandemic in India taking into account the different age structures of the country. We have made predictions about the disease dynamics, identified the most infected age groups and analysed the effectiveness of social distancing measures taken in the early stages of infection. This encompasses modeling the dynamics of invaded population, parameter estimation of the model, study of qualitative dynamics, and optimal control problem for non-pharmaceutical interventions (NPIs) and vaccination events such that the cost of the combined measure is minimized. The investigation reveals that disease persists with the increase of exposed individuals having comorbidity in society. The extensive computational efforts show that mean fluctuations in the force of infection increase with corresponding entropy. Further, an increasing trend to the mean force of infection has been indicated through the composite effect. Higher Shannon entropy production, i.e., more disorder in mean force of infection has indicated more strengthen the force of infection according to dynamical perspective. This might cause a dangerous situation in the population. This is a piece of evidence that the outbreak has reached a significant portion of the population. However, optimal control strategies with combined measures provide an assurance of effectively protecting our population from COVID-19 by minimizing social and economic costs. From an epidemiological perspective, comorbidity individuals get gradually infection due to lack of precautions and surveillance and like, social distancing, proper sanitation wearing masks, etc. In this situations, susceptible individuals become infected and turned to exposed individuals. Indeed, exposed individuals can prevent COVID-19 infection due to strong immunity in this connection. Based on the observed data, 7-days moving average curves are plotted for pre-lockdown, lockdown and unlock 1 phases. Following the trend of the curves for the infection, a generalized exponential function is used to estimate the data and corresponding 95% confidence intervals are simulated to estimate the parameters. The effect of control measures, such as quarantine and isolation are discussed and systematically explore the impact of lockdown strategy in order to control the recent outbreak of COVID-19 transmission in India.
  • Christopher Hoover (Francis I. Proctor Foundation, UCSF, USA)
    "Targeted allocation of testing and vaccination reduces transmission of SARS-CoV2 and improves health equity: An agent-based modeling study"
  • Effectively allocating scarce resources to combat infectious disease outbreaks is essential to reducing their impact. The ongoing pandemic of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2) has been characterized by extreme heterogeneity in individual spread and higher spread among underserved sub-populations such as the Latinx community in San Francisco and New York City, and similarly marginalized racial and ethnic minority groups across the U.S. This heterogeneity in transmission creates challenges for control efforts when those experiencing the highest rates of transmission also have limited access to resources to mitigate transmission. However, even imperfect interventions that are efficiently targeted to individuals or groups driving transmission can have a far greater impact than interventions that are evenly distributed in the population. Here we describe an agent-based model (ABM) developed to simulate the transmission of SARS-CoV2 in the City and County of San Francisco (SF). The ABM incorporates a synthetic population developed to capture drivers of racial and ethnic disparities in transmission observed in SF over the course of the pandemic. Challenges in ABM calibration are discussed in light of the large parameter space and limited reliable data sources on which to calibrate. We then describe how the ABM can be used to explore counterfactual scenarios in which resources such as testing, work from home support, and vaccination are targeted towards population strata with the highest rates of infection. Using the ABM, we demonstrate the benefit of these targeted strategies on both reducing the spread of SARS-CoV2 and improving metrics of health equity.
  • Morganne Igoe (University of Tennessee, Knoxville, USA)
    "ZCTA-level Predictors of COVID-19 Hospitalization Risk in the St. Louis Area"
  • COVID-19 has overwhelmed U.S. healthcare systems, with almost 30 million cases and over 500,000 deaths as of March 28, 2021. Older age, male gender, race, and underlying medical conditions have been identified as factors among hospitalized patients. There are also geographic disparities in COVID-19 hospitalization risk that are at least partly driven by geographic differences in sociodemographic, economic, and co-morbid factors. If these factors could be identified, they could help inform control efforts. The aim of this study is to identify ZCTA-level predictors of COVID-19 hospitalization risk in the St. Louis Area using sociodemographic, economic, and chronic disease factors. ZCTA-level sociodemographic, economic, and chronic disease factors were evaluated for correlation with each other and univariable associations with the age-adjusted number of COVID-19 hospitalizations. The ZCTA population was used as the offset. A multivariable negative binomial regression model was then fit using a backwards elimination process. Percent black population, percent of the population with some college education, number of diabetes discharges per 100 population, and population adjusted cases were all positively associated with COVID-19 hospitalization risk. A number of sociodemographic and chronic conditions are important determinants of disparities in COVID hospitalization risk. These findings will inform health care systems of where large numbers of patients may occur to reduce overburdening of hospitals and to guide vaccination efforts.
  • Preeti Dubey (Francis I. Proctor Foundation, UCSF, USA)
    "Optimal vaccine prioritization for COVID-19 between high-risk and core group in California"
  • The COVID-19 pandemic has caused record numbers of daily confirmed cases and deaths in USA during the winter of 2020-2021. With the approval of Moderna and Pfizer vaccines, a substantial mitigation of the epidemic is expected by mid-2021. During the initial rollout, it was unclear whether or not vaccine should be targeted at elderly individuals at highest risk of mortality and morbidity, or towards younger individuals responsible for a majority of transmission. In this study, we sought to investigate the optimal prioritization of COVID-19 vaccination in California. We constructed a compartmental model based on the natural history of COVID-19 transmission. The model involved two transmission risk groups (low and high), and two age prioritization groups. We considered the case of random mixing vs. positive assortative mixing, as well as the relative rate of high COVID-19 risk behavior in the high transmission risk group. The model considered incomplete reporting and reporting delays and was calibrated to California case data. All 24 possible orderings of age/risk prioritization were simulated suggesting that age prioritization was optimal when the relative riskiness of the high-risk group was low. The randomness in mixing has also played a role in making the decision of optimality of risk prioritization when the relative riskiness was high. Our results are aligned with the findings of other modeling groups that some risk targeting can be a valuable consideration in controlling the pandemic.

Evolutionary Game Theory under Uncertainty

Organized by: Hong Duong (University of Birmingham, UK), The Anh Han (Teesside University, UK)

  • Hye Jin Park (Asia Pacific Center for Theoretical Physics, Korea)
    "Extinction dynamics from meta-stable coexistences in an evolutionary game"
  • Jorge Peña (Institute for Advanced Study in Toulouse, University of Toulouse 1 Capitole, France)
    "Evolutionary dynamics of discrete public goods under threshold uncertainty"
  • Isamu Okada (Soka University, Japan)
    "Social dilemma, scoring dilemma, and punishment dilemma in indirect reciprocity"
  • Marco A. Javarone (University College London, UK)
    "Cooperative behaviours and sources of noise"

Predicting ecological dynamics in fluctuating environments

Organized by: Anna Miller (Department of Integrated Mathematical Oncology, Moffitt Cancer Center, United States), Nancy Huntly (Ecology Center and Department of Biology, Utah State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS07-EVOP.

  • Ivana Gudelj (Biosciences, University of Exeter, UK)
    "Predicting community dynamics of antibiotic sensitive and resistant species in fluctuating environments"
  • Microbes occupy almost every niche within and on their human hosts. Whether colonising the gut, mouth or bloodstream, microorganisms face temporal fluctuations in resources and stressors within their niche. Yet we still know little of how environmental fluctuations mediate certain microbial phenotypes, notably antimicrobial resistant ones. For instance, do rapid or slow fluctuations in nutrient and antimicrobial concentrations select for, or against, resistance? We tackle this question using an ecological approach by studying the dynamics of a synthetic and pathogenic microbial community containing two species, one sensitive and one resistant to an antibiotic drug where the community is exposed to different rates of environmental fluctuation. We provide mathematical models, supported by experimental data, to demonstrate that simple community outcomes, like competitive exclusion, can shift to coexistence and ecosystem bi-stability as fluctuation rates vary. Theory gives mechanistic insight into how these dynamical regimes are related. Our approach highlights a fundamental difference between resistance in single species populations and in communities. While fast environmental changes are known to select against resistance in single-species populations, here we show that they can promote the resistant species in mixed-species communities. Our theoretical observations are verified empirically using a two-species Candida community.
  • Shota Shibasaki (Department of Fundamental Microbiology, University of Lausanne, Switzerland)
    "Environmental and demographic stochasticity together changes microbial interactions and diversity"
  • Microorganisms live in environments that fluctuate between mild and harsh conditions. As harsh conditions may cause extinctions, the rate at which fluctuations occur can shape microbial communities and their diversity, but we still lack an intuition on how. Here, we build a mathematical model describing two microbial species living in an environment where substrate supplies randomly switch between abundant and scarce. We then vary the rate of switching as well as different properties of the interacting species, and measure the probability of the weaker species driving the stronger one extinct. We find that this probability increases with the strength of demographic noise, and peaks at either low, high, or intermediate switching rates depending on both species' ability to withstand the harsh environment. This complex relationship shows why finding patterns between environmental fluctuations and diversity has historically been difficult. In parameter ranges where the fittest species was most likely to be excluded, however, the beta diversity in larger communities also peaked. In sum, while we find no simple rules on how the frequency of fluctuations shapes species diversity, we show that their effect on interactions between two representative species predicts how diversity in the whole community will change.
  • Audrey Freischel (Department of Integrated Mathematical Oncology, Moffitt Cancer Center, USA)
    "Utilizing a Consumer-Resource model to hypothesize foraging trade-offs in “cream skimmers” and “crumb pickers”"
  • Solid tumors consist of heterogeneous clones presenting unique metabolism and function. Metabolic variation allows cancer cells to be characterized as either “cream-skimmers,” which consume resources quickly at the cost of efficiency (glycolysis), or “crumb-pickers,” which consume resources slowly but have a higher metabolic payoff (oxidative phosphorylation). As observed in nature, fluctuating resources allow for coexistence of different species. To better understand the coexistence of “cream-skimmers” and “crumb-pickers” in the tumor, we utilized a classic consumer-resource model with fluctuating resource to evaluate tradeoffs in encounter probability, handling time, and fixed and variable costs. These models elucidate novel hypotheses in tumor cell competition as well as provide new insights to consumer-resource dynamics.
  • David Demory (School of Biological Sciences, Georgia Institute of Technology, USA)
    "Temperature drives virus-host coexistence in the ocean"
  • Diverse marine viruses coexist with microbial hosts across a range of fluctuating marine environments. Here, we used population dynamic models to explore the role of temperature variation in modulating virus-phytoplankton coexistence. Dynamic models suggest that variation in sea surface temperature influences the range of viral life-history traits underlying coexistence amongst virus-microbe pairs, including the prediction that warmer temperatures can suppress viral persistence. Using in situ ocean datasets, we find evidence of a latitudinal trend in viral diversity, decreasing in warmer regions. Yet, we also find that temperature fluctuations can be a driver of coexistence, allowing for a succession of (in)favorable conditions, potentially promoting the coexistence of different virus types infecting the same host via the storage effect. These findings highlight the importance of integrating environmental feedback into the study of host-virus coexistence in the global oceans.

Predicting ecological dynamics in fluctuating environments

Organized by: Anna Miller (Department of Integrated Mathematical Oncology, Moffitt Cancer Center, United States), Nancy Huntly (Ecology Center and Department of Biology, Utah State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS06-EVOP.

  • Peter Adler (Department of Wildland Resources and the Ecology Center, Utah State University, USA)
    "Challenges in quantifying fluctuation-dependent coexistence mechanisms in nature"
  • Although modern coexistence theory is 20 yrs old, empirical tests remain scarce. We review the formidable challenges in conducting invasibility analyses in natural ecosystems that make such tests rare. Theory asks, how quickly would each species in a community increase from low abundance in the presence of competitors near their stochastic equilibrium abundances, and how do various features of the environment or the species themselves affect this invasion growth rate? Answering these questions experimentally requires removing a focal species from a community, allowing the remaining species to approach equilibrium, reintroducing the focal species at low abundance, and then repeating these steps under different experimental treatments and for all species in the community. Logistical problems make this approach impractical for macroscopic species growing in nature. An alternative approach is building a model that captures the essential dynamics of the community, and then simulating invasion experiments using the model. The challenges for this approach include naïve application of statistical conventions that may predetermine results, and uncertainty about whether models fit to observational data can accurately project dynamics outside the range of conditions that were directly observed.
  • Robin Snyder (Department of Biology, Case Western Reserve University, USA)
    "Quantifying fluctuation-dependent coexistence mechanisms for populations of spatially-structured, discrete individuals"
  • We traditionally analyze coexistence by asking when each species in a system could invade a community made up of the others. To do this, we assume that the invader is rare enough that it does not compete with itself and yet is common enough that we can ignore demographic stochasticity. Spatially extended systems with discrete individuals cause these assumptions to break down. Local dispersal and competition create clumpy invader distributions, so that invaders are common over the scale with which they interact, yet populations are small within the limited scale of interaction, so that discreteness cannot be ignored. Here we present a simulation-based method for quantifying how much different processes or traits contribute to coexistence in spatially structured community models with discrete individuals. We demonstrate our method using simulations of the lottery model and consider contributions from environmental fluctuations (E), competition fluctuations (C), demographic stochasticity, and their interactions. As the spatial scales of competition and dispersal decrease, invaders become more clustered and invader-invader competition increases. This weakens the positive contribution of Cov(E, C) and strengthens the negative effects of fluctuations in C. The effect of demographic stochasticity is small and the trend with increased invader clustering is not statistically significant.
  • Virginia Turati (Department of Integrated Mathematical Oncology, Moffitt Cancer Center, USA)
    "An integrated approach to understanding the clonal dynamics of childhood B-cell precursor acute lymphoblastic leukemia during treatment to relapse"
  • Comparison of intratumor genetic heterogeneity at diagnosis and relapse suggests that chemotherapy induces bottleneck selection of subclonal genotypes. However, evolutionary events after chemotherapy could also explain changes in clonal dominance seen at relapse. We investigated mechanisms of selection in BCP-ALL during induction chemotherapy where maximal cytoreduction occurs. To distinguish stochastic versus deterministic events, individual leukemias were transplanted into xenografts and chemotherapy administered. We subsequently leveraged the Hybrid Automata Library (HAL) to implement a mathematical model and, based on the experimental data, infer the evolutionary trajectories leading from initial treatment response to relapse. Analyses of the immediate post-treatment leukemic residuum at single-cell resolution revealed that chemotherapy has little impact on genetic heterogeneity. Instead, treatment acts on the extensive transcriptional and epigenetic heterogeneity of untreated BCP-ALL, selecting a phenotypically uniform population with hallmark signatures of deep quiescence and primitive developmental stage. The mathematical model further suggests that in those leukemias in which most subclones display similar fitness, subclonal selection happens later and not as a direct result of treatment. Instead, in those rarer leukemias in which genotype and phenotypes broadly related to treatment resistance (i.e., proliferation potential) co-segregate, only a few lineages survive through relapse.
  • Jeff Maltas (Cleveland Clinic, USA)
    "Reversibility of evolution in tunably correlated environments"
  • Naturally evolving populations constantly face changing environmental conditions. One interesting question is to explore if adaptations that occur as a result of a new environment can be reversed by returning to the previous environment. Using simulations we quantify the genotypic and phenotypic reversibility of an asexually reproducing population. We show that the interlandscape correlation between landscape pairs can dramatically impact the reversibility of this population. Finally, we show that slowly vs quickly switching between landscapes can significantly impact reversibility.

The Study of Diffusive Dispersal in Population Dynamics

Organized by: Chiu-Yen Kao (Claremont McKenna College, United States), Bo Zhang (Oklahoma State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS09-EVOP. The third session is MS10-EVOP.

  • Suzanne Lenhart (University of Tennessee, United States)
    "Optimal control for management of an invasive population model with diffusion in a river"
  • Invasive species in rivers may be managed by changing flow rates. Using a partial differential equation model with diffusion representing an invasive population in a river, we consider optimal control of the time-varying water discharge rate to keep the population downstream. We will present some numerical results with varying parameters to illustrate the movement of the invasive population.
  • Idriss Mazari (Institute of Analysis and Scientific Computing, TU Wien, Austria)
    "Fragmenting and concentrating resources to optimise the total population size: a qualitative analysis"
  • In this talk, we investigate the optimal way to spread resources inside a domain in order to maximise the total population size. More specifically, we will explain why, when the individuals disperse quickly, it is much better to concentrate resources while, when they disperse slowly, it is more relevant to scatter the resources throughout the domain. The talk will mostly be descriptive, and is based on collaborations with G. Nadin, Y. Privat and D. Ruiz-Balet.
  • Yun Kang (Arizona State University, United States)
    "Dynamics of a Diffusion Reaction Prey-Predator Model with Delay in Prey: Effects of Delay and Spatial Components"
  • We study the complex dynamics of a Monod-Haldane-type predator-prey interaction model that incorporates: (1) A constant time delay in the prey growth; and (2) diffusion in both prey and predator. We provide the rigorous results of our system including the asymptotic stability of a positive equilibrium; Hopf bifurcation; and the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. We also perform numerical simulations on the effects of diffusion or/and delay when the corresponding ODE model has either a unique interior equilibrium with two interior attractors or two interior equilibria. Our theoretical and numerical results show that diffusion can either stabilize or destabilize the system; large delay could destabilize the system; and the combination of diffusion and delay could intensify the instability of the system. Moreover, when the corresponding ODE system has two interior equilibria, diffusion or time delay in prey or both could lead to the extinction of predator. Our results may provide us useful biological insights on population managements for prey-predator interaction systems.
  • Noelle Beckman (Biology Department & Ecology Center, Utah State University, United States)
    "Population persistence of plants under global change"
  • Climate change and habitat loss are two of the primary causes of global biodiversity loss. Habitats gradually become unsuitable as temperature, rainfall, and related climatic variables change. In addition to climate change, 75% of the land surface around the world has been converted by humans. As habitats shift, species must adapt to the new conditions, move to stay within their suitable habitat, or die. We examine the global distribution of species’ vulnerabilities to climate change and habitat loss using integrodifference equations. With information on demography and dispersal, we can quantify a population’s spreading speed -- the ability of a population to shift its range -- and its critical patch size – the size of habitat where population growth due to reproduction balances population loss through dispersal. We analyze the distributions of spreading speeds and critical patch sizes across a defined set of species within a system (e.g., community or taxonomic group). We use a range of distributions for population growth rates and dispersal. We analyzed the distributions for spreading speeds and critical patch sizes when dispersal variance and the geometric growth rates are independent and either fixed or distributed according to an exponential, gamma, modified gamma, or log-normal. We can use these distributions to estimate the proportion of species that can shift their ranges in response to climate change or persist based on a minimum critical patch size. This approach allows us to predict responses to environmental change across a broad range of species for which data may be lacking, and this is particularly important for developing indicators of biodiversity loss and planning of remedial actions.

The Study of Diffusive Dispersal in Population Dynamics

Organized by: Chiu-Yen Kao (Claremont McKenna College, United States), Bo Zhang (Oklahoma State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS08-EVOP. The third session is MS10-EVOP.

  • Rachidi Salako (University of Nevada at LasVegas, United States)
    "Study of a diffusive multiple-strains epidemic model"
  • Infectious diseases are one of the leading causes of many deaths around the world. As a result, health officials and the World Health Organization have devoted several resources to educate populations on safety measures which prevent the spread of infectious diseases. Hence restricting population’s movement has been widely used in an effort to limit the outbreak of an infectious disease. In this talk, we will study a multiple-strains PDE infectious disease epidemic model and discuss how population movement can affect the dynamics of the disease.
  • Kurt Anderson (Department of Evolution, Ecology, and Organismal Biology, University of California, Riverside, United States)
    "Body size dependent dispersal influences stability in heterogeneous metacommunities"
  • Body size affects key biological processes across the tree of life, with particular importance for food web dynamics and stability. Traits influencing movement capabilities depend strongly on body size, yet the effects of allometrically-structured dispersal on food web stability are less well understood than other demographic processes. Here we study the stability properties of spatially-arranged model food webs in which larger bodied species occupy higher trophic positions, while species' body sizes also determine the rates at which they traverse spatial networks of heterogeneous habitat patches. Our analysis shows an apparent stabilizing effect of positive dispersal rate scaling with body size compared to negative scaling relationships or uniform dispersal. However, as the global coupling strength among patches increases, the benefits of positive body size-dispersal scaling disappear. A permutational analysis shows that breaking allometric dispersal hierarchies while preserving dispersal rate distributions rarely alters qualitative aspects of metacommunity stability. Taken together, these results suggest that the oft-predicted stabilizing effects of large mobile predators may, for some dimensions of ecological stability, be attributed to increased patch coupling per se, and not necessarily coupling by top trophic levels in particular.
  • Harunori Monobe (Okayama University, Japan)
    "Singular limit of a mathematical model related to controlling invasive alien species"
  • In this talk, we suppose simple PDE models related to controlling invasive alien species. Also we consider the singular limit of the PDE and show that solutions of the PDE problem converge to that of free boundary problems called Fisher-Stefan problem.
  • King-Yeung Lam (Department of Mathematics, The Ohio State University, United States)
    "Defining the Ideal Free Distribution in Spatio-temporally Heterogeneous Environments."
  • A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing for the effects of crowding. In this paper, we extend the idea of individual fitness associated with a specific location in space to account for the full path that an individual organism takes in space and time over a periodic cycle, and extend the mathematical formulation of an ideal free distribution to general time periodic environments. We find that, as in many other cases, populations using dispersal strategies that can produce a generalized ideal free distribution have a competitive advantage relative to populations using strategies that do not produce an ideal free distribution. A sharp criterion on the environmental functions is found to be necessary and sufficient for such ideal free distribution to be feasible. In the case the criterion is met, we showed that there exist dispersal strategies that can be identified as producing a time-periodic version of an ideal free distribution, and such strategies are evolutionarily steady and are neighborhood invaders from the viewpoint of adaptive dynamics.

The Study of Diffusive Dispersal in Population Dynamics

Organized by: Chiu-Yen Kao (Claremont McKenna College, United States), Bo Zhang (Oklahoma State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS08-EVOP. The third session is MS09-EVOP.

  • Seyyed Abbas Mohammadi (Yasouj University, Iran)
    "Optimal Chemotherapy for Brain Tumor Growth in a Reaction-Diffusion Model"
  • We address the question of determining optimal chemotherapy strategies to prevent the growth of brain tumor population. To do so, we consider a reaction-diffusion model which describes the diffusion and proliferation of tumor cells and a minimization problem corresponding to it. It is established that the optimization problem admits a solution and we obtain a necessary condition for the minimizer . In a specific case, the optimizer is calculated explicitly, and we prove that it is unique. Then, a gradient-based efficient numerical algorithm is developed in order to determine the optimizer. Our results suggest a bang-bang chemotherapy strategy in a cycle which starts at the maximum dose and terminates with a rest period. Numerical simulations based upon our algorithm on a real brain image show that this is in line with the maximum tolerated dose (MTD), a standard chemotherapy protocol.
  • Daozhou Gao (Shanghai Normal University, China)
    "Effects of asymmetric dispersal on total biomass in a two-patch logistic model"
  • The impact of animal dispersal on the total population abundance is one of the core issues in theoretical and applied ecology. In this talk, for the two-patch logistic model, we study how dispersal intensity and dispersal asymmetry affects the total population abundance. Two complete classifications of the model parameter space are given: one concerning when dispersal causes smaller or larger total biomass than no dispersal, and the other addressing how the total biomass changes with dispersal intensity and dispersal asymmetry. This improves some existing results, e.g., a recent work of Arditi et al. (Theor. Popul. Biol., 120: 11-15, 2018).
  • Alfonso Ruiz-Herrera (University of Oviedo, Spain)
    "Network Topology vs. Spatial Scale of Movement in Trophic Metacommunities"
  • A central question in spatial ecology is understanding the interplay between the different types of movement and (spatial) network topology in the dynamics of a metacommunity. However, this is not an easy task as most fragmented ecosystems have trophic interactions involving many species and complex path-way structures. Recent attempts to solve this challenge have introduced certain simplifying assumptions or focused on a limited set of examples. However, these results do not cover many real situations. The goal of the talk is to compare the influence of the different topologies for a given configuration of nodes on the population abundances of the species of a trophic metacommunity. In particular, we are able to describe optimal movements/topologies that maximize the total population size of a target species. Regarding methodology, we first distinguish between species with low and high mobility. In the first group, we analyze the role of each path in isolation. In the second, we study the kernel of a matrix obtained from the adjacency matrices. Our main result reveals that the influence of network topologies on the population abundances depends, to a great extent, on the movement time scale. Moreover, we will prove that some directed graphs are useful in maximising the population abundance of a target species. Our framework can be readily used with any metacommunity and, therefore, represents a unification of biological insights. Moreover, we shed light on some folkloric discussions such as the role of the symmetric movement or the number of paths of a landscape.
  • Xiaoqing He (East China Normal University, China)
    "On the effects of carrying capacity of intrinsic growth rate on single and multiple species in spatially heterogeneous environments"
  • We consider a diffusive logistic model of a single species in a heterogeneous environment, with two parameters, r(x) for intrinsic growth rate and K(x) for carrying capacity. When r(x) and K(x) are proportional, i.e., r=cK, it is proved by Prof. Lou Yuan that a population diffusing at any rate will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. In this talk, we study another case when r(x) is a constant, i.e., independent of K(x). In such case, a striking result is that for any dispersal rate, the logistic equation with spatially heterogeneous resources will always support a total population strictly smaller than the total carrying capacity at equilibrium, which is just opposite to the case r = cK. These two cases of single species models also lead to two different forms of Lotka-Volterra competition-diffusion systems. We then report the consequences of the aforementioned difference on the two corresponding forms of the competition systems. Our results indicate that in heterogeneous environments, the correlation between r(x) and K(x) has more profound impacts in population ecology then we had previously expected, at least from a mathematical point of view. This is joint work with Qian Guo and Prof. Wei-Ming Ni.

Recent developments in phylogenetic network reconstruction and beyond

Organized by: Guillaume Scholz (University of Leipzig, Germany), Katharina Huber (University of East Anglia, United Kingdom)
Note: this minisymposia has multiple sessions. The second session is MS17-EVOP.

  • Magnus Bordewich (Durham University, United Kingdom)
    "Diversity in phylogenetic networks"
  • Dating back to 1992, phylogenetic diversity (PD) is a prominent quantitative tool for measuring the biodiversity of a collection of species. This measure is based on the evolutionary distance among the species in the collection. Loosely speaking, if T is a phylogenetic tree whose leaf set X represents a set of species and whose edges have real-valued lengths (weights), then the PD score of a subset S of X is the sum of the weights of the edges of the minimal subtree of T connecting the species in S. In this talk we will discuss recent work on extending this concept from phylogenetic trees to phylogenetic networks and consider the computational complexity of the associated optimisation problems.
  • Simone Linz (University of Auckland, New Zealand)
    "Superfluous arcs in phylogenetic networks"
  • The last 15 years have seen a shift from the reconstruction of phylogenetic trees towards phylogenetic networks. The latter not only capture speciation events but also evolutionary processes such as hybridization and lateral gene transfer that cannot be explained by a single phylogenetic tree. Nevertheless, since the evolutionary history of a single gene or short DNA fragment is, in most cases, correctly described by a tree, the set of phylogenetic trees that are embedded in a network continue to be of recurring interest. For example, to score a phylogenetic network in a maximum parsimony or likelihood framework, one often scores each embedded tree instead of the network directly. In practice this often comes down to scoring a multiset of embedded trees whose size is exponential in the number of reticulations in the network. In this talk, we introduce the notion of a non-essential arc of a phylogenetic network N which is an arc whose deletion from N results in a phylogenetic network N’ whose set of embedded trees is equal to that of N. We investigate the class of tree-child networks and characterize which arcs are non-essential. This characterization is based on a family of directed graphs. Moreover, we show that identifying non-essential arcs in a tree-child network takes time that is polynomial in the number of leaves of the network.
  • Kristina Wicke (The Ohio State University, United States of America)
    "Linking phylogenetics and classical graph theory: edge-based phylogenetic networks and their relation to GSP graphs"
  • Recently, tree-based phylogenetic networks have attracted considerable attention in the literature. Roughly speaking, these networks can be constructed from a phylogenetic tree by inserting additional edges. However, in general, it is an NP-completeproblem to decide whether an unrooted phylogenetic network is tree-based or not. In this talk, I will introduce a class of unrooted networks, namely edge-based networks, that are necessarily tree-based and can be recognized in linear time. Surprisingly, the class of edge-based networks is closely related to a well-known family of graphs in classical graph theory, the class of generalized series-parallel (GSP) graphs, and I will explore this relationship in full detail.
  • Vincent Moulton (University of East Anglia, United Kingdom)
    "Reconstructibility of unrooted level-k phylogenetic networks from distances"
  • A phylogenetic network is a graph-theoretical tool that is used by biologists to represent the evolutionary history of a collection of species. One potential way of constructing such networks is via a distance-based approach, where one is asked to find a phylogenetic network that in some way represents a given distance matrix, which gives information on the evolutionary distances between present-day taxa. In this talk, we consider the following question. For which k are unrooted, edge-weighted level-k networks uniquely determined by their distance matrices? We consider this question for shortest distances as well as for the case that the multisets of all distances is given.

Social Networks and Opinion Dynamics

Organized by: Daniel Simonson (University of California, Irvine, USA), Samuel Lopez (University of California, Irvine, USA)

  • Maxi San Miguel ( Institute for Cross-Disciplinary Physics and Complex Systems - Campus Universitat de les Illes Balears, Spain)
    "Coevolution dynamics of opinion and social network"
  • Modeling opinion dynamics of a set of interacting agents requires specifying the social network of interactions and the state (opinion) of the agents, represented as nodes of the network. The links of the network can also have a state, representing for instance attractive or repulsive interactions. In addition, the network might not be fixed, but adaptive with a time dependent topology in which agents can choose and change their neighbors. We introduce such a general dynamical model for binary opinions including the coupled dynamics of the states of the nodes, the states of the links and the topology of the network. We find a transition from a dynamical state of coexisting opinions to a consensus state showing network fragmentation at the transition line. Our results contribute to the description of processes of emergence of social fragmentation and polarization.
  • Tomasz Raducha ( IFISC, Institute for Cross-disciplinary Physics and Complex Systems (UIB-CSIC), Spain)
    "Vulnerabilities of democratic electoral systems: zealot and media-susceptibility"
  • The vulnerability of democratic processes is under scrutiny after scandals related to Cambrige Analytica (2016 U.S. elections, the Brexit referendum, and elections in Kenya). The deceptive use of social media in the US, the European Union and several Asian countries, increased social and political polarization across world regions. Finally, there are straightforward frauds like Crimea referendum and Belarus elections. These challenges are eroding democracy, the most frequent source of governmental power, and raises multiple questions about its vulnerabilities. Democratic systems have countless ways of performing elections, which create different electoral systems (ES). It is therefore in citizens' interest to study and understand how different ESs relate to different vulnerabilities and contemporary challenges. These systems can be analyzed using network science in various layers -- they involve a network of voters in the first place, a network of electoral districts connected by commuting flow for instance, or a network of political parties to give a few examples. It is essential to provide new tools and arguments to the discussion on the evaluation of electoral systems. We aim at comparing different ESs in a dynamical framework. Our novel approach of analyzing electoral systems in such way with all its aspects included, from opinion dynamics in the population of voters to inter-district commuting patterns to seat appointment methods, will help answering questions like: Which electoral systems are more predictable/stable under fluctuations? Which electoral systems are the most robust (or vulnerable) under external and internal influences? Which features of electoral systems make them more (less) stable?
  • Daniel Simonson (University of California, Irvine, USA)
    " The effects of opinion weighting, (dis)agreement, and external influence on social group formation"
  • Opinion dynamics can be modeled by using agent-based simulations, where agents in a population are characterized by binary opinions on a number of different issues. They engage in pairwise interactions, whereby if the agreement level is high, the interlocutor is recognized as an ``ally' and the individual will flip one of their opinions to coincide with the interlocutor; if the agreement is low, they will switch away from the interlocutor. While it is usually assumed that all issues in the opinion vector are equally important, here we investigate how breaking this symmetry influences the dynamics. We find that the model outcomes can be predicted by a single Agreement-Disagreement Score (ADS) in [-1,1]. ADS characterizes how likely individuals in the population are to regard an interlocutor as an ally; low-ADS (very ``cautious') populations tend to converge to a two-faction system with exponentially high convergence times, while high-ADS (very ``trusting') populations tend to converge to a single-faction system relatively fast. In heterogeneous populations characterized by individual issue weighting, individuals that are more ``trusting' are more likely to join the majority group compared to those that are more ``cautious'. In the presence of an influencer, for ADS both near -1 and 1, a single faction tends to emerge, but in the former case it coincides with the influencer's opinions, while in the latter case it is the opposite. Time to fixation is also affected by the presence of an influencer, especially for negative-ADS populations, where it no longer experiences such a large increase near -1. One can say that an influencer unifies the population to align with the source of influence if ADS>1 and to disagree with it if ADS<1, and consensus is reached relatively fast for both extremely ``trusting' and extremely ``cautious' populations.
  • Gyorgy Korniss ( Rensselaer Polytechnic Institute, USA)
    "The Impact of Heterogeneous Thresholds on Social Contagion and Influencing with Multiple Initiators"
  • The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We observe a non-monotonic change in the cascade size as we vary the standard deviation. Further, for a sufficiently large spread in the threshold distribution, the tipping-point behavior of the social influencing process disappears and is replaced by a smooth crossover governed by the size of initiator set. P.D. Karampourniotis, S. Sreenivasan, B.K. Szymanski, and G. Korniss, The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators', PLoS ONE 10(11): e0143020 (2015); http://dx.doi.org/10.1371/journal.pone.0143020. P. D. Karampourniotis, B.K. Szymanski, G. Korniss, 'Influence Maximization for Fixed Heterogeneous Thresholds', Scientific Reports 9, 5573 (2019); https://doi.org/10.1038/s41598-019-41822-w.

Going backward in time with the coalescent and other ancestral structures

Organized by: Fernando Cordero (Bielefeld University, Germany), Sebastian Hummel (Bielefeld University, Germany)

  • Cornelia Pokalyuk (Goethe University Frankfurt, Institute for Mathematics, Germany)
    "Haldane’s formula in Cannings models with moderate selection"
  • A rule of thumb known as Haldane’s formula states that the probability of fixation for a single beneficial individual with small selective advantage s >0 and offspring variance v in a large population of N individuals is approximately equal to 2s/v. In my presentation I will report on a proof of this asymptotics in the regime of moderate selection, i.e. s_N∼ N^{−b} and b∈(0,1), for a class of Cannings models which allow for a paintbox construction. A forwards as well as a backwards point of view of the paintbox construction turns out to be suitable for the analysis. Via the backwards view we arrive at a time-discrete analogue of the ancestral selection process which is in sampling duality to the wildtype frequency process. In the regime of moderately weak selection (i.e. 1/2< b <1) and under conditions on the paintbox which ensure convergence of the neutral genealogy to Kingman’s coalescent, this sampling duality leads to a proof of Haldane’s formula (EJP 26(4), 2021). In the case of moderately strong selection (0< b <1/2) we make use of the forward construction and approximate the frequency process by Galton-Watson processes (arxiv:2008.02225). The results are joint work with Florin Boenkost, Adrián González Casanova and Anton Wakolbinger.
  • Maite Wilke Berenguer (Humboldt-Universität zu Berlin, Germany)
    "Can dormancy induce skewed offspring distributions?"
  • Dormancy naturally occurs in several forms. A classic example is seasonal dormancy: populations that switch into a dormant form during 'winter', only to wake up in 'spring' to resume reproduction. If single individuals wake up significantly earlier than the main population, the additional time for reproduction might be reflected in the offspring numbers at the end of summer, with the early birds' offspring constituting a positive fraction of the population in the following year. We give a simple model for the evolution of such a population and show that for some choices of model parameters the genealogy of the population will be described by a Lambda-coalescent. In particular, the Beta-coalescent can describe the genealogy when the rate at which individuals wake up increases exponentially over time. We also characterize the set of all Lambda-coalescents that can arise in this framework.
  • Airam Blancas (Departamento de Estadística, ITAM, Mexico)
    "A coalescent model with recombination and population structure"
  • We introduce a Markov model to describe the backwards evolution of l-linked loci from p-structured populations. More precisely, we define a continuous time Markov chain with jumps at recombination, coalescence, and migration events. We delineate the space states in a way a that it is possible to keep track the ancestral populations at every locus as well as the population location of the lineages. We prove that the state space cardinality of the process is polynomial for admixture populations and provide an analytic expression for 3-loci lineages from without admixture populations.
  • Dario Spanò (University of Warwick, England)
    "Asymptotic genealogies for interacting particle systems"
  • We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman n-coalescent in the infinite system size limit in the sense of finite-dimensional distributions.Thus, the tractable n-coalescent can be used to predict the shape and size of SMC genealogies, as we illustrate by characterising the limiting mean and variance of the tree height. SMC genealogies are known to be connected to algorithm performance, so that our results are likely to have applications in the design of new methods as well.

Modeling and Simulation of Hydrodynamics in Cell Biology

Organized by: Thomas Fai (Brandeis University, USA), Ying Zhang (Brandeis University, USA)

  • Paul Atzberger (UC Santa Barbara, USA)
    "Surface Fluctuating Hydrodynamics Approaches for Proteins Kinetics and Transport within Curved Lipid Bilayer Membranes"
  • We introduce surface fluctuating hydrodynamics approaches for investigating transport and fluid-structure interactions arising in cell mechanics within curved lipid bilayer membranes. We focus particularly on drift-diffusion dynamics of interacting proteins and microstructures. We show how a mesoscale stochastic description of the mechanics can be formulated (SPDEs) accounting for geometric contributions, hydrodynamic coupling, and thermal fluctuations. The underlying stochastic equations (SPDEs) pose practical challenges for use in simulations, including, (i) a need for accurate and stable discretizations of geometric terms and differential operators on curved geometries, (ii) techniques for hydrodynamics handling surface incompressibility constraints, and (iii) stiffness from rapid time-scales introduced by the thermal fluctuations. We show how practical spectral methods and meshfree computational approaches can be developed for simulations over long spatial-temporal scales. We then present results for protein and microstructure interactions within membranes and the roles played by hydrodynamic coupling and geometry.
  • Luoding Zhu (Indiana U-Purdue U Indianapolis, USA)
    "Modeling and simulation of fluid flow over osteocyte"
  • Bone’s structure, development, and remodeling are highly complex. Bone is permeated by an intricate system of interconnected canals (lacuno-canalicular network) that are filled with interstitial fluid and connect mechanosensing osteocytes. These networks multiply macroscale strains that occur during normal motion (e.g. walking or running) approximately tenfold by the time they reach the osteocytes. The amplification mechanism is still not well characterized. Due to the extreme complexity of the osteocyte-fluid-lacuno-canalicular system and the hard bone that encases the system, in-vivo laboratory experiments are challenging to conduct. Mathematical modeling, however, can provide a viable approach for shedding insights into the force amplification that occurs in the system. We introduce two mathematical models for modeling and simulation of fluid- osteocyte interaction. The first models fluid-osteocyte interactions in a lacuna- canalicular network in two dimensions by using the lattice Boltzmann approach. The model considers the influence of the number and geometry of the canaliculi on the wall shear and wall normal stress on the osteocyte. The second models an osteocyte exposed to viscous shear flow in three dimensions by using the immersed boundary approach. The osteocyte is represented by a network of fibers constructed based on images taken during experiments. The model considers how force is distributed throughout the osteocyte when external forcing is applied to the cell. These studies are ongoing and we will report our current progress on these efforts.
  • Nicholas Chisholm (Worcester Polytechnic Institute, USA)
    "Novel Regularized Stokeslets for Biological Fluid Flow Problems"
  • The method of regularized Stokeslets is well suited for simulating micro-scale biological fluid dynamics. Over the past two decades, it has proven very useful for describing the locomotion of microorganisms and the fluid-structure interactions of propulsive organelles such as cilia and flagella. However, there are many possible choices for regularizing the (singular) fundamental solution to the Stokes equations (the 'Stokeslet'), and this choice often requires tailoring to the specific problem at hand for best results. In this talk, we generate regularized Stokeslets using their associated biharmonic and vector potentials. These regularized Stokeslets are automatically divergence free, and they may be chosen to be equivalent (or arbitrarily close) to the singular Stokeslet outside a small region surrounding the point of forcing. Regularized Stokeslets having this latter property may be especially useful with known image systems for, e.g., the flow inside of a spherical cavity because boundary conditions at the cavity boundary may be satisfied exactly. We validate the usefulness of these regularized Stokeslets by quantifying their behavior for well-known problems such as flow due to the motion of a rigid cylinder/sphere and of thin, flexible filaments (e.g., cilia). We anticipate that our method will be useful for simulating intracellular forces and fluid flows during active cellular processes such as mitosis.
  • Thomas Fai (Brandeis University, USA)
    "Hydrodynamics of cell suspensions near walls"
  • Many real-world examples of fluid-structure interaction, such as the motion of red blood cells through blood vessels, involve the near-contact of elastic structures with boundaries. We use the immersed boundary method to simulate the interactions of deformable objects with walls. In practice, the near-contact with the wall and resulting lubrication layer are often under-resolved, and we show how certain formulations of the boundary conditions lead to spurious behaviors. We show how the lubricated immersed boundary method can be used to increase the accuracy of simulations in the case of dense cell suspensions, in which near-contact occurs through cell-wall, cell-cell, and intracellular interactions.

Collective Behavior and Social Evolution

Organized by: Daniel Cooney (University of Pennsylvania, USA) & Olivia Chu (Princeton University, USA)
Note: this minisymposia has multiple sessions. The second session is MS18-EVOP.

  • Heather Zinn Brooks (Harvey Mudd College)
    "Rounding out the corners: Smooth approximations for bounded-confidence models of opinion dynamics"
  • Vandana Venkateswaran (University of Illinois)
    "Modeling the interplay between life-history, sexual, and social traits"
  • Males and females have distinct life-history strategies that have co-evolved with diverse sex-specific traits. Previous studies have addressed how resource allocation towards single sex-specific traits impacts lifetime reproductive success (LRS). However, the tradeoffs between diverse sex-specific characteristics and their impact on LRS remain largely unassessed impeding our understanding of life-history evolution. We present a theoretical framework (informed by experimental data and evolutionary genetics) that explores the effects of multiple sex-specific traits and assessed how they influence LRS. From the individual sex-specific traits, we show the consequences at the population level (by evaluating adult sex ratios or ASR). We present how sex-specific resource allocation towards the assessed traits (parental investment, ornamentation and immunocompetence) resulted in a biased ASR. In general, this framework can be employed to understand the combined impact of diverse sex-specific traits on the LRS and the eventual population dynamics of particular model systems.
  • Taylor Kessinger (University of Pennsylvania)
    "Models of institution formation and breakdown under indirect reciprocity"
  • We live in a society. Societies require a high level of cooperation, and they cannot flourish unless defectors are punished. How do we ensure this? Indirect reciprocity models offer a potential solution: individuals may track the reputations of others, cooperating with those they consider good and punishing those they consider bad. But if individuals rely solely on their own private, personal assessments of others, disagreement about reputations makes it prohibitively difficult for cooperation to proliferate. We provide a mechanism for fomenting consensus about reputations: adherence to centralized institutions that track and broadcast reputational assessments. We show that, by tweaking the size of the institution and its tolerance to occasional antisocial behavior, cooperation can spread even under social norms that ordinarily are inhospitable to cooperation. We also show that adherence to institutional evaluation can spread in a population of private assessors and is robust against invasion. Finally, we consider mechanisms that may lead to the breakdown of institutional evaluation: ingroup/outgroup dynamics, corruption, competing institutions, and systemic bias. Our models underscore the importance of ensuring that institutions are fair and inclusive.
  • Sara Loo (University of New South Wales)
    "The evolution of learned behaviour and strategy: with applications to reproduction and disease emergence"
  • The question of why males invest more into competition than offspring care is an age old problem in evolutionary biology. On the one hand, paternal care could increase the fraction of offspring surviving to maturity. On the other hand, competition could increase the likelihood of more paternities and thus the relative number of offspring produced. We present a simple dynamic model to investigate the benefits of these two alternative fitness-enhancing pathways. Using this framework, we evaluate the sensitivity of equilibrium dynamics to changes in payoffs for male allocation to mating versus parenting. We then consider an application of the model that includes men’s competition for hunting reputations where big game supplies a benefit to all and find a frequency-dependent parameter region within which either strategy may outperform the other. Results demonstrate that allocation to competition gives males greater fitness than offspring care for a range of circumstances that are dependent on life-history parameters and, for the large-game hunting application, frequency dependent. We then consider an extension to the model that explores the effect of female life-history on male reproductive strategies and compare three different life histories to study conditions where paternal care may arise. This is driven by observations of paternal care in callitrichids.

Recent developments in phylogenetic network reconstruction and beyond

Organized by: Guillaume Scholz (University of Leipzig, Germany), Katharina Huber (University of East Anglia, United Kingdom)
Note: this minisymposia has multiple sessions. The second session is MS11-EVOP.

  • Steven Kelk (Maastricht University, The Netherlands)
    "Quantifying the dissimilarity of trees using phylogenetic networks and data reduction"
  • Purely topological methods for constructing rooted phylogenetic networks often operate by puzzling multiple incongruent trees together in a parsimonious fashion. Early results in this area established a link between the construction of networks and distance measures on pairs, or sets, of trees. In some cases 'pre-network' distance measures turned out to have an unexpected relevance when applied to network construction. Interestingly, it is not only the case that distance measures can help in constructing networks. In this talk I give a brief summary of recent work in which networks are used 'backwards' to establish improved results for the computation of computationally intractable distance measures. I will focus in particular on using networks to develop aggressive kernelization (i.e. data reduction / pre-processing) rules for computation of the NP-hard TBR (Tree Bisection and Reconnect) distance, and present some empirical results demonstrating the impact of these aggressive rules in practice. This is based on ongoing joint work with several authors.
  • Mike Steel (University of Canterbury, New Zealand)
    "Ranked tree-child networks"
  • Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics. Although these networks have a number of attractive mathematical properties, many combinatorial questions concerning them remain intractable. However, endowing these networks with a biologically-relevant ranking structure yields mathematically tractable objects, which we term ranked tree-child networks (RTCNs). We explain how to derive exact and explicit combinatorial results concerning the enumeration and generation of these networks. We also explore probabilistic questions concerning the properties of RTCNs when they are sampled uniformly at random. These questions include the lengths of random walks between the root and leaves (both from the root to the leaves and from a leaf to the root); the distribution of the number of cherries in the network; and sampling RTCNs conditional on displaying a given tree.
  • Marc Hellmuth (Stockholm University, Sweden)
    "From modular decomposition trees to rooted median graphs"
  • The modular decomposition of a symmetric map $deltacolon Xtimes X to Upsilon$ (or, equivalently, a set of symmetric binary relations, a 2-structure, or an edge-colored undirected graph) is a natural construction to capture key features of $delta$ in labeled trees. A map $delta$ is explained by a vertex-labeled rooted tree $(T,t)$ if the label $delta(x,y)$ coincides with the label of the last common ancestor of $x$ and $y$ in $T$, i.e., if $delta(x,y)=t(lca(x,y))$. Only maps whose modular decomposition does not contain prime nodes, i.e., the symbolic ultrametrics, can be explained in this manner. Here we consider rooted median graphs as a generalization to (modular decomposition) trees to explain symmetric maps. We first show that every symmetric map can be explained by ``extended'' hypercubes and half-grids. We then derive a a linear-time algorithm that stepwisely resolves prime vertices in the modular decomposition tree to obtain a rooted and labeled median graph that explains a given symmetric map $delta$. We argue that the resulting ``tree-like'' median graphs may be of use in phylogenetics as a model of evolutionary relationships.
  • Barbara Holland (University of Tasmania, Australia)
    "Modelling convergence and divergence of species in phylogenetic networks"
  • In a 2018 paper we gave a non-technical introduction to convergence–divergence models, a new modelling approach for phylogenetic data that allows for the usual divergence of lineages after lineage-splitting but also allows for taxa to converge, i.e. become more similar over time. We show that these models are sufficiently flexible that they have some interesting identifiability issues. Specifically, we show many 3-taxon data sets can be equally well explained by supposing violation of the molecular clock due to change in the rate of evolution along different edges, or by keeping the assumption of a constant rate of evolution but instead assuming that evolution is not a purely divergent process. Given the abundance of evidence that evolution is not strictly tree-like, this is an illustration that as phylogeneticists we need to think clearly about the structural form of the models we use. For cases with four taxa, we show that there will be far greater ability to distinguish models with convergence from non-clock-like tree models. This talk will describe the convergence-divergence model and discuss some potential applications.

Collective Behavior and Social Evolution

Organized by: Daniel Cooney (University of Pennsylvania, USA) & Olivia Chu (Princeton University, USA)
Note: this minisymposia has multiple sessions. The second session is MS16-EVOP.

  • Ricardo Martinez-Garcia (ICTP South American Institute for Fundamental Research)
    "The exploitative segregation of plant roots: a game-theory approach to below-ground plant growth"
  • Plant roots determine carbon uptake, survivorship, and agricultural yield and represent a large proportion of the world’s vegetation carbon pool. The study of below-ground competition, unlike above-ground shoot competition, is hampered by our inability to observe roots. We have few observations of intact root systems in soil and lack a comprehensive theory for root system responses to their environment and the presence of other individuals. In this presentation, I will first review previous efforts to explain plant below-ground interactions and discuss how they lead to seemingly contradictory predictions. Then, I will introduce our recent work and show how it resolves existing controversy and provides a unifying framework to study below-ground plant interactions. I will conclude by discussing future research lines that depart from our results and how they can be addressed with extensions of our original model.
  • Max Souza (Fluminense Federal University)
    "Stochastic evolution of finite populations: the fingerprints of fixation"
  • On the one hand, once we are given a finite population stochastic finite population model without mutations and a (possibly frequency dependent) fitness function, the computation of the corresponding fixation probability is straightforward. On the other hand, one might ask what the fixation probability can tell us about the underlying process. Starting from classical Moran and Wright-Fisher processes, we will discuss some qualitative properties of the corresponding fixation probability. We also address when the fixation probability uniquely characterises knowing the fixation characterises these processes. In particular, we will see that for each fixation probability vector that is strictly increasing, there is exactly one Moran process that realises it. For the Wright-Fisher process, however, the situation is more involved and almost any fixation pattern is attainable — though not necessarily in a unique way. If time allows, we will also address the corresponding inverse problem and some asymptotic results for large populations.
  • Nina Fefferman (University of Tennessee)
    "How infectious diseases may have shaped the evolution of social organization"
  • Sociality itself represents a tradeoff between pooled benefits and shared risks. Looking at societal organization in social species may reveal the footprints of selective pressures to find balance between two major constraints: mitigation of the transmission of infection and population-level efficiency of division of labor. In this talk, we'll discuss a simple model that abstracts the organization of collaborative roles from different social insect taxa and contrasts their performance under disease-free and outbreak scenarios. We'll explore how infectious diseases may have selected for organizational strategies that maintain cohort stability and show why this trait would be unlikely to have been maintained in the absence of outbreak risks.
  • Joseph Johnson (University of Michigan)
    "A Dynamical Model for the Origin of Anisogamy"
  • The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike some prior work, we do not assume the existence of mating types. We also model frequency dependent selection via “mean-field coupling,” whereby the likelihood that a gamete survives is an increasing function of its size relative to the population’s mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

Evolutionary Theory of Disease

Organized by: Jesse Kreger (University of California, Irvine, United States), Natalia Komarova (University of California, Irvine, United States)
Note: this minisymposia has multiple sessions. The second session is MS20-EVOP.

  • Joceline Lega (University of Arizona, United States)
    "A novel take on outbreak dynamics"
  • During an outbreak, public health data typically consist of time series for the daily or weekly incidence (reported new cases) of the disease. This information is location-specific (e.g. at the level of a county, a state, or a country) and noisy. For each such time series, plotting incidence as a function of cumulative cases instead of time leads to a remarkable simplification: the data appear to fluctuate about a mean curve of universal shape. In this talk, I will illustrate the previous statement through examples of Influenza A and COVID-19 outbreaks, and describe recent work aimed at elucidating this behavior [1, 2]. In particular, exact results will be provided for the deterministic and stochastic SIR models. In addition, I will explain how this property can be combined with data assimilation to provide short-term forecasts of COVID-19 cases and deaths in the US [3]. This is joint work with Hannh Biegel, Bill Fries, Faryad Sahneh, and Joe Watkins. [1] J. Lega, Parameter estimation from ICC curves, Journal of Biological Dynamics 15, 195-212 (2021). [2] F.D. Sahneh, W. Fries, J.C. Watkins, J. Lega, The COVID-19 Pandemic from the Eye of the Virus (2021); arxiv.org/abs/2103.12848 [3] H. Biegel & J. Lega, EpiCovDA: a mechanistic COVID-19 forecasting model with data assimilation (2021).
  • Dylan H. Morris (University of California, Los Angeles, United States)
    "Evolving fast and slow: how asynchrony between virus diversity and antibody selection limits influenza virus evolution"
  • Seasonal influenza viruses create a persistent global disease burden by evolving to escape immunity induced by prior infections and vaccinations. New antigenic variants have a substantial selective advantage at the population level, but these variants are rarely selected within-host, even in previously immune individuals. Using a mathematical model, we show that the temporal asynchrony between within-host virus exponential growth and antibody-mediated selection could limit within-host antigenic evolution. If selection for new antigenic variants acts principally at the point of initial virus inoculation, where small virus populations encounter well-matched mucosal antibodies in previously-infected individuals, there can exist protection against reinfection that does not regularly produce observable new antigenic variants within individual infected hosts. Our results provide a theoretical explanation for how virus antigenic evolution can be highly selective at the global level but nearly neutral within-host, and providing a clear example of how evolution and ecology only make sense in light of one another. Relevant reading: https://elifesciences.org/articles/62105
  • Jesse Kreger (University of California, Irvine, United States)
    "The role of migration in mutant evolution in fragmented populations"
  • Complex population structures are an important determinant of the evolutionary dynamics of mutants. In fragmented populations, this has been studied using metapopulation models, which have been of great interest for questions related to ecology and population conservation. However, such models also have high relevance in a biomedical context – such as deme population structures that apply to evolution in hematopoietic systems. In this talk, we investigate the effects of population fragmentation on mutant cell dynamics using stochastic metapopulation modeling in conjunction with in vitro laboratory experiments. In the case of neutral mutations, we find that migration makes the demes look homogeneous to each other, resulting in a one-humped (unimodal) distribution, which matches well with experimental simulations. For disadvantageous mutations, we find that migration not only similarly impacts the distribution of mutant cells, but it can also change the expected frequency of mutants at stationary state compared to the selection-mutation balance. This could play an important role in disease progression.
  • Ali Mahdipour-Shirayeh (University of Toronto, Canada)
    "Clonal evolution and Intra-tumoral heterogeneity in cancer: A single-cell viewpoint"
  • Despite intense therapeutic advances, therapy failures in diverse cancers may suggest the existence of intra-tumoral diversity and presumably rare subclones of minimal residual disease that are persistent to current therapies. Although there is no comprehensive technique to determine such subclones and to identify evolution of the disease, single-cell data can shed light on intra-cellular heterogeneity and clonal evolution of individual cells in alternative cell contexts. Utilizing single-cell data, the potential genetic pathways can be detected across diverse pheno/geno-types within a heterogeneous population of cells. Moreover, in many cancers, particularly in Multiple Myeloma, the most reliable clonal features are copy number variations (CNVs) which can be best inferred from single-cell DNA/RNA study. To address all these challenges, we developed an extensive pipeline, referred to as sciCNV, which covers a range of analysis from a novel normalization to inferring CNV from single-cell data. During this talk, we first introduce some fundamental tools which are commonly used in studying single cells and then will introduce the sciCNV pipeline to be implemented to segregate tumor cells from normal individuals and to understand the genetic background of the disease. This technique may offer an efficient way to clone distinct CNV-compartments and to construct a phylogeny of subclonal structure and pathogenesis of the disease. Such analysis can reflect evolutionary dynamics and clonal dependencies of cancer in time/space frame. Our approach is general and can be applied to any transcription data and may tend to a better understanding of histological/pathogenesis of diverse cancers and their associated therapeutic strategies.

Evolutionary Theory of Disease

Organized by: Jesse Kreger (University of California, Irvine, United States), Natalia Komarova (University of California, Irvine, United States)
Note: this minisymposia has multiple sessions. The second session is MS19-EVOP.

  • Chadi M. Saad-Roy (Princeton University, United States)
    "The evolution of an asymptomatic infectious stage: analysis of a simple evolutionary-epidemiological model"
  • Pathogens exhibit numerous life-history strategies. An important pathogen characteristic is the degree of symptoms exhibited by hosts at the onset of infectiousness. Additionally, mediated by host immunity, a pathogen may elicit reduced (or no) symptoms in the first stage leading to simultaneously slower progression and lower transmission. In this talk, we examine the evolutionary implications of these trade-offs. We couple a simple epidemiological model with evolutionary analyses, and we find that numerous evolutionary outcomes are possible. For simple trade-off formulations, these include a fully symptomatic or asymptomatic first infectious stage, a subsymptomatic first stage, or bistability between a fully symptomatic and asymptomatic first stage. Then, we discuss the ensuing implications for disease mitigation measures.
  • Jasmine Foo (University of Minnesota, United States)
    "Power law transitions in site frequency spectra of neutrally evolving tumors"
  • The site frequency spectrum (SFS) is a popular genomic summary statistic that tracks the frequencies of mutations in a population sample. In the context of cancer, the site frequency spectrum of tumor samples are commonly used to gain insights into tumor evolutionary processes. However, recent analyses of the SFS in tumor population models have generally dealt with special or limiting cases, such as considering only cells with an infinite line of descent, assuming deterministic tumor growth, or taking large time/population limits. I will discuss recent work in which we derive exact expressions for the mean SFS in a neutrally evolving tumor. We find that the rates of cell birth and death change the shape of the SFS at the small frequency end, inducing a transition between power laws as cell viability decreases. We demonstrate how, in principle, this insight may be used to estimate the ratio between cell birth and cell death rates, as well as the mutation rate, using SFS data alone.
  • Mohammad Kohandel (University of Waterloo, Canada)
    "Predicting mutability of the genomic segments of a pathogen"
  • There is an essential need to better understand how a pathogenesis, like SARS-CoV-2, is affected by mutations and to determine the conserved segments in the genome that can serve as stable targets for novel therapeutics. We introduce a text-mining method to estimate the mutability of genomic segments directly from a reference (ancestral) whole genome sequence. The method relies on calculating the importance of genomic segments based on their spatial distribution and frequency over the whole genome. To validate our approach, we perform a large-scale analysis of the viral mutations in nearly 80,000 publicly-available SARS-CoV-2 predecessor whole genome sequences and show that these results are highly correlated with the segments predicted by the text-mining method. Importantly, these correlations are found to hold at the codon and gene levels, as well as for gene coding regions.
  • Alison Hill (Johns Hopkins University, Institute for Computational Medicine, United States)
    "Selection for SARS-CoV-2 variants at the within-host and population scale"
  • The evolution of novel variants has become an increasing concern as the COVID-19 pandemic has progressed into 2021. In this talk we will discuss modeling work to understand the factors driving SARS-CoV-2 evolution within individual hosts and across populations. We examine and compare mutations that increase transmission and those that evade adaptive immunity. We build models to include and analyze the roll of within-host clinical course, heterogeneities in transmission, population structure, and the nature of acquired and vaccine-induced immunity on the fate of variants emerging at different times and places throughout the pandemic. We find that several unique features of COVID-19, including the timing of peak infectiousness vs the onset of adaptive immune responses in infected individuals, and the asynchronous spatiotemporal nature of epidemics around the world, contribute to patterns observed in the evolution of new variants.

Sub-group contributed talks

EVOP Subgroup Contributed Talks

  • Hannah Götsch Faculty of Mathematics - University of Vienna, Vienna Graduate School of Population Genetics
    "A mathematical model for the adaptation of a quantitative trait in a panmictic population"
  • The genetic architecture of a quantitative trait ranges from selective sweeps at few loci to subtle allele frequency shifts at many loci. By genetic architecture we mean the number of loci responding evolutionarily to adaptation, their mutation rates and the distribution of their mutational effects, their linkage relations, as well as their epistatic interactions. Höllinger et al. [1] showed for a panmictic population that the population-scaled background mutation rate determines crucially the shape of the mutant allele frequency distribution at the end of the adaptive phase. Remarkably, the strength of selection is not important as long as the locus effects are all the same.We report about results how variation among locus effects alter these findings. For the infinite sites model, we present analytical results for the locus-based distribution of the mutants as well as the phenotypic mean and variance, which are based on a combination of branching process theory (for the initial stochastic phase) and deterministic theory. They are compared with comprehensive computer simulations.[1] I. Höllinger, P.S. Pennings, and J. Hermisson, Polygenic adaptation: From sweeps to subtle frequency shifts, PLOS Genetics, 15: 1–26, 2019.
  • Alexander B. Brummer Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, Beckman Research Institute, City of Hope National Medical Center
    "Cancer as a model system for testing metabolic scaling theory"
  • Biological allometries, such as the scaling of metabolism to mass, are hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to blood flow. Metabolic scaling theory argues two guiding principles—conservation of fluid flow and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Yet, absent from these past efforts are studies that independently measure both metabolic function and vascular form. We present simultaneous and consistent measurements of metabolic scaling exponents from clinical lung cancer imaging, and identify potential quantitative imaging biomarkers indicative of tumor growth.We analyze 65 clinical PET-CT scans of patients with non-small cell lung carcinoma. Examination of the scaling of maximum standard uptake value with metabolic tumor volume, and metabolic tumor volume with gross tumor volume, yields metabolic scaling exponents of 0.64 (0.20) and 0.70 (0.17), respectively. We compare these to the value of 0.85 (0.06) derived from the geometric scaling of the tumor-supplying vasculature. These results (1) identify imaging biomarkers in vascular geometry related to blood volume and flow and (2) inform energetic models of growth and development for tumor forecasting.
  • Bo Zhang Oklahoma State University
    "How to integrate mechanical treatment and biological control to improve field treatment efficiency on invasions"
  • Projecting controlling outcomes of different management strategies on invasive populations has broad implications in field management. Different to herbicide usage that may cause environmental pollution and non-target effects on native plants, nonchemical methods, have shown great targeted effectiveness on invasion. However, an interesting and important question remains unclear is that how to decrease the repetition of nonchemical treatments. One possible approach is to integrate nonchemical treatments with biological control agents, which can attack and limit invasion spread after being established in the field. We hypothesize that applying nonchemical methods to remove occurring invasive plant while establishing biological control agents, then using the established biological control agents to limit future regrowth of invasive plant will decrease the use of nonchemical treatments. We developed a spatial modeling framework, including their dispersal processes, to capture population dynamics change under various strategies of control. We found that applying nonchemical treatment in a higher frequency with smaller treated areas per time is a more efficient approach than vice versa. More importantly, we emphasized that a high biological control efficiency can continuously decrease the requirement of repeated treatment of nonchemical methods and maintain the invasive population at a low level.

EVOP Subgroup Contributed Talks

  • Glenn Young Kennesaw State University
    " The interplay between costly reproduction and unpredictable environments shape the evolution of cooperative breeding"
  • All sexually reproducing organisms are faced with a fundamental decision: to invest valuable resources and energy in reproduction or in their own survival. This trade-off between reproduction and survival represents the 'cost of reproduction' and occurs across a diverse range of organisms. It is widely assumed that cooperative breeding behavior in vertebrates — when individuals care for young who are not their own — results in part from costly parental care. When caring for young is too costly, parents need help from related or unrelated individuals to successfully raise their offspring. Cooperatively breeding birds and mammals are also more commonly found in unpredictable environments than non-cooperative species, suggesting that decisions about when to breed or help may represent complex yet critical choices that depend on the energy individuals have available to dedicate to reproduction given the harshness of the current environment. Here, we introduce a novel, socially-tiered model of a cooperatively breeding species that incorporates the influence environmental stochasticity. Through numerical and analytical methods, we use this model to show that costly reproduction and environmental variability are compounding factors in the evolution and maintenance of cooperation.
  • Linh Huynh Case Western Reserve University
    "Identifying Birth and Death Rates Separately to Disambiguate Mechanisms for the Same Observed Population Dynamics"
  • In studying the dynamics of drug resistance, many models have used net growth rates of cell populations. However, we have discovered that cell populations with the same net growth rate but different birth and death rates have dramatically different tendencies to escape extinction and develop drug resistance. Therefore, it is important to identify birth and death rates separately. We develop a method to parse out birth and death rates from cell count time series of populations that follow logistic birth-death processes. We validate our method on in-silico data generated using the tau-leaping approximation. With separate birth and death rates, we infer different underlying mechanisms and drug effects for the same observed population dynamics. From our results, we propose to replace a one-dimensional 'fitness' phenotype (net growth rate) with a two-dimensional 'fitness vector' phenotype (birth and death rates).
  • Enrico Sandro Colizzi Leiden University, Origins Center
    "Evolution of genome architecture to divide labor through mutations"
  • Some forms of reproductive division of labor, e.g. multicellular organisation in eukaryotes, are coordinated through differential gene expression. Recent experiments have shown an alternative mechanism in antibiotic producing bacteria, where division of labor is coordinated by mutations. Somatic cells are generated from a germline through genomic deletions. These mutants produce antibiotics but their replication rate is strongly reduced. To understand the evolutionary origin of these findings, we have built a spatial model of bacteria evolution. Bacteria are given a genome, represented as beads on a string, which determines replication and antibiotic production. We find that bacterial genomes evolve to incorporate several fragile sites which increases the rate of deletions. Concurrently, genomes become structured such that fragile sites-induced deletions generate antibiotic-producing mutants from a non-producing germline. These mutants protect their colony from competitors, but they are unable to grow because they lack growth-promoting genes. Altogether, our model suggests a novel mechanism for the evolution of reproductive division of labor in Streptomyces through genome reorganization. Through this mechanism, social conflicts become impossible because altruists lack the genetic means to replicate. These results also help conceptualise the many examples of division of labor through genome manipulation found in other microorganisms and multicellular life.
  • Anudeep Surendran University of Montreal, Canada
    "Population dynamics with spatial structure and an Allee effect"
  • Population dynamics including a strong Allee effect describe the situation where long-term population survival or extinction depends on the initial population density. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to extinction, whereas initial densities above the threshold lead to survival. Mean-field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as competition and dispersal. The influence of non-mean-field effects has not been studied in the presence of an Allee effect. To address this, we develop an individual-based model that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure neglected by mean-field models. For example, there are cases where the mean-field model predicts extinction but the population actually survives. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

EVOP Subgroup Contributed Talks

  • Anthia Le The University of Queensland
    "The Evolution of Menopause"
  • When we examine the life history of humans against our close primate relatives, the great apes, we see that human adult lifespans include a post-menopausal life stage. This led to the question, “how did human females evolve to have old-age infertility?”Morton et al. suggested that ancestral male mating choices, particularly forgoing mating with older females, was the driving force behind the evolution of menopause. As their agent-based model is difficult to analyse, we propose an analogous system of ordinary differential equations (ODE) to examine their conclusions. Our conclusions contradict that of Morton et al., as we find that even the slightest deviation from an exclusive mating preference for younger females would counteract the evolution of menopause.
  • Gabriela Lobinska Weizmann Institute of Science
    "Should you inherit your parent's mutaiton rate?"
  • Mutators (individuals with uncommonly high mutation rate) are subject to second-order selection on the mutations they acquire. Mutators can be selected for since they can attain adaptive genotypes faster than their non-mutator counterparts. However, when the population is well-adapted to its environment, most mutations will be deleterious and hence mutators will be selected against. A mutator phenotype can be due to mutations in mismatch repair genes and DNA polymerases, and hence be strongly inherited from parent to offspring. But, it can also be caused by stochastic factors, such as protein concentrations, and hence be only inherited for few generations. Recently, an epigenetic mechanism for generating variability in mutation rate within the population and between parent and offspring was observed (Uphoff et al. Science 2016). We wondered which level of mutation rate inheritance – high, due to genetic factors, intermediate, due to epigenetic factors, or random, due to stochastic factors - leads to fastest adaptation. Using a combination of stochastic simulations and mathematical modelling, we show that intermediate levels of mutation rate inheritance, corresponding to epigenetic inheritance, result in fastest adaptation over rugged landscapes. This is due to an association between mutator phenotypes and pre-existing mutations, which aids crossing fitness valleys.
  • Peter Harrington University of Alberta
    "A framework for studying transients in marine metapopulations"
  • Transient dynamics can often differ drastically from the asymptotic dynamics of systems. In this talk we provide a unifying framework for analysing transient dynamics in marinemetapopulations, from the choice of norms to the addition of stage structure. We use the $ell_1$ norm, because of its biological interpretation, to extend the transient metrics of reactivityand attenuation to marine metapopulations, and use examples to compare these metrics under the more commonly used $ell_2$ norm. We then connect the reactivity and attenuation of marine metapopulations to the source-sink distribution of habitat patches and demonstrate how to meaningfully measure reactivity when metapopulations are stage-structured.

EVOP Subgroup Contributed Talks

  • Barbara Boldin Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Slovenia
    "The evolution of respiratory disease virulence and diversity"
  • Theoretical studies of virulence evolution typically assume a positive trade-off between infectivity and harmfulness. This is a valid assumption for diseases where both quantities are determined solely by within-host infection load. However, epidemiological parameters in highly structured host organisms, such as mammals, are largely determined by how the disease agents distribute themselves over body compartments. In respiratory diseases there is even a negative trade-off, with diseases of the lower respiratory tract being both less infective and more harmful. In this talk, we discuss the evolutionary consequences of the interplay between virulence that decreases with an increase in transmission and cross-immunities between pathogen strains. The most salient outcomes of our study are that (i) the upper respiratory tract will support a higher disease diversity, (ii) that emerging respiratory diseases will tend to be more harmful and less infective and (iii) that disease diversity increases with host population density.
  • Yuanxiao Gao Max Planck Institute for Evolutionary Biology
    "Evolution of irreversible somatic differentiation"
  • A key innovation emerging in complex animals is irreversible somatic differentiation: daughters of a vegetative cell perform a vegetative function as well, thus, forming a somatic lineage that can no longer be directly involved in reproduction. Primitive species use a different strategy: vegetative and reproductive tasks are separated in time rather than in space. Starting from such a strategy, how is it possible to evolve life forms which use some of their cells exclusively for vegetative functions? Here, we developed an evolutionary model of development of a simple multicellular organism and found that three components are necessary for the evolution of irreversible somatic differentiation: (i) costly cell differentiation, (ii) vegetative cells that significantly improve the organism's performance even if present in small numbers, and (iii) large enough organism size. Our findings demonstrate how an egalitarian development typical for loose cell colonies can evolve into germ-soma differentiation dominating metazoans.
  • Yoav Ram Tel Aviv University
    "Non-Vertical Cultural Transmission , Assortment , and the Evolution of Cooperation"
  • We present a model for the evolution of cooperation under vertical, horizontal, and oblique cultural transmission. We find that the evolution of cooperation is facilitated by its horizontal transmission and by an association between social interactions and horizontal transmission. The effect of oblique transmission depends on the horizontal transmission bias. Stable polymorphism of cooperation and defection can occur, and when it does, reduced association between social interactions and horizontal transmission evolves, which leads to a decreased frequency of cooperation and lower population mean fitness. We compare our results to outcomes of stochastic simulations of structured populations. Parallels are drawn with Hamilton's rule incorporating assortment and relatedness.
  • Christin Nyhoegen Max Planck Institute for Evolutionary Biology, Plön, Germany
    "Within-host evolution of antibiotic resistance under sequential therapy"
  • The rapid evolution of antibiotic resistance and the resulting loss in treatment options call for the development of sustainable treatment strategies. Supported by laboratory experiments, alternating antibiotics during treatment has been proposed as a promising approach. Evolutionary trade-offs, especially collateral sensitivity, could potentially further improve the outcome.A limitation of in-vitro evolution experiments is that they do not account for the complex environment of the patient's body. Drugs persist in the body for some time at continuously decreasing concentrations, leading to a temporal overlap of the drugs in a cycling schedule. It is a priori not clear how drug-drug-interactions during these periods of drug overlap influence the outcome of sequential therapy. To close this gap, we set up a pharmacokinetic-pharmacodynamic model that incorporates drug-drug-interactions. We aim to reveal the treatment settings that optimize the outcome of sequential therapy, given the risk of resistance evolution. Our results suggest that drug-drug-interactions strongly influence the optimal protocol. For synergistic drugs pairs, rapid switching of drugs minimizes the time to eradication of the pathogen population. For antagonistic drugs, the decision is not as straightforward, and switching the drugs less often is sometimes preferable. Collateral sensitivity only improves the efficiency if cycling is slow.

EVOP Subgroup Contributed Talks

  • Matthew Edgington The Pirbright Institute
    " Population-level multiplexing: A strategy to manage gene drive resistance"
  • Gene drives are predicted to increase in frequency within a population even when harmful to individuals carrying them. This allows associated desirable genetic material to also increase in frequency, potentially allowing their use against globally important issues including disease vectors, crop pests and invasive species. The most high-profile - CRISPR-based gene drives - bias inheritance by “cutting” a target DNA sequence and tricking the system into using the gene drive as a repair template – converting drive heterozygotes into homozygotes. Unfortunately, alternate repair mechanisms can create cut-resistant alleles, causing drive failure. A commonly stated solution is multiplexing – targeting multiple DNA sequences – since this requires resistance at all target sites for drive failure. However, simultaneous DNA “cuts” can lead to the deletion of large DNA sequences and thus the removal of multiple (or all) target sequences within a single event. Here we consider novel approaches for overcoming these issues by multiplexing at the population rather than the individual level. Stochastic mathematical models demonstrate that significant performance improvements can be obtained from these approaches. Based on technical feasibility, we further investigate one approach – demonstrating robustness to key performance parameters and the potential for control of biologically relevant population sizes.
  • Christof Mast
    "Heat flows adjust local ion concentrations in favor of prebiotic chemistry"
  • Kalle Parvinen University of Turku, Finland
    "Evolution of dispersal in a spatially heterogeneous population with finite patch sizes"
  • Dispersal is one of the fundamental life-history strategies of organisms, so understanding the selective forces shaping the dispersal traits is important. In the Wright's island model, dispersal evolves due to kin competition even when dispersal is costly, and it has traditionally been assumed that the living conditions are the same everywhere. In order to study the effect of spatial heterogeneity, we extend the model so that patches may receive different amounts of immigrants, foster different number of individuals and give different reproduction efficiency to individuals therein. We obtain an analytical expression for the fitness gradient, which shows that directional selection consists of three components: as in the homogeneous case, direct cost of dispersal selects against dispersal and kin competition promotes dispersal. The new component, spatial heterogeneity, more precisely the variance of so-called relative reproductive potential, tends to select against dispersal. We also obtain an expression for the second derivative of fitness, which can be used to determine whether there is disruptive selection: Unlike the homogeneous case, we found that divergence of traits through evolutionary branching is possible in the heterogeneous case. Existing spatial heterogeneity in the real world is a key determinant in dispersal evolution.
  • Ewan Flintham Imperial College London
    "Dispersal alters the nature and scope of sexually antagonistic variation"
  • Intralocus sexual conflict, or sexual antagonism, occurs when alleles have opposing fitness effects in the two sexes. Previous theory suggests that sexual antagonism is a driver of genetic variation by generating balancing selection. However, most of these studies assume that populations are well-mixed, neglecting the effects of spatial subdivision. Here we use mathematical modelling to show that limited dispersal changes evolution at sexually antagonistic autosomal and X-linked loci due to inbreeding and sex-specific kin competition. We find that if the sexes disperse at different rates, kin competition within the philopatric sex biases intralocus conflict in favour of the more dispersive sex. Furthermore, kin competition diminishes the strength of balancing selection relative to genetic drift, reducing genetic variation in small subdivided populations. Meanwhile, by decreasing heterozygosity, inbreeding reduces the scope for sexually antagonistic polymorphism due to non-additive allelic effects, and this occurs to a greater extent on the X-chromosome than autosomes. Overall, our results indicate that spatial structure is a relevant factor in predicting where sexually antagonistic alleles might be observed. We suggest that sex-specific dispersal ecology and demography can contribute to interspecific and intragenomic variation in sexual antagonism.

EVOP Subgroup Contributed Talks

  • Renee Dale Donald Danforth Plant Science Center
    "Describing root structural traits using characteristics of the multivariate normal distribution"
  • The structure of plant roots has a large impact on the environment through ground nutrient usage and underground carbon fixation. Crop plants can be improved to reduce fertilizer usage and combat climate change through identification of the genes controlling root structural traits. However, this remains challenging due to the highly variable and responsive nature of root growth. I derive new traits using characteristics of matrices and multivariate normal distributions (MVN) of roots from a diversity panel. The Sorghum diversity panel consists of 600 unique genotypes from around the world. The genotypes were grown in controlled conditions and X-ray imaged. From these images I obtain square matrices of root locations as a function of depth. The matrices are then analyzed and MVN distributions estimated to obtain root distribution information of each Z-slice. The resulting features include entropy, eccentricity, and the two largest eigenvalues of the covariance matrix. The ability of these characteristics to measure root structural traits are benchmarked against existing highly heritable traits, such as root depth and mass. Finally, after applying dimension reduction techniques, we can identify significant changes over depth and the genetic loci controlling highly heritable structural traits.
  • Thomas Tunstall Living Systems Institute and Physics and Astronomy, University of Exeter, Exeter, United Kingdom
    "Two subcritical processes combine into a supercritical process during range expansion into a heterogeneous environment"
  • We investigate the role of landscape structure on a range expansion with mutation and selection, using a generalised Eden model. In this lattice model, sites are occupied by wild type or mutant, or empty until infected by a neighbouring site. A phase transition between long-term mutant domination of the population front and coexistence has been characterised in a homogeneous environment for slower-growing mutants in the absence of back mutations [Kuhr et al., NJP, 2011].We here investigate the effect of randomly distributed circular patches that can only be invaded by the mutant - reminiscent of pesticide-treated areas that can only be invaded by resistant pests. Our simulations show that at surprisingly low patch density, mutants can dominate even at fitness lower than which is required in a homogeneous environment. Patches bestow a spatial advantage upon the mutants, enlarging mutant domains that can then overlap with downstream patches, leading to a cascade of patch to patch infection by the mutant domain. This argument can be quantified by combining geometrical arguments for domain boundaries with percolation theory.Our results provide an indication for the long-term dynamics of an expanding population frontier in an inhomogeneous medium, under the effects of mutation and selection.
  • Jody Reimer University of Utah
    "Beyond the mean: incorporating small scale heterogeneity into algal bloom models using generalized polynomial chaos"
  • When parameterizing dynamical systems models of biological processes, we often use summary statistics (e.g., the mean) reported in experimental or observational studies. However, these summary statistics are abstractions, concealing variation occurring over space, time, or among individuals. Further, we know that the behavior of a nonlinear model using mean parameter values will differ from the mean model behavior if the parameter is instead treated as a random variable. Algae growing within polar sea ice provides an example of a system where extreme local heterogeneity in environmental conditions results in local heterogeneity in algal growth rates. Ignoring this and using a fixed, mean growth parameter to approximate regional dynamics can result in incorrect predictions of bloom timing and magnitude. Instead, algal growth rates at a given location should be treated as a random variable capturing the known heterogeneity. In this talk, I will provide an introduction to generalized polynomial chaos as an elegant, computationally efficient method for incorporating heterogeneous growth rates into standard algal bloom models, resulting in improved predictions of bloom dynamics. This method is broadly applicable for any system where local heterogeneity needs to be accounted for when considering aggregate dynamics over larger scales.
  • Olivia Chu Princeton University
    "Opinion dynamics in heterogeneous environments"
  • In human social systems, it is natural to assume that individuals' opinions influence and are influenced by their interactions. Mathematically, it is common to represent such systems as networks, where nodes are individuals and edges between them denote a connection. Adaptive network models explore the dynamic relationship between node properties and network topology. In the context of opinion dynamics, these models often take the form of adaptive voter models, where there are two mechanisms through which network changes can take place. Through homophily, an edge forms between two individuals who already agree. Through social learning, an individual adopts a neighbor's opinion. In these models, individuals are more frequently attached to those who share their opinion, seen through the formation of sub-communities of like-minded individuals. However, it is not always the case that individuals want to cluster into homogeneous groups. Instead, they might attempt to surround themselves with those who both agree and disagree with them to attain a balance of inclusion and distinctiveness in their social environments. In this work, we explore the effects that such heterogeneous preferences have on the dynamics of the adaptive voter model.

EVOP Subgroup Contributed Talks

  • Laurence Ketchemen Tchouaga University of Ottawa
    "Population density in fragmented landscapes under monostable and bistable dynamics"
  • A model for a single species population which propagates in a heterogeneous landscape in a one dimensional space is presented. The landscape is composed of two kind of patches with different diffusivities. The dynamics of the population is studied through a reaction diffusion model on which the net growth function can be a monostable or bistable function. In addition, we consider that at the interface between patch types, individuals may show preference for more favorable regions. We study the different nonlinear steady state models. We prove existence of monotone solution in each model and classify their qualitative shape. An analysis is done to study the effect of the diffusivity coefficient. A stability analysis is also done for each model.
  • Luigi Esercito Bielefeld University
    "Lines of descent in a Moran model with frequency-dependent selection and mutation"
  • Dealing with the interplay of mutation and selection is one of the important challenges in population genetics. We consider two variants of the two-type Moran model with mutation and frequency-dependent selection, namely a scheme with nonlinear dominance and another with what we name fittest-type-wins scheme. We show the equivalence of the two variants and pursue the latter for further analysis.In particular, we trace the genealogy of a sample of individuals backward in time, via an appropriate version of the so-called ancestral selection graph (ASG), originally introduced by Krone and Neuhauser. We use the information contained in mutation events to reduce the ASG to the parts informative with respect to the type distribution of the present population and their ancestors, respectively. This leads to the killed ASG and the pruned lookdown ASG in this setting, which we use to derive representations for the (factorial) moments of the type distribution and the ancestral type distribution by connecting forward and backward graphical models via duality relationships.Finally, we show how the results carry over to the diffusion limit.[1] Baake, Ellen, Luigi Esercito, and Sebastian Hummel. 'Lines of descent in a Moran model with frequency-dependent selection and mutation.' textit{arXiv preprint arXiv:2011.08888} (2020).
  • Léonard Dekens Institut Camille Jordan, Université Claude Bernard Lyon 1
    "Quantitative Trait in a Patchy Environment: Beneath the Gaussian Approximation"
  • Assuming Gaussian trait distributions is central in quantitative genetic models in order to describe complex evolutionary dynamics, like source-sink scenarii in heterogeneous environments. However, the mechanisms of why and when this is a reasonable approximation remain unclear. Here, we investigate the underlying role of sexual reproduction by introducing a new framework that directly involves the dynamics of the trait distributions. We opt for an infinitesimal model operator to model the transmission of a complex trait under sexual reproduction. We apply this approach to revisit a classical study in a patchy environment (following Ronce and Kirkpatrick 2001). We first justify the Gaussian assumption in a small variance regime with perturbative techniques. We next perform a rigorous separation of ecological and evolutionary time scales to complete the analytical description of source-sink type equilibria, numerically described in Ronce and Kirkpatrick 2001. Our analysis highlights the relative influence of the blending effects of migration and sexual reproduction on local adaptation patterns.

EVOP Subgroup Contributed Talks

  • Hong Duong University of Birmingham
    "Statistics of the number of equilibria: Evolutionary Game Theory meets Random Polynomial Theory"
  • Random evolutionary games, where the payoff entries are random variables, play an important role in the modelling of social and biological systems under uncertainty which is due to, for instance, the lack of information or the rapidly change of environment. As in classical game theory with the foundational concept of Nash equilibrium, the analysis of equilibrium points in evolutionary game theory has been of special interest because these equilibrium points provide essential understanding of complexity in a dynamical system, such as its behavioural, cultural or biological diversity and the maintenance of polymorphism.In this talk, I will discuss our recent works on the statistics of the number of equilibriums in multi-player multi-strategy games. Existing methods in the literature involve solving a system of polynomial equations, thus are restricted to systems consisting of small numbers of players and/or strategies due to Abel's impossibility theorem. By connecting to the rich theory of random polynomial theory, our approach allows overcoming this difficulty, enabling us to study general systems with arbitrarily large numbers of strategies and players.
  • Enrico Di Gaspero Bielefeld University
    "Phylogeny and population genetics: The mutation process on the ancestral line"
  • We consider a well-known observation at the interface of phylogeny and population genetics: Mutation rates estimated via phylogenetic methods tend to be much smaller than direct estimates from pedigree studies. To understand this, we consider the Moran model with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the distant past, far beyond the most recent common ancestor of the population (thus connecting population genetics to phylogeny) and analyze the mutation process along this line. We use a probabilistic tool, namely the pruned lookdown ancestral selection graph, which consists of the set of potential ancestors of the sampled individual at any given time. A crucial observation is that the mutation process on the ancestral line is not a Markov process by itself, but it becomes Markov when consindering a broader state space. Relative to the neutral case (that is, without selection), we obtain a general bias towards beneficial mutations, while (depending on the parameters) both a speedup and a slowdown of the mutation process are possible. These results shed new light on previous analytical findings of Fearnhead (2002).
  • Yuriy Pichugin Max Planck Institute for Evolutionary Biology
    "Mass conservation restricts the possible modes of microbial reproduction"
  • Multiple modes of asexual reproduction are observed among microbial organisms in natural populations. These modes are not only subject to evolution, but may drive evolutionary competition directly through their impact on population growth rates. The most prominent transition between two such modes is the one from unicellularity to multicellularity. So far, an analysis of general reproduction modes in terms of the optimality of the biomass distribution between daughter organisms is missing. We found that such considerations can greatly reduce the number of possible reproduction modes. This has important direct implications on microbial life: For unicellular species, the interplay between cell shape and kinetics of the cell growth implies that the largest and the smallest possible cells should be rod-shaped rather than spherical. For primitive multicellular species, these considerations can explain why rosette cell colonies evolved a mechanistically complex binary split reproduction. Finally, we show that the loss of organism mass during sporulation can explain the macroscopic sizes of the formally unicellular microorganism Myxomycetes plasmodium. Our findings demonstrate that a number of seemingly unconnected phenomena observed in unrelated species may be different manifestations of the same underlying process.
  • Max Schmid University of Lausanne, Switzerland
    "Spatial heterogeneity and frequency-dependent selection under limited dispersal: Where kin, divergent and disruptive selection meet"
  • Different ecological processes lead to polymorphism at different spatial scales. While spatially divergent selection favors phenotypic differentiation between habitats, competitive exclusion promotes variation within patches. Both of these processes have been shown to depend on dispersal. High dispersal can restrict spatial phenotypic variation when counteracting local adaptation, while facilitating phenotypic variation within groups when reducing kin competition. Here, we investigate the evolution of quantitative traits that control the feeding rate on resources when both processes act in concert. Using the adaptive dynamics framework, we study intra-specific competition for locally and globally varying resources that triggered both divergent and negative frequency-dependent selection. We derive explicit expressions for the selection gradient and the disruptive selection coefficient for an infinite island model, while accounting for kin selection when patch sizes were small. We further tested the analytical predictions using individual-based simulations. Our results illustrate the relationship between the spatial scale of resource variation and the resulting intra-specific polymorphism in consumer traits. We further discuss how phenotypic polymorphism varies with regard to dispersal rate, patch size, and life history. All in all, our results shed light on the interaction between two major drivers of biological diversity in spatially varying environments when dispersal was limited.

Sub-group poster presentations

EVOP(POPD) Posters

POPD-11 (Session: PS02)
Amanda Laubmeier Texas Tech University
"Interplay between pesticide use and natural predator behaviors"

We are interested in the combination of natural predators and conventional pesticides which contribute to the control of aphids, an agricultural pest. Although aphids are prey to many insects, the unique landscape for large-scale farming can reduce migration to and mobility within agricultural fields. In contrast, some small-scale and natural practices can foster an efficient natural predator community. Alongside these landscape choices, insecticide use can cause predator disorientation and sluggishness, further impacting mobility. To investigate how these different effects come together to determine pest control, we develop a partial differential equation model for predator-prey interactions within an agricultural field for a single season. We describe realistic use of pesticide sprays, which occur in pulses after pests pass a threshold abundance. The model also describes predator prey-taxis, or movement towards food sources, and how this behavior is impacted by pesticides. We consider these effects for a variety of migration and hunting behaviors and discuss the implications of our results for different agricultural practices.

POPD-12 (Session: PS02)
Nusrat Tabassum Texas Tech University
"The effects of temperature change on prey suppression by natural predators"

The sustainability of an ecosystem is determined by the relationship between predators and prey. The factors that play an important role in this context are temperature, body mass, foraging area, intraspecific competition and intraguild predation, all of which impact a predator's functional response. In the context of global warming, changing temperature could play a key role in changing prey suppression. Depending on the temperature, prey and predator can become active or inactive and temperature can affect other behaviors such as eating habit, foraging area, body growth etc. We use a dynamic model to describe prey suppression. We illustrate how predator behaviors would change with temperature at different times in a day or when average temperature increases.

POPD-13 (Session: PS02)
Jorge Arroyo-Esquivel Department of Mathematics, UC Davis
"Long transients appear in predator-prey systems with group defense and nonreproductive stages"

During recent years, the study of long transients has been expanded in ecological theory to account for shifts in long-term behavior of ecological systems. These long transients consist of long periods of time where a system is apparently in equilibrium; after which the system undergoes an abrupt change into qualitatively different dynamics. In this work, we analyze the potential for long transients in a model for a predator-prey system in which the prey present group defense, and their nonreproductive stages do not contribute to predator growth. This model has been previously used to analyze kelp-urchin dynamics, but it can be used in other systems such as colonial spider-wasp or honeybee-hornet systems. We have identified this system presents crawl-by transients near the extinction and carrying capacity states of prey. In addition, we identify a transcritical bifurcation in our system, under which a ghost limit cycle appears. We are able to estimate the escape time of our system from these transients using perturbation theory. This work advances an understanding of how systems shift between alternate stable states and their duration of staying in a given regime.

POPD-14 (Session: PS02)
Russell Milne University of Waterloo
"Effects of overfishing on coral reefs over local and regional scales"

Coral reefs are highly connected habitats, with dynamics that take place over very large spatial scales. However, performing field work over these large scales is challenging, and most mathematical modelling of coral reefs has focused on local dynamics. Here, we use a mechanistic, spatially explicit coral reef model to simulate the regional and local effects of three coral reef stressors (overfishing, nutrient loading and crown-of-thorns starfish invasions). We find three different local regimes (coral-dominant, macroalgae-dominant, macroalgae-only with no coral or fish), with sharp boundaries that depend on the interaction between fishing rate and nutrient loading rate. We also find that overfishing within a single patch can decrease coral cover by significant amounts in non-overfished patches. Additionally, increasing the proportion of patches that are overfished causes nonlinear declines in coral cover in non-overfished patches; this decline is strongly dependent on the configuration of which patches are overfished. The combination of crown-of-thorns starfish presence and high nutrient loading increases the variability of coral populations, and limits the space covered by both coral and macroalgae. These effects are present systemwide even when nutrient loading is restricted to one patch. Our findings have implications for both future field work and implementing conservation objectives.

POPD-15 (Session: PS02)
Clara Woodie University of California, Riverside
"The stabilizing and destabilizing effects of cannibalism in an intraguild predation system"

Intraguild predation (IGP), an interaction in which the intraguild (IG) predator competes with its intraguild (IG) prey for a shared resource, is ubiquitous in nature despite original theory predicting limited coexistence. A proposed stabilizing mechanism is cannibalism in the IG predator through its regulation of the predator population, which decreases predation pressure on the IG prey. We add cannibalism to an IG predator and include a cannibalism preference parameter to explore how the predator's preference for IG prey vs. conspecifics affects dynamics. We perform linear stability analyses. Our results show that strong cannibalism preference in the IG predator can 1) stabilize unstable IGP systems or 2) destabilize already-stable IGP systems depending on prey competitive ability. When the prey is a superior competitor, keeping with the assumption of original IGP theory, strong cannibalism preference drives the predator extinct. When the predator is a similar competitor for the resource as the prey, a common occurrence in natural IGP systems, preference for conspecifics over heterospecifics stabilizes this otherwise unstable system where the prey goes extinct. These results suggest that cannibalism preference, by altering the relative strengths of competition vs. predation between the predator and prey, determines the long-term stability of an IGP system.

POPD-16 (Session: PS02)
Thaddeus Seher University of California, Merced
"AddTag, a two-step approach that overcomes targeting limitations of precision genome editing"

CRISPR/Cas-induced genome editing is a powerful tool for genetic engineering, however targeting constraints limit which loci are editable with this method. Since the length of a DNA sequence impacts the likelihood it overlaps a unique target site, precision editing of small genomic features with CRISPR/Cas remains an obstacle. We introduce a novel genome editing strategy that virtually eliminates CRISPR/Cas targeting constraints and facilitates precision genome editing of elements as short as a single base-pair at virtually any locus in any organism that supports CRISPR/Cas-induced genome editing. Our two-step approach first replaces the locus of interest with an “AddTag” sequence, which is subsequently replaced with any engineered sequence, and thus circumvents the need for direct overlap with a unique CRISPR/Cas target site. In this study, we demonstrate the feasibility of our approach by editing transcription factor binding sites within Candida albicans that could not be targeted directly using the traditional gene editing approach. We also demonstrate the utility of the AddTag approach for combinatorial genome editing and gene complementation analysis, and we present a software package that automates the design of AddTag editing.

POPD-17 (Session: PS02)
Benjamin Garcia de Figueiredo Instituto de Física Teórica - Unesp
"Investigating first-crossing statistics in movement models with home-ranging behavior"

Ecological populations are, in general, not well mixed, and their non-homogeneous use of space modulates their local interactions. Although this range-residency is known to affect important observables such as encounter rates between individuals, many models in population dynamics implicitly or explicitly assume that populations make homogenous use of space. The Ornstein-Uhlenbeck (OU) process is a stochastic process in space that displays the basic characteristics of movement bounded by and centered around a home-range. Within the framework of OU movement models, the crossing statistics of two simultaneous processes serve as a proxy for the encounter statistics of two individuals. While this mathematical problem has been investigated, especially in one dimension, fewer studies have addressed the more ecologically relevant two-dimensional case (2D). In this work, we conduct a numerical and semi-analytical study of the first-crossing statistics of a pair of 2D OU models. We believe this can help build the foundations of more mechanistic and realistic models of population dynamics, based on the scaling properties of individual interactions. Further analytical investigation of this problem may elucidate its general properties.

POPD-18 (Session: PS02)
Rafael Menezes University of São Paulo
"Feasibility and Resilience in Randomly Assembled Communities"

As our world faces ever-increasing pressure upon many natural environments, it is essential to understand the stability of ecological communities. One of the crucial aspects of stability in rich communities is resilience, which entails information on how quickly the community can recover from small fluctuations in the densities of the populations. Equally relevant is their feasibility, which is indicative of how likely all the populations in the community can coexist, on the assumption that relative growth rates are variable. Despite substantial advancements in the investigation of these measures of stability, their interplay remains largely unexplored. In this work, we performed a comprehensive ecologically-informed exploration of the parameter space of the generalized Lotka-Volterra model integrating variability in type, intensity, and distribution of interspecific ecological interactions to study the broad patterns linking these two aspects of stability. We found a positive correlation between resilience and feasibility, suggesting that more resilient communities are more likely to be feasible. Additionally, we also found that communities with lower densities and intensities of interactions and more competition/exploitation are more resilient, and communities with equal proportions of positive and negative interactions are more feasible. Our study highlights the importance of investigations integrating different aspects of ecological stability.

POPD-19 (Session: PS02)
Joany Mariño Memorial Univesity of Newfoundland
"Resource seasonality explains latitudinal size and clutch size patterns in a Dynamic Energy Budget model "

Animals show a vast array of geographical variation in phenotypic traits. The most common patterns are the tendency of size and clutch size to increase with latitude among related species. Nevertheless, the precise mechanisms behind these patterns remain controversial. Here, we show how resource seasonality can drive latitudinal trait variation. We conducted numerical simulations of a dynamic energy budget model, quantifying individual biomass and reproductive output, both under constant and seasonal resource conditions. We evaluated 48 different genetically-determined physiological characters (equivalent to different species and represented by the model parameters for assimilation, mobilization, and energy allocation). In both scenarios, we found that resource availability determines interspecific trait differences in the DEB model. Our findings show that individuals can reach greater biomass and reproductive output in a seasonal environment than in a constant environment of equal average resource due to the peaks of food surplus. Our results agree with the classical patterns of interspecific trait variation and provide a mechanistic understanding supporting recent explanatory hypotheses: the resource and the eNPP (net primary production during the growing season) rules. The current alterations to ecosystems and communities make disentangling trait variation increasingly important to understand and predict biodiversity dynamics under environmental change.

POPD-20 (Session: PS02)
Anuraag Bukkuri Moffitt Cancer Center
"Tortoise and the Hare: On the Contribution of Evolvability to Eco-Evolutionary Dynamics of Competing Species"

Evolvability, the capacity for a population to generate heritable variation and respond to natural selection, is a fundamental concept influencing the adaptations and fitness of individual organisms. For many species, evolvability may be a trait that is subject to natural selection. Evolvability plays a critical role in eco-evolutionary dynamics and may help us understand how species respond to changes in their environment and how species coexistence can arise and be maintained. We create a model of competing species, each with a different evolvability. We then analyze the population and strategy dynamics of the two populations under the conditions of clade initiation, evolutionary tracking, adaptive radiation, and evolutionary rescue. We find that more stable environments favor slower evolving species, while unstable environments favor faster evolving ones. When several niches are available for species to occupy, slower evolving species outcompete faster evolving ones due to the cost of evolvability. Finally, we promote coexistence by disrupting the environment at intermediate frequencies, allowing for cyclical population dynamics of species with differential evolvabilities. Though we frame our discussion in the context of ecology and cancer, our model and analyses are agnostic of any specific application and thus broadly apply to any system capable of evolving.

POPD-21 (Session: PS02)
Evan Haskell Nova Southeastern University
"Attraction-Repulsion Taxis Mechanisms in a Predator-Prey Model"

We consider a predator-prey model where the predator population favors the prey through biased diffusion toward the prey density, while the prey population employs a chemical repulsive mechanism. This leads to a quasilinear parabolic system. We first establish the global existence of positive solutions. Thereafter we show the existence of nontrivial steady state solutions via bifurcation theory, then we discuss the stability of these branch solutions. Through numerical simulation we analyze the nature of patterns formed and interpret results in terms of the survival and distribution of the two populations.

POPD-22 (Session: PS02)
Rebecca Everett Haverford College
"Stoichiometric regulation of immune responses in primary producers"

All organisms require carbon and nutrients such as nitrogen for their growth and reproduction. In the presence of pathogens, host defense has been shown to increase with enhanced nutrient availability. Thus, availability of nitrogen may stimulate a host by enhancing its growth as well as immunity response. However, at the same time, nutrient availability may promote infection as higher host growth trades-off with reduced resistance as well as through enhanced pathogen performance. We explore the role of nitrogen availability on infection dynamics of a primary producer host and its pathogen using a stoichiometry-based disease model. Specifically, we test how changes in nitrogen investments in host immune response will alter host biomass build-up and pathogen infection rates.

POPD-23 (Session: PS02)
Daniel Cooney University of Pennsylvania
"Persistence vs Extinction of Cooperation via Multilevel Selection: The Dynamical Shadow of Lower-Level Selection"

Natural selection often acts simultaneously upon multilevel levels of biological organization, inducing a tension between traits favoring selfish individuals and traits providing collective benefit for the group. Examples of such conflicts arise in settings including the evolution of the early cell, the evolution of virulence, and the sustainable management of common-pool resources. In this talk, we consider a PDE model for the evolution of a cooperative trait in which competition takes place both within groups through individual-level reproduction and between-groups through a group-level birth-death process. Generalizing previous work from evolutionary game theory, we show that there exists a threshold intensity of between-group competition separating regimes in which cooperation goes extinct or persists in the population. We additional provide bounds on the long-time average payoff of the population, showing that the population cannot outperform the payoff of a full-cooperator group in the long run and allowing us to determine when measure-valued solutions to the multilevel dynamics converge to a steady-state density or forever oscillate. When intermediate levels of cooperation are most favorable to the group, this means that multilevel selection will always promote suboptimal collective outcomes, and no level of between-group competition can erase the shadow of lower-level selection.

POPD-24 (Session: PS02)
Vahini Reddy Nareddy University of Massachusetts Amherst
"Transition states in two-cycle ecological oscillators: dynamics and forecasting"

Many spatially-extended systems of ecological oscillators exhibit spatial synchrony with periodic oscillations in time. If the individual oscillators have two-cycle behavior, the transition to synchrony as a function of noise and coupling strength is in the Ising universality class, ensuring that the stationary properties of the ecological systems can be replicated by the simple Ising model [1]. In the Ising representation, the two phases of oscillations (high at odd times or high at even times) of an individual oscillator are represented by spin-up and spin-down. However, the behavior of an individual ecological oscillator suggests the existence of a transition state along with the two phases of oscillations. The oscillations at this transition state have amplitude very close to zero. To study such systems, we use Blume-Capel representation where the spin can take three values S={+1,-1,0} with S=0 as the transition state and S={-1,+1} as the two phases of oscillations. We model the spatially-extended ecological systems with coupled lattice maps in two-cycle regime and represent them with three state model. We also discuss maximum likelihood methods to infer the Blume-Capel representation. [1] V.Nareddy,et.al,J R Soc Interface(2020)

POPD-25 (Session: PS02)
Silas Poloni Lyra Institute for Theoretical Physics - UNESP
"Intraguild Predation in Periodic Habitats"

Fragmentation of natural landscapes is an ongoing process, mainly led by human activities, such as urban growth, roadway construction and farming. This phenomena may lead to many changes in the dynamics of populations that live in such landscapes, posing new challenges to our understanding of population persistence and diversity therein. In this work we consider an Intraguild Predation (IGP) model, a community module composed of two consumers of a shared resource, with a predation relation between such consumers, usually referred as IG-Prey and IG-Predator. Using Cobbold and Yurk's homogenization technique, we formulate and investigate the problem in a periodic habitat, composed of two types of patches where IGP relations are present, but allowed to have different parameters, such as less resource consumption, enhanced mortality or reduced resource productivity in one of the patches. Our results show that coexistence between IG-Prey and IG-Predator in heterogeneous landscapes is facilitated or hardened depending on the resource's habitat preference, allowing for coexistence in parameter regions which, in homogeneous landscapes, would be impossible, for example.

POPD-26 (Session: PS03)
Vitor De Oliveira Sudbrack DEE - UniL
"Population dynamics in highly fragmented landscapes"

It's important to study how populations respond to changes in habitat distribution in landscapes. In this project, we use numerical methods to simulate reaction-diffusion equations in artificial binary landscapes with different structural distributions of the same habitat amount. We discuss the net effects of fragmentation into the steady total population in those landscapes. These effects are dependent on matrix hostility and we analyse 3 different scenarios: soft, intermediate and hostile matrices. In soft matrices, highly fragmented landscapes support greater total populations compared to slightly fragmented landscapes - and the opposite is true for hostile matrices. Regarding conservation, highly fragmented landscapes eventually led to the extinction of species for a sufficiently hostile matrix in low HA. We compared statistical models to conclude those where the effects of fragmentation and HA are interdependent presented the best statistical descriptions of average abundance in landscapes. Our synthetic data supported that fragmentation effects are not negligible compared to habitat loss, and effects of fragmentation considering linear interdependence with HA and effects of fragmentation per se are similar in direction across the HA gradient. The model we present can generate synthetic data to elucidate patterns of the effects of fragmentation on the ecological value of landscapes.

POPD-27 (Session: PS03)
Simon Syga TU Dresden
"Studying the interplay of spatio-temporal interactions and evolutionary dynamics during cancer cell invasion"

Genome instability and mutations as well as the activation of invasion are defining characteristics of cancer. However, in most mathematical models only one of the two aspects is studied at a time, neglecting the complex interplay between the spatio-temporal interactions and evolutionary dynamics. To fill this gap, we here propose a mathematical model of individual cells that migrate, proliferate, die, and pass on their properties to their offspring with small variations.In particular, we assume that the set of individual properties results in a phenomenological fitness of each cell influencing its proliferation rate.In computer simulations, we show that the interplay of evolution and spatio-temporal dynamics leads to a propagating wave of invading cells, where the wave speed increases over time and clones of higher fitness appear preferably at the wave front.We use a mean-field approach to show that the system can be approximated by a PDE that is similar to the KPP-Fisher equation.We also show that the increase in average fitness over time is proportional to the variance in fitness in the population, in agreement with Fisher's fundamental theorem of natural selection.

POPD-28 (Session: PS03)
Peter Nabutanyi Bielefeld University, Germany
"Modelling Interaction of Genetic Problems in Small Populations and Minimum Viable Population Size"

An important goal for conservation is to define minimum viable population sizes (MVPs) for long-term persistence in the face of ecological and genetic problems. Such genetic problems include mutation accumulation (MA), inbreeding depression (ID) and loss of genetic variation at loci under balancing selection, but most studies on MVPs only include ID. Verbal arguments suggest that extinction risk is exacerbated when genetic problems interact, but a comprehensive quantitative theory is missing. Using deterministic and stochastic eco-evolutionary models, we estimated MVP size as the lowest population size that avoids an eco-evolutionary extinction vortex after sufficient time for mutation-selection-drift equilibrium to establish. As mutation rates increase, MVP size decreases rapidly under balancing selection but increases rapidly under ID and MA. MVP sizes also increase rapidly with increasing number of loci with the same or different selection mechanism until a point is reached at which even arbitrarily large populations cannot survive. However, when keeping the number of loci constant, the observed MVP size is dominated by the mechanism which when in isolation yields the smallest MVP estimate. For better estimates, there is need for more empirical studies to reveal how different genetic problems interact in the genome.

POPD-29 (Session: PS03)
Martin Pontz Tel Aviv University
"Aneuploidy as a transient evolutionary step to adaptation"

Aneuploidy, i.e. the change to a different number of chromosomes in single cells, occurrs quite frequently in nature. Prominent examples are human cancer cells and yeast populations under stress. We investigate if and under which conditions aneuploidy can facilitate local adaptation. We analyze both mathematical models and numerical simulations in which aneuploidy acts as a transient step towards a better adapted population. The main methods are based on the Wright-Fisher model and the theory of branching processes. One example for an important quantity that is derived, is the expected time until the population is successfully adapted. It depends heavily on the mutation rate, which is the rarest event that has to occur in order to achieve adaptation. This work can be seen as a first step towards establishing basic evolutionary theory for the process of aneuploidy as it seems currently to be lacking.

POPD-30 (Session: PS03)
Ayan Das Center for Ecological Sciences, Indian Institute of Science, Bengaluru
"Demographic noise can promote abrupt transitions in ecological systems"

Strong positive feedback is considered a necessary condition to observe abrupt shifts of ecosystems. A few previous studies have shown that demographic noise - arising from the probabilistic and discrete nature of birth and death processes in finite systems - makes the transitions gradual or continuous. In this paper, we show that demographic noise may, in fact, promote abrupt transitions in systems that would otherwise show continuous transitions. We begin with a simple spatially-explicit individual-based model with local births and deaths influenced by positive feedback processes. We then derive a stochastic differential equation that describes how local probabilistic rules scale to stochastic population dynamics. The infinite-size well-mixed limit of this SDE for our model is consistent with mean-field models of abrupt regime-shifts. Finally, we analytically show that as a consequence of demographic noise, finite-size systems can undergo abrupt shifts even with weak positive interactions. Numerical simulations of our spatially-explicit model confirm this prediction. Thus, we predict that small-sized populations and ecosystems may undergo abrupt collapse even when larger systems - with the same microscopic interactions - show a smooth response to environmental stress.

POPD-31 (Session: PS03)
Wissam Barhdadi Ghent University
"Analyzing eco-evolutionary dynamics under environmental change in a physiologically-structured individual-based model"

Recent rapid changes in the environment increasingly affect populations around the globe. Theoretical and empirical studies show that both individual life-history traits as well as evolutionary responses could mediate a population's response to these changes. Population models that integrate both ecological processes arising from individual life-history traits and the evolutionary forces acting on these traits can provide better predictions and a general approach for analyzing eco-evolutionary dynamics of populations facing rapid environmental change.We propose an individual-based modelling (IBM) framework adopting standardized submodels representing the life-history of individuals as well as inheritance mechanisms of adaptive traits. IBMs provide an intuitive approach to integrate ecological and evolutionary processes. Adopting an energy-budget based submodel to represent an individual's life-history allows for the emergence of individual fitness within the local environment. Further integration of a quantitative genetic approach to inheritance of adaptive life-history traits (resulting from energy-budget parameters), allows for the modelling of eco-evolutionary feedbacks as a function of the population's environment. In this simulation-based work, we explore the modelling framework to analyze the emerging eco-evolutionary dynamics in a Daphnia magna laboratory population. This analysis underpins the further coupling of evolutionary and ecological theory in populations models.

POPD-32 (Session: PS03)
Connah Johnson University of Warwick
"ChemChaste: Modelling chemical dynamics in spatially distributed bio-films"

Biofilms are ubiquitous in medical settings. Biofilms can contain multiple distinct bacterial strains which complicate the task of tackling infections. Mathematical modelling can help us improve our understanding of, and design better-informed experiments to probe, the dynamics of such systems. We seek to understand the biofilm wide dynamics through developing a hybrid continuum-discrete software library, ChemChaste. Building upon the multi-scale simulation package Chaste, ChemChaste introduces the means to simulate general reaction-diffusion PDEs coupled to individual based cell cycle models. Each cell within the simulation contains its own metabolic pathways, cell cycle model, and membranous transport to enable the simulation of complex chemical interactions between heterogeneous communities. The emergence of structure within the communities is simulated through the segregation of cell types driven by the chemical signaling and external reaction systems. This combination of cell based and external domain reactions enables ChemChaste to simulate chemical dynamics occurring within biofilms. From this we probe the role of microenvironment-metabolism feedback on the community structure and infer how the distribution of cell types may protect the community from external stress. Our results provide insights which may further our understanding of bacterial infections in clinical practice.

POPD-33 (Session: PS03)
Sou Tomimoto Mathematical Biology Laboratory, Department of Biology, Faculty of Sciences, Kyushu University
"Modeling mutation accumulation and expansion in long-lived trees with complex branching structure"

Somatic mutations accumulated in trees have now become quantitatively detectable with recent progresses in next-generation sequencing (NGS) technology. This is the first step to understand the impacts of somatic mutations on longevity of trees. However, NGS can only detect mutations that are shared by majority of stem cells. Minor somatic mutations may be hidden in many branches in the same individual. Because the processes of mutation accumulation and expansion remain poorly understood, we constructed a mathematical model at the stem cell population level to simulate these processes in silico. In our model, the growth of tree is described as a combination of elongation and branching processes. At these processes, stem cells in each meristem can be selected randomly or cell lineage persists for each stem cell without random selection. Depending on the randomness in stem cell selections, we developed three different models and compared the number and pattern of accumulated mutations among models in a branching structure measured in a Popular tree. We found that randomness in the selection process contributes to a decreased accumulation of somatic mutations. Comparison of our predictions with the data highlighted the possibility that more somatic mutations are accumulated in long-lived trees than previously expected.

POPD-34 (Session: PS03)
Baeckkyoung Sung KIST Europe / UST Korea
"Endocrine dynamics modelling on the hypothalamic-pituitary-gonadal axis of the aquatic lower vertebrates"

The endocrine signalling pathways of the lower vertebrates in the aquatic environments (e.g., fish and amphibians) comprise multiscale biochemical networks ranging from the subcellular transcriptomes, cell and tissue-specific metabolisms, and hormone-mediated inter-organ communications. The entire signalling circuitry thus typically demonstrates a dynamic complexity controlled by the physiological mechanisms such as cardiovascular circulation and neurosecretory regulations. The primary cross-talk paths involved in this circuitry can be effectively reduced to the serial multi-organ system linking the brain, ovary or testis, and liver, which is often called the hypothalamic-pituitary-gonadal (HPG) axis.In this presentation, we develop a general theoretical framework as a model for the signalling pathway network that regulates the HPG axis of the aquatic lower vertebrates. A linear system of ordinary differential equations was constructed to represent the metabolic networking structure where the uni- and bi-directional signalling flows and homeostatic feedback loops were coupled together. The model was designed to predict the dynamic behaviours of hormone syntheses in the HPG axis by simulating the environmentally relevant steroidogenic perturbations. Using this mechanistic model, it was shown that some potential scenarios of ecological risks could be quantitatively predicted in terms of the reproductive toxicology.

POPD-35 (Session: PS03)
Samuel Dijoux Dept. of Ecosystem Biology, Faculty of Science, University of South Bohemia, České Budejovice, Czech Republic
"'Symmetry in asymmetries' of body sizes and productivities drives consumer coexistence in multi-channel food webs"

Multi-channel food webs are shaped by the ability of apex predators to link asymmetric energy flows in mesohabitats differing in productivity and community traits. While body size is a fundamental trait underlying life histories and demography, its implications for structuring multi-channel food webs are unexplored. To fill this gap, we develop a model that links population responses to predation and resource availability to community-level patterns using a tri-trophic food web model with two populations of intermediate consumers and a size-selective top predator. We show that asymmetries in mesohabitat productivities and consumer body sizes drive food web structure, merging previously separate theory on apparent competition and emergent Allee effects (i.e., abrupt collapses of top predator populations). Our results yield theoretical support for empirically observed stability of asymmetric multi-channel food webs and discover three novel types of emergent Allee effects involving intermediate consumers, multiple populations or multiple alternative stable states.

POPD-1 (Session: PS05)
Emmanuel Adabor Ghana Institute of Management and Public Administration
"On the analysis of antigenic relatedness of influenza A (H3N2) viruses"

An accurate assessment of antigenic relatedness between influenza viruses is important for vaccine strain recommendations and influenza surveillance. Due to the mechanisms that result in frequent changes in the antigenicities of strains, it is desirable to obtain an antigenic relatedness measure that account for specific changes in strains that are of epidemiological importance in influenza. A computational model was developed using distinguishing features of antigenic variants to analyze antigenic relatedness among influenza strains. The features comprised of cluster information, amino acid sequences located in known antigenic and receptor-binding sites of influenza A (H3N2). In order to assess validity of parameters, accuracy and relevance of model to vaccine effectiveness, the model was applied to influenza A (H3N2) viruses due to their abundant genetic data and epidemiological relevance to influenza surveillance. It was found that all model parameters were determinants of antigenic relatedness between strains and that the model accurately predicts the antigenic relatedness between influenza A (H3N2) viruses. The methods presented in this study will potentially complement the global efforts in influenza surveillance.

POPD-10 (Session: PS05)
Robert West Department of Physics at Bar-Ilan University
"Evolution of a Fluctuating Population in a Switching Environment: Random versus Periodic"

Environmental changes greatly influence the evolution of populations. In this talk, we discuss the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity that switches either randomly or periodically between states of resources abundance and scarcity [1,2]. The population dynamics is characterized by demographic noise (birth and death events) coupled to the fluctuating population size [2,3]. By combining analytical and simulation methods, we elucidate the similarities and differences of evolving subject to stochastic and periodic switching. The population size distribution is generally found to be broader under intermediate and fast random switching than under periodic variations. This results in markedly different asymptotic behaviors of the fixation probability under random and periodic switching environments [1]. We also determine the conditions under which the fixation probability of the slow strain is maximal [1].[1] A. Taitelbaum, R. West, M. Assaf, and M. Mobilia, Physical Review Letters 125, 048105:1-6 (2020).[2] K. Wienand, E. Frey, and M. Mobilia, Physical Review Letters 119, 158301:1-6 (2017) and J. Royal Society Interface 15, 20180343:1-12 (2018).[3] R. West and M. Mobilia, Journal of Theoretical Biology 491, 110135:1-14 (2020).

POPD-2 (Session: PS05)
Matthew Edgington The Pirbright Institute
"Split drive killer-rescue: A novel threshold-dependent gene drive"

A wide range of gene drive mechanisms are predicted to increase in frequency within a population even when deleterious to individuals carrying them. This should also allow associated desirable genetic material to increase in frequency. Gene drives have garnered much attention for their potential use against a range of globally important problems including disease vectors, crop pests and invasive species. Here we propose a novel gene drive mechanism that could be engineered using a combination of toxin-antidote and CRISPR components, each of which are already being developed for other gene drive designs. Population genetics mathematical models are developed here and used to demonstrate the threshold-dependent nature of the proposed system alongside its robustness to a wide range of performance parameters, each of which are of practical significance given that real-world components are inevitably imperfect. We show that although a mechanism known to cause resistance may cause the system to break down, under certain conditions, it should persist over time scales relevant for genetic control programs. This work proposes a promising new class of gene drive (with several highly desirable characteristics) that may be engineered by combining components already widely in development.

POPD-3 (Session: PS05)
Lucy Lansch-Justen The University of Edinburgh
"Quantifying Stress-induced Mutagenesis"

Exposure to low concentrations of antimicrobials selects for resistance mutations and can induce phenotypic stress responses in microbes. Some of these responses increase the mutation rate, called stress-induced mutagenesis (SIM). But because stress responses additionally influence the whole population dynamics it is unclear whether SIM actually results in more or fewer resistant mutants. Moreover, SIM affects mutation rate estimates via fluctuation assays (a standard lab approach for measuring microbial mutation rates) because underlying modelling assumptions are not met. We describe an appropriate model of a microbial population which is exposed to stress and expresses a stress response and propose a new method for inferring the mutation rate in this case. Using the bacterial SOS response as an example we demonstrate that our derived mutant count distribution fits simulated data. In contrast, current methods are able to estimate the mean mutation rate in the population but not distinct mutation rates of subpopulations with low/high stress response levels.

POPD-4 (Session: PS05)
Pierre Lafont University of Edinburgh
"Capturing Bacterial Ecology in models of antibiotic treatments"

Understanding how bacteria react to antibiotic challenge is key in optimising treatments. Bacteria grow in an ever-changing environment, where growth is limited by competition for space and/or resources. But bacteria can also cross-protect or help each other, for instance by absorbing or degrading antibiotics. When faced with treatment, a denser population may thus be able to tolerate a higher dose. Upon lysis, bacteria cells can also release nutrients that will be recycled for others. These multiple potentially counteracting factors highlight the need for mathematical models to understand the effects of these ecological interactions. From simple to complex formulations, even in ODE systems, there are many modelling choices one can make depending on the processes of interest. Here we aim at a clear overview of the different modelling approaches available and what they mean biologically. We recognise a lack of extended mathematical analysis in the literature and aim to develop a more thorough understanding of model behaviours through equilibrium and stability analysis. Ultimately, we aim to understand how ecological forces of both competition and cooperation affect bacterial population response to antibiotics and probability of resistance emergence.

POPD-5 (Session: PS05)
Tahani Alkarkhi University of Essex
"Population Dynamics and Pattern Formation in a Plankton Model"

We study a spatio–temporal prey–predator model of plankton. This model has spatial interaction terms, which has the DeAngelis-Beddington functional response, to describe the grazing pressure of microzooplankton (M) on phytoplankton (P) is controlled through external info–chemical (C) mediated predation by copepods (Z). The Beddington DeAngelis functional response plays a critical role in modeling plankton. It is an advance on the prey-dependent Holling's type II functional response. It can be used to explain the predators' per capita feeding rates on prey. This functional response can also be used to provide better descriptions of predator prey abundances and how these affect predator feeding, discussed that in their predator prey system, Beddington DeAngelis was used to describe mutual interference by predators within the ecosystem. In relation to this, the concept was used to highlight the effect of changes in prey density on the predator density attached per unit time.The Beddington DeAngelis functional response can be used to perform a detailed mathematical analysis of the intra-specific competition among predators. We undertake a stability analysis of the two species model and compare the system dynamics. In relation to this, the critical conditions for Kinesis are derived; these are necessary and sufficient.

POPD-6 (Session: PS05)
Anni S. Halkola Department of Mathematics and Statistics, University of Turku, Finland
"Strategy dynamics in a metapopulation model of cancer cells"

Tumors consist of cells with abnormal phenotypes. These cells might be or become cancerous, which can lead to increased cell growth and even metastases. In this work, we have considered cancer as a metapopulation, in which habitat patches correspond to possible sites for a cluster of cancer cells. Cancer cells may emigrate into dispersal pool ( e.g. circulation system) and spread to new areas (i.e. metastatic disease). In the patches, cells divide and new mutations may arise, possibly leading into an invasion if the mutation is favorable. We consider various relevant strategies (phenotypes), such as the emigration rate and their contribution to angiogenesis, which is an important part of early stages of tumor development. We use the metapopulation fitness of new mutations to investigate how these strategies evolve in cancer through natural selection and disease progression. We further add treatment effects and investigate how different therapy regimens affect the evolution of the strategies. These aspects are relevant, for example, when examining the process of a benign tumor becoming cancerous, and how to best treat the early stages of cancer development.

POPD-7 (Session: PS05)
Kyohei Suzuki Akita Prefectural University
"Collective behavior and ambient flow in barnacle cypris larvae"

Barnacles are small crustaceans, having two types of larval periods. While both of them swim, cypris larva is specialized in searching for and attaching to a surface without feeding. They tend to live in groups. It is known that the grouping can be induced by the settlement-inducing protein complex (SIPC). However, the grouping may be induced by various other factors such as phototaxis, water flow, substrate state, and communication between individuals. Few studies have focused on the detailed behavior of cypris larva, and none has on its collective nature. The phenomenon of collective behavior can be confirmed in various organisms. It is natural to expect some collective behavior of cyprids while swimming, since they live in groups, but no definitive evidence has been found. In this work, we visualized the flow around cypris larva during swimming, quantified the state of collective behavior, and calculated various statistics such as the correlation coefficient, in order to elucidate the communication between allogeneic individuals. We found the surrounding viscous flow and the small yet nontrivial correlation between them.

POPD-8 (Session: PS05)
Román Zapién-Campos Max Planck Institute for Evolutionary Biology
"The effect of fitness differences in death-birth models with immigration"

Mathematical models have been instrumental in understanding the dynamics of ecological systems. Notable examples are models where the events of death, birth, and migration of individuals within a community only depend on their abundance. In other words, rates are equal regardless of the specific population.The proven utility of such models, used from gut microbiomes to forests, lies in their capacity to contrast experimental data to a 'neutral' prediction. Surprisingly, such predictions often agree with experimental data, indicating that population-specific rates might be absent or at most irrelevant.But what if, instead, rates are assumed to be population-specific in these models? What patterns emerge? How resilient are the neutral community patterns? Our work addresses these questions incrementally, going from simple to many-populations communities. We focus on changes in various community composition indicators, specifically, on the occurrence-abundance pattern and how to identify 'non-neutrality' in data.

POPD-9 (Session: PS05)
Alan Scaramangas City, University of Lodnon
"Evolutionarily stable aposematic signalling in prey-predator systems where the prey population consists of one species."

Aposematism is the signalling of a defence for the deterrence of predators. Our research focuses on aposematic organisms that exhibit chemical defences, which are usually signalled by bright skin pigmentation; although our treatment is likely transferable to other forms of secondary defence. This setup is a natural one to consider and opens up the possibility for robust mathematical modelling: the strength of aposematic traits (signalling and defence) can be unambiguously realised using variables that are continuously quantifiable, independent from one another and which together define a two-dimensional strategy space. We develop a mathematical model and explore the joint co-evolution of aposematic traits within the context of evolutionary stability. Even though empirical and model-based studies are conflicting regarding how aposematic traits are related to one another in nature, most allude to a positive correlation. We suggest that both positively and negatively correlated combinations of traits can achieve evolutionarily stable outcomes and further, that for a given level of signal strength there can be more than one optimal level of defence. Our findings are novel and relevant to a sizeable body of physical evidence, much of which could, until presently, not be addressed in terms of a single, well-understood mechanism.