Population Dynamics & Ecology (ECOP)

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Sub-group minisymposia

Mathematical modeling of gene drives

Organized by: Gili Greenbaum (The Hebrew University of Jerusalem, Israel), Jaehee Kim (Cornell University, USA)
Note: this minisymposia has multiple sessions. The second session is MS06-ECOP.

  • Marcus Feldman (Stanford University, USA)
    "The antecedents of modern gene-drive models: Some history of meiotic drive models"
  • In the late 1950s, it was discovered that factor on the second chromosome of Drosophila melanogaster produced extreme departure from Mendelian segregation in males. This segregation distorter (SD) factor reached a frequency as high as 30 percent in some populations. In small isolated populations of Mus musculus a similar phenomenon, the t-factor, was found to be produce strong segregation distortion as well as infertility in males. Even earlier, segregation distortion has been observed in the XY sex determination of Drosophila pseudoobscura. In all cases models for the balance of pre- and post-zygotic types of selection were invoked to explain the existence of polymorphism for these “anti-Darwinian” meiotic drive phenomena. Dynamics of evolutionary genetic systems with Mendelian segregation are very special, and most well-known results in population genetic theory do not apply if there is meiotic drive. Modern approaches to gene-drive analysis have their antecedent in this early research.
  • Chaitanya Gokhale (Max Planck Institute for Evolutionary Biology, Germany)
    "Synthetic gene drives and the control problem"
  • Synthetic gene drives are a marvel at par with any other technologies with a capacity for massive global impact. However, the discussion about drive control or intervention dilemmas is not at the same level as with some other technologies that are further behind but overhyped, such as generalized AI. With mathematical models, we show the resultant dynamics of synthetic drive technologies given the forces ecological forces they may face in the wild- particularly mate choice, different mating systems and structured populations. We assess the risk of the drive succeeding, failing or going rogue. In closing, we discuss the control problem from AI while simultaneously acknowledging the differences between artificial and natural selection
  • Philipp Messer (Cornell University, USA)
    "Suppression gene drive in continuous space can result in unstable persistence of both drive and wild‐type alleles"
  • Rapid evolutionary processes can produce drastically different outcomes when studied in panmictic population models vs. spatial models. One such process is gene drive, which describes the spread of “selfish” genetic elements through a population. Engineered gene drives are being considered for the suppression of disease vectors or invasive species. While laboratory experiments and modelling in panmictic populations have shown that such drives can rapidly eliminate a population, it remains unclear if these results translate to natural environments where individuals inhabit a continuous landscape. Using spatially explicit simulations, we show that the release of a suppression drive can result in what we term “chasing” dynamics, in which wild‐type individuals recolonize areas where the drive has locally eliminated the population. Despite the drive subsequently reconquering these areas, complete population suppression often fails to occur or is substantially delayed. This increases the likelihood that the drive is lost or that resistance evolves. We analyze how chasing dynamics are influenced by the type of drive, its efficiency, fitness costs, and ecological factors such as the maximal growth rate of the population and levels of dispersal and inbreeding. Our results demonstrate that the population dynamics of suppression gene drives are determined by a complex interplay of genetic and ecological factors, highlighting the need for realistic spatial modelling to predict the outcome of drive releases in natural populations.
  • John Marshall (University of California Berkeley, USA)
    "Modeling priorities as gene drive mosquito projects transition from lab to field"
  • Despite significant reductions in malaria incidence and prevalence over the last decade following the wide-spread distribution of long-lasting insecticide-treated nets, malaria is not expected to be eliminated with currently available tools. Consequently, there is interest in novel interventions that complement existing ones, including gene drive-modified mosquitoes. Mathematical modeling has a central role to play in determining the impact that gene drive systems could have, alongside other interventions, towards the goal of malaria elimination. In this talk, we survey modeling priorities as gene drive mosquito projects advance from the lab to the field. We begin by highlighting priorities in model building, including: i) capturing nuances in the inheritance-biasing impacts of gene drive systems, ii) incorporating data and insights on mosquito vector ecology, including life history, habitat distribution and movement patterns, and iii) aligning entomological models with detailed models of malaria transmission, including the impacts of currently available and novel interventions. We then highlight several priorities in model application as gene drive products advance from the lab to the field. These include informing target product profiles for gene drive products to assess when they satisfy safety and efficacy criteria, and informing the design of cage trials, field trials and eventually vector and disease control interventions. Other priorities include developing monitoring programs to assess the safety and efficacy of trials and interventions, developing surveillance programs to detect unintended spread, and addressing risk and regulatory questions requiring a quantitative analysis.

The complex adaptive dynamics of honeybee societies

Organized by: Jun Chen (Arizona State University, USA), Yun Kang (Arizona State University, USA), Gabriela Zuloaga (Arizona State University, USA)
Note: this minisymposia has multiple sessions. The second session is MS03-ECOP.

  • Chelsea Cook (Marquette University, Biological Sciences, Milwaukee Wisconsin, United States)
    "Individual Learning Phenotypes Drive Collective Foraging Behavior in Honey Bees"
  • Variation in cognition can influence how individuals respond to and communicate about their environment, which may scale to shape how a collective solves a cognitive task. However, few empirical examples of variation in collective cognition emerges from variation in individual cognition exist. Here, I show that interactions among individuals that differ in the performance of a cognitive task drives collective foraging behavior in honey bee colonies by utilizing a naturally variable and heritable learning behavior called latent inhibition (LI). I artificially selected two distinct phenotypes: high LI bees that are better at ignoring previously unrewarding familiar stimuli, and low LI bees that can learn previously unrewarding and novel stimuli equally well. I then provided colonies composed of these distinct phenotypes with a choice between a familiar feeder or a novel feeder. Colonies of high LI individuals preferred to visit familiar food locations, while low LI colonies visited novel and familiar food locations equally. However, in colonies of mixed learning phenotypes, the low LI bees showed a preference to visiting familiar feeders, which contrasts with their behavior when in a uniform low LI group. I show that the shift in feeder preference of low LI bees is driven by foragers of the high LI phenotype dancing more intensely and attracting more followers. I also present potential mechanisms that may be mediating the individual variation. These results reveal that cognitive abilities of individuals and their interactions drive emergent collective outcomes in social insects.
  • Hermann Eberl ( University of Guelph, Canada)
    "Between hive transmission of nosemosis by drifitng"
  • The vast majority of mathematical models of honeybee diseases is for single colonies that have no interaction with other colonies. This misses an important aspect of the ecoepidemiology in an apiary. For an earlier model of nosemosis with direct and indirect transmission routes we formulate a metapopulation model that accounts for the transmission of the disease between colonies by drifting. Since even the underlying single hive model is too complex for a thorough rigorous analysis, we explore the model in extensive numerical simulations. Our results suggest that for the model at hand the spread of the disease in the apiary is primarily controlled by seasonal effects, whereas the actual drifting rate has little quantitative effect.
  • Natalie J. Lemanski (Rutgers University New Brunswick (current), University of California Los Angeles (where work was performed), United States)
    "Individual learning affects the accuracy of collective decisions for honey bee colonies foraging on different quality resources"
  • To survive, animals need to find resources and make decisions about which resource patches to invest time in exploiting. Balancing these tasks can be a complex decision-making challenge, particularly when patches are rapidly changing, heterogeneously distributed, and variable in quality. Social insects, such as honeybees, navigate this challenge in the absence of centralized control by allocating different individuals to exploration or exploitation based on differences in individual behavior. To investigate how differences in individual learning affect a colony’s collective ability to locate and choose among different quality food resources, we develop an agent-based model and test its predictions empirically using two genetic lines of honey bees (Apis mellifera), selected for differences in their learning behavior. We show that colonies containing individuals that are better at learning to ignore unrewarding stimuli are worse at collectively choosing the highest quality resource. This work highlights how differences in individual behavior may have unexpected consequences for the emergence of collective behavior.
  • Gloria DeGrandi-Hoffman (USDA-ARS, United States)
    "Simulating how combinations of stress factors can affect honey bee colony growth and survival"
  • Biotic and abiotic factors can exert stress on honey bee colonies and limit their growth ultimately causing colony death. A colony population dynamics model was used to predict effects on colony growth of pesticide stress exerted during different times of year. Poor queen quality and infestation by parasitic Varroa mites were added into the simulations to determine the impact of multiple stress factors on colony growth and survival. The model predicts that colony survival after pesticide exposure depends on the time of year when exposure occurred. Poor queen quality makes colonies more vulnerable to loss from pesticide exposure as do high infestations of Varroa mites. Predictions highlight the difficulties is assigning causation of colony loss to a single factor.

The complex adaptive dynamics of honeybee societies

Organized by: Jun Chen (Arizona State University, USA), Yun Kang (Arizona State University, USA), Gabriela Zuloaga (Arizona State University, USA)
Note: this minisymposia has multiple sessions. The second session is MS02-ECOP.

  • Adrian Fisher II (Arizona State University, School of Life Sciences, United States)
    "A widely-used mito-toxic fungicide negatively affects honey bee (Apis mellifera) health"
  • The honey bee (Apis mellifera) is an essential contributor to crop pollination in the United States. However, honey bees, and other pollinators, have been undergoing population declines for poorly understood reasons. Pollinators may frequently encounter fungicides in foraging environments as they are applied to crop plants during bloom. To assess the impact of the fungicide Pristine® (25.2% boscalid, 12.8% pyraclostrobin) we partially tested the hypothesis that Pristine® negatively affects protein digestion or absorbance. Field colonies were maintained for 13 months with pollen containing four concentrations of Pristine®, bracketing concentrations measured in pollen collected by bees while foraging on fungicide-sprayed almond trees We found that Pristine® negatively affects colony growth and winter survival. Additionally, we observed several individual outcomes including early foraging, elevated rates of pollen foraging and consumption, and reduced longevity. Pristine® consumption also lowered hemolymph protein levels, and this effect increased with bee age. Together, these findings support the hypothesis that fungicides such as Pristine® negatively impact honey bee health at least partly by impairing protein balance. This research was supported by USDA 2017-68004-26322.
  • Yixiang Wu (Middle Tennessee State University, United States)
    "An Environmental Model of Honey Bee Colony Collapse Due to Pesticide Contamination"
  • We develop a model of honey bee colony collapse based on the contamination of forager bees in environmental regions contaminated with pesticides. An important feature of the model is the daily homing capacity each day of foragers bees. The model consists of difference equations describing the daily homing of uncontaminated and contaminated forager bees, with an increased homing failure of contaminated bees. The model quantifies colony collapse in terms of the fraction of contaminated bees subject to this increased homing failure. If the fraction is sufficiently high, then the hive falls below a viability threshold population size that leads to rapid disintegration. If the fraction is sufficiently low, then the hive can rise above the viability threshold and attain a stable population level.
  • Mary R Myerscough (School of Mathematics and Statistics University of Sydney, Australia)
    "Modelling the role of temperature stress in honeybee colony collapse."
  • Honey bees raise their brood (bee larvae and pupae) inside the hive, ideally at a temperature of between 34 and 36 degrees Celsius. If the brood experiences lower temperatures then it will develop into sub-standard adult bees. These low quality adults will have an impact on the hive as they will less effective workers. Previous modelling work has strongly suggested that effective foraging and, in particular, the prevention of premature death of foragers is crucial for hive health and survival. In this talk we will examine the effect of temperature stress on hive populations, using a delay-differential equation model that includes the effect on adult bees of poor temperature regulation when they were pupae. We show that the equilibrium of these equations has two fold bifurcations. The right most fold bifurcation produces hive collapse in the model. We show that increasing temperature stress makes the hive more prone to collapse if it experiences increased rates of premature forager death.
  • M. Gabriela Navas-Zuloaga (School of Human Evolution and Social Change, Arizona State University, United States)
    "From Individual Phenotypes to Collective Behavior in Honeybee Foragers: A Mathematical Model"
  • Recent studies have shown that discrete heritable attention phenotypes in individual honey-bee foragers drive their foraging behavior, thus affecting colony fitness. In particular, individual and collective preference for familiar or novel resources is dependent on the relative presence of high and low attention individuals in the colony. Previous models of honey-bee foraging have not included this phenotype-dependent preference. In order to understand how colony-level preferential exploitation of novel and familiar resources emerges from the interactions between individuals with different preferences and levels of influence, I developed an ordinary differential equation model of self-organized foraging based on the different phenotypes. The model reproduces the observed increased foraging activity in colonies with higher proportions of high-attention foragers, as well as the preference for familiar sources in such colonies. It also provides mechanistic support for the empirical hypothesis that individual preference, amplified by efficient communication, is sufficient to produce collective preference at the observed levels in different colonies. The model contributes to understanding the role of individual cognitive variation in regulating the collective trade-off between exploring for new resources and exploiting known ones.

Mathematical modeling of gene drives

Organized by: Gili Greenbaum (The Hebrew University of Jerusalem, Israel), Jaehee Kim (Cornell University, USA)
Note: this minisymposia has multiple sessions. The second session is MS01-ECOP.

  • Keith Harris (The Hebrew University of Jerusalem, Israel)
    "Rescue by gene swamping as a fail-safe strategy in gene drive deployment"
  • Gene drives are genetic constructs that can spread deleterious alleles in wild populations by generating non-Mendelian inheritance patterns. Lab experiments of CRISPR-Cas9-based gene drives have been shown to drive populations to extinction within a few generations, paving the way for deployment of gene drives to control disease vectors and invasive species. However, given that a gene drive can potentially spill over to and modify other populations or even other species, they must be designed in a way that allows this process to be controlled. Due to the ecological risks involved in deployment, studying behaviors of gene drive spread in wild populations currently relies on mathematical and computational models. We developed a model of gene drive spillover that combines evolutionary and demographic dynamics, in a two-population setting. The model demonstrates how feedback between these dynamics produces additional outcomes to those demonstrated by the evolutionary dynamics alone. We identify an outcome where the short-term suppression of the target population is followed by gene swamping and loss of the gene drive. Using our model, we demonstrate the robustness of this outcome to spillover and the evolution of resistance, and suggest it as a fail-safe strategy for gene drive deployment.
  • Leo Girardin (Université Claude Bernard Lyon-1, France)
    "Demographic feedbacks can hamper the spatial spread of a gene drive"
  • This talk is concerned with a reaction--diffusion system modeling the fixation and the invasion in a population of a gene drive (an allele biasing inheritance, increasing its own transmission to offspring). In our model, the gene drive has a negative effect on the fitness of individuals carrying it, and is therefore susceptible of decreasing the total carrying capacity of the population locally in space. This tends to generate an opposing demographic advection that the gene drive has to overcome in order to invade. While previous reaction--diffusion models neglected this aspect, here we focus on it and try to predict the sign of the traveling wave speed. It turns out to be an analytical challenge, only partial results being within reach, and we complete our theoretical analysis by numerical simulations. Our results indicate that taking into account the interplay between population dynamics and population genetics might actually be crucial, as it can effectively reverse the direction of the invasion and lead to failure.
  • Lena Klay (Sorbonne Université, France)
    "Spatial spread of suppression and eradication drives"
  • Understanding the spatial and temporal spread of gene drive (mechanism that disrupts the laws of heredity by biasing transmission) through modeling is an essential step before any field experiments. In this talk, I will present a work based on a deterministic reaction-diffusion system proposed by L. Girardin and F. Débarre (presented in L. Girardin’s talk). I will focus on the case of eradication, when the population goes extinct after the drive has spread. Firstly, I will extend the original model to various timings of gene conversion (considering conversion can happen in the zygote or in the germline) and different probabilities of gene conversion (instead of assuming 100% conversion). In contrast with the initial model assuming systematic gene conversion in the zygote, heterozygous individuals must be accounted for. As the model is then quite complex, numerical studies will provide us with information regarding the emergence conditions of eradication waves. If time allows on a second part, I will simplify the system through linearization, to better understand the theoretical behavior (shape, speed…) of those waves.
  • Richard Gomulkiewicz (Washington State University, USA)
    "Resistance-proofing Gene Drives for Population Suppression"
  • The advent of CRISPR technology has brought us to the cusp of engineering gene drives capable of eradicating plant and animal species and with it urgent concerns about the evolution of resistances that could undermine the drives. This talk will present results from a mathematical modeling study that reveal the fundamental mechanics of how non-allelic resistance evolves and especially how one may design a gene drive to evade resistance. The findings are used to suggest design principles to guide the engineering of resistance-proof suppression drives.

Population dynamics of interacting species

Organized by: Rebecca Tyson (University of British Columbia, Canada), Maria Martignoni (Memorial University of Newfoundland, Canada), Frithjof Lutscher (University of Ottawa, Canada)
Note: this minisymposia has multiple sessions. The second session is MS08-ECOP.

  • Jimmy Garnier (CNRS - Universite de Savoie-Mont Blanc, France)
    "Genetic diversity in age-structured populations"
  • In many population, the individuals behavior might differ according to their age. The emerging structure have profound influence on the population dynamics as well as its genetic diversity. I will investigate the dynamics of the genetic diversity in metapopulations. I show that the duration of the juvenile stage or the reproduction strategy might have profound influence on the local diversity of sub--population composing the metapopulation.
  • Maria Martignoni (Memorial University of Newfoundland, Canada)
    "Mechanisms for coexistence and competitive exclusion among mutualist guilds."
  • Mutualistic interactions are gaining increasing attention in the scientific literature, especially as pollination and plant-microbe symbioses play a key role in agricultural productivity. In particular, the widespread symbiosis between plants and arbuscular mycorrhizal (AM) fungi, offers a promising sustainable alternative for maintaining productivity in farmland. Despite the potential benefits for soil quality and crop yield associated with the use of AM fungi, experiments assessing the effective establishment of the fungi in the field have given inconsistent results. Additionally, it is not clear whether the introduction of commercial AM fungi could lead to a biodiversity loss in the native fungal community, and ultimately have a negative impact on plant growth. We developed a series of mathematical models for plant and AM fungal growth to assess the establishment, spread and impact of an introduced species of AM fungi on the native fungal community and on plant productivity. Our models provide a theoretical framework to determine the circumstances under which the inoculated fungal species can coexist with the native fungal community and effectively boost productivity, versus when inoculation constitutes a biodiversity risk and, ultimately, a detriment to crop yield. Overall, our results show that diversity within mutualistic communities promotes productivity and reduces the risk of invasion and biodiversity loss posed by the introduction of a less mutualistic, or even parasitic, species. Although my analysis focuses on plant-fungal interactions, my findings provide valuable criteria to assess the impact of species introduction in mutualistic communities in general, such as other beneficial microbes or pollinator communities.
  • Frithjof Lutscher (University of Ottawa, Canada)
    "A seasonal hybrid model for the evolution of flowering onset in plants"
  • In temperate climates with strong seasonal changes, plants need to decide how to allocate resources to vegetative growth or to reproduction during a potentially short favorable season. Many plants switch from mostly vegetative growth early in the season to mostly reproduction late in the season. The onset of flowering marks the transition between the two phases. Later onset of flowering typically implies a larger size at maturity and higher reproductive capacity. At the same time, it limits the remaining time in the favorable season for pollination and seed development. Hence, plants face a trade-off for some optimal flowering onset. In this talk, I will present a seasonal hybrid model for the density of a plant population, structured by onset of flowering as a trait. I will apply two complementary approaches to analyze the system. Overall, I find that evolution favours some intermediate flowering times.
  • Kelsey Marcinko (Whitworth University, USA)
    "Host-Parasitoid Dynamics and Climate-Driven Range Shifts"
  • Climate change has created new and evolving environmental conditions that cause the habitat ranges of many species to shift upward in elevation and/or towards the poles. To investigate the impact of climate-driven range shifts on host and parasitoid insect species, I consider an integrodifference equation (IDE) model. Using this IDE model, I determine criteria for coexistence of the host and parasitoid species as the habitat shifts spatially. I compare several methods of determining the critical habitat speed, beyond which the parasitoid cannot survive. To make the analysis tractable, I determine the critical speed from a spatially-implicit model that uses an approximation of the dominant eigenvalue of an integral operator. Because the kernel is asymmetric, classical methods for determining the dominant eigenvalue perform poorly. Instead, I approximate the dominant eigenvalue with a method known as geometric symmetrization. The critical speed for parasitoid survival, as computed from the spatially-implicit model, is a good lower bound for the critical speed as determined from simulations of the full IDE model. This framework allows for further exploration of how biological factors impact the coexistence of the host and parasitoid species.

Population dynamics of interacting species

Organized by: Rebecca Tyson (University of British Columbia, Canada), Maria Martignoni (Memorial University of Newfoundland, Canada), Frithjof Lutscher (University of Ottawa, Canada)
Note: this minisymposia has multiple sessions. The second session is MS07-ECOP.

  • Juliana Berbert (Universidade Federal do ABC, Brazil)
    "Dessication-rehydration stress revealed by sugar-metabolite-reserve model"
  • We focus on the evaluation of photosynthetic organisms. Some species and tissues can endure periods of the dry season because they rely on robust dynamics of metabolites. The metabolic dynamics are complex and challenging to address because the system involves several steps, usually with hundreds of metabolites. The metabolite densities vary among species and tissues and respond to external conditions, such as an environmental stimulus like water supply. Understanding these responses, particularly the dessication-rehydration processes, are important both economically and evolutionarily, especially in the presence of climate change. Therefore, we propose a new way to analyze the dynamics of metabolites with a compartmental model which explores the metabolites’ density-dependence on water explicitly. We use a mathematical formulation to model the dynamics among three essential metabolite classes: sugar (S), active metabolite (A), and reserve accumulation (R). Through stability analysis and numerical solutions, we characterize regions on the phase space, defined by the transition rates between the classes S to A and S to R, where the system diverges or approaches zero. We show that different species and tissues respond distinctly to dessication processes, being more or less resilient according to the transition rates between the compartments of the model. Furthermore, the effects of water supply fluctuation, due to the dessication-rehydration processes, show that unless the organism has a robust reservoir for metabolism, the system cannot support itself for a long time. Many results corroborate experimental observations, and others provide a new perspective on the studies of metabolic dynamics, such as the significance of the metabolism reservoir. We understand that knowing the organism’s response to abiotic changes, particularly that of the water supply, may improve our management of the use of these organisms, for example, in the crop field during climate changes.
  • Chris Heggerud (University of Alberta, Canada)
    "Niche differentiation in the light spectrum promotes coexistence of phytoplankton species: a spatial modeling approach."
  • The paradox of the plankton highlights the contradiction between Gause's law and the observed diversity of phytoplankton. It is well known that phytoplankton dynamics depend heavily on two main resources; light and nutrients. Here we consider light as a continuum of resources rather than a single resource. We propose a spatially explicit RD model to explore under what circumstance coexistence is possible from a mathematical and biological perspective. Furthermore, we provide biological context as to when coexistence is expected based on the degree of niche differentiation within the light spectrum and overall turbidity of the water.
  • Pau Capera Aragones (University of British Columbia Okanagan, Canada)
    "Differential equation model for central-place foragers with memory: Implications for bumble bee crop pollination"
  • Bumble bees provide valuable pollination services to crops around the world. However, their populations are declining in intensively farmed landscapes. Understanding the dispersal behaviour of these bees is a key step in determining how agricultural landscapes can best be enhanced for bumble bee survival. In our work, we develop a partial integro-differential equation model to predict the spatial distribution of foraging bumble bees in dynamic heterogeneous landscapes. In our model, the foraging population is divided into two subpopulations, one engaged in an intensive search mode (modeled by diffusion) and the other engaged in an extensive search mode (modeled by advection). Our model considers the effects of resource-dependent switching rates between movement modes, resource depletion, central-place foraging behaviour, and memory. We use our model to investigate how crop pollination services are affected by wildflower enhancements. We find that planting wildflowers adjacent to a crop can increase the pollination services to the crop, and we quantify this benefit as a function of the location, quantity, and quality of the planted wildflowers.
  • Rebecca Tyson (University of British Columbia Okanagan, Canada)
    "Phase-sensitive tipping: Cyclic ecosystems subject to contemporary climate"
  • Global change is expected to lead to increased reddening and amplitude of climate noise. In this paper we explore how these changes in climate variability could interact with systems that are already oscillating, namely, predator-prey systems. We include an Allee effect in the prey equation so that we can determine whether or not extinction is deterministically possible. We identify the phase of the predator-prey cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. Our analysis of these examples uncovers a counter-intuitive behaviour, which we call phase-sensitive tipping (or P-tipping), where tipping to extinction occurs only from certain phases of the cycle. We find that P-tipping can occur in both the Rosenzweig-MacArthur (RM) and Leslie-Gower-May (LGM) model systems, and for realistic parameter values for the Canada lynx and snowshoe hare. Our work identifies a new mechanism for climate-induced extinction.

Spatial approaches to ecological population monitoring and management

Organized by: Tae-Soo Chon (Pusan National University/Ecology and Future Research Association, Republic of Korea), Fugo Takasu (Nara Women’s University, Japan)
Note: this minisymposia has multiple sessions. The second session is MS10-ECOP.

  • Tae-Soo Chon (Ecology and Future Research Institute/Pusan National Univ., Republic of Korea)
    "Patterning local cooccurrence patterns of Nutria individuals using Geo-self-organizing map applied to telemetry data"
  • Nutria populations expanded rapidly in Korea since 1990s, causing biodiversity loss, local habitat disturbances and agricultural damages in ecosystems. The geo-self-organizing map (Geo-SOM) was applied to radio-tracked individual data to cluster geographical areas in association with plant types, land cover states and biological parameters. The minimum nearest neighbor distances for the different sexes were overall in accord with the minimum distances for the same sex. Local cooccurrences of female and male individuals were negatively associated with male-male cooccurrences compared with female-female cooccurrences, suggesting male dominance in group formations. Movement and cooccurrence information extracted by Geo-SOM aids understanding of population dispersal to help formulating management strategies for nutria populations.
  • Thakur Dhakal (Kangwon National Univ., Republic of Korea)
    "Unraveling Behavior States of Wild Boar Movements in Habitat Transitions Using Hidden Markov Model"
  • Wild boar (Sus scrofa) population dispersal is a critical issue in Korea nowdays, being closely linked with epizootics of African swine fever. Understanding movement of wild boar is a key issue in predicting spatial advancement patterns of the population. Movements of animals, however, are highly complex and difficult to analyze. We addressed behavior states of wild boar individuals by applying the hidden Markov model (HMM) to field data. Movements of wild boar individuals were continuously tracked at the Bukhan Mountain, Seoul, Korea, with the interval of approximately 2 hours up to 313 days from June, 2018 to May, 2019. Observable events were expressed as visiting by wild boar individuals to habitats with different resources (forest, leaf types and water). Transition probability matrices (TPMs) and emission probability matrices (EPMs) were estimated according to different initial conditions. Self-organizing map (SOM) was utilized to cluster output parameters produced from initial conditions to find the global optimum of parameters. Characteristic TPMs were observed according to different number of states. The event with most favorable habitat with “broad-leaf and water” shows the maximum probability of visit in EPM, followed by the habitats with “coniferous-leaf and water”. As the number of states increased, other habitats including “coniferous-leaf without water” and “no-forest without water” had higher probabilities of visit in EPMs. HMM in linking with SOM is useful for addressing behavior states of movements of wild boar individuals and would provide basic information on monitoring wild boar population dispersal.
  • Sung-Won Hong (Kyungpook National Univ., Republic of Korea)
    "Ensemble species distribution models proved habitat characteristics coincidence of dead and living long-tailed gorals (Naemorhedus caudatus) according to extreme snowfall"
  • Ensemble species distribution models (SDMs) have been used to define the vulnerable areas for critically endangered species and establish the conservation planning. The long-tailed goral (Naemorhedus caudatus) is a critically endangered herbivore in South Korea. Despite government efforts to recover the population through reintroduction programs, the animal remains vulnerable to heavy snowfall. From March to June 2010, 24 animals were found dead due to heavy snowfall in the Wangpi Stream basin. In this study, we hypothesized that gorals that died due to snowfall are low-status individuals that lived in the sub-optimal or non-suitable areas. Using the occurrence data from extensive field surveys from 2008 to 2010 in the Wangpi Stream and the carcass location data as well, we (1) defined the goral habitat characteristics and (2) compared the habitat characteristics between dead and living gorals using ensemble species distribution modeling (BIOCLIM, Domain, generalized linear models, generalized additive models, random forests, boosted regression trees, classification and regression trees and Maxent). The ensemble models had high levels of goodness-of-fit and suggested that the sites where dead gorals were found were closely related to typical goral habitats. These results implied that the optimal goral habitats could become uninhabitable following heavy snowfall. Most of the dead animals were pregnant females or were young, implying that they could not escape their primary habitats due to lower mobility. Thus, when there is a climate catastrophe, the optimal goral habitats should be considered for rescue and artificial feeding.
  • Taeyong Shim (Korea University, Republic of Korea)
    "Evaluating Distribution Shifts of Invasive Largemouth Bass under Climate Change"
  • The spread of largemouth bass (Micropterus salmoides) is a rising concern in South Korea. This study aims to evaluate the distribution shifts of largemouth bass in South Korea using classification algorithms. The candidate classification algorithms include RF (Random Forest), C5.0 and cforest (Conditional Inference Random Forest) which are built in the caret package in R. Largemouth bass occurrence records and environmental variables (temperature, precipitation, flow, water quality, and topography) from 2011 to 2015 were used in model training. In training, grid and random searching methods were compared for identifying the hyperparameters within an algorithm (RF, C5.0, and cforest). As a result, grid searching applied RF showed the highest accuracy. RF showed that largemouth bass will shift to the upstream regions in the Han river. This study is expected to be helpful for predicting distribution shifts and establishing management policy of largemouth bass.

Spatial approaches to ecological population monitoring and management

Organized by: Tae-Soo Chon (Pusan National University/Ecology and Future Research Association, Republic of Korea), Fugo Takasu (Nara Women’s University, Japan)
Note: this minisymposia has multiple sessions. The second session is MS09-ECOP.

  • Hyo Gyeom Kim (Chonnam National Univ, Republic of Korea)
    "Importance of spatial clustering and environmental parameters on classification of the relationships between chemical composition of water body and sediment, and indices of various trophic level biotic communities in river system"
  • Water and sediment quality influence the biotic communities, and the relationships between the chemical compositions and the communities concurrently give an important information for the regulation and management of river system. Our hypotheses are that the importance of spatial clustering and environmental parameters vary among trophic levels. To address these issues, we applied the clustering results from self-organizing map (SOM) and geo-self-organizing map (Geo-SOM) as a random effect for linear mixed-effect models (LMMs). The datasets were composed of 12 water-quality and 10 sediment variables with indices of benthic diatoms, macroinvertebrates, and fish communities surveyed from 84 stations of rivers of South Korea for 2 years. The SOM proposed 8 clusters based on the relationships between parameters, and the Geo-SOM proposed 13 clusters based on those relationships plus the geographical characteristics. Inclusion of the random effects to SOM and Geo-SOM clustering improved the performance of all the LMMs. In particular, benthic diatom index was best explained with the Geo-SOM clusters, while macroinvertebrate and fish indices were best explained with the SOM clusters. This indicates that benthic diatoms appear to be more affected by spatial heterogeneity caused from the effects of either local pollutant variables or land-use patterns. While the SOM and Geo-SOM suggested that water quality variables were more important than sediment variables, the LMM revealed the importance of Cu for diatom, Cr for macroinvertebrate, and As for fish communities. The parameter for geographical tolerance is useful for determining the necessity of spatial clustering for each trophic level, and the combined method of LMM and SOM provides us an efficient means of establishing target environmental parameters.
  • Byungjoon Min (Chungbuk National University, Republic of Korea)
    "Identifying an influential spreader in epidemics on meta-population models"
  • Identifying the most influential spreaders is one of the most important problems in epidemic modeling. So far, some approaches have attempted to rank the influence of spreaders in meta-population models based on heuristics. Here, we derive a theory for calculating the expected size of epidemic outbreaks originated from a single node in a network with a meta-population model by using a message-passing approach. We also test and validate our theory using real-world airline data. Our study provides an analytical tool to predict the most dangerous city for epidemic spreading.
  • KyoungEun Lee (National Institute of Ecology, Republic of Korea)
    "Network analysis for predicting invasive alien species dispersal in a novel cell-based metapopulation model"
  • We introduce a cell-based metapopulation model for muskrat (Ondatra zibethicus) dispersal dynamics in the Geum River watershed area in Korea. Muskrat dynamics on the cell is described by a phenomenological metapopulation rate equation, including growth rate, carrying capacity, Allee effect, and especially moving tendency as a function of muskrat population and habitat preference. Diffusive spreading of muskrats is proportional to the growing rate and diffusive deviation rate, whereas decreasing with the Allee effect. The dynamical network using causal decomposition methods was effective in addressing key network properties such as hubs and edge strength similarity. Numerical database construction along with simulation-based prediction framework will enable us to identify ecological as well as environmental properties in revealing invasion causality of muskrats in the target area (Geum River, in this study). Network approaches to modelling and analysing the spreading dynamics can be useful for detecting significant habitats and eco-corridors for either survival or management of invasive species. Furthermore, the dynamical network analyses can be applied to the control scenarios of invasive species concurrently with system sensitivity tests.
  • Fugo Takasu (Nara Women’s Univ, Japan)
    "Estimation of spatial interaction kernel from time series data - a point pattern approach"
  • In spatial and invasion ecology, more and more empirical data are available and provided as mapped point pattern; individuals' location in space, status, etc., are recorded as time series data. Examples include spatial expansion of tree diseases such as the pine wilt disease and epidemic/meta-population dynamics, a process made of infection/colonization and recovery/local extinction, etc., over space. Observed time series data as point pattern, however, often contain sampling errors, noises and factors driven by unknown processes, all of which make it difficult to explore true mechanistic processes involved behind the data. In order to explore mechanistic interactions at individual level, we aim to explore methods that better estimate spatial 'interaction kernel'. As an example, in this talk, we extend the classical epidemic models to stochastic point pattern models where infection rate depends on the distance from infectious to susceptible with a certain functional form (infection kernel). We then explore several methods that better estimate the infection kernel based on the time series data generated from the stochastic model. Results of our analyses will be presented and discussed. Our approach is a kind of 'inverse problem' in which we explore methods that better estimate unknowns from data generated from known processes.

Ecological models at the interface of empirical and theoretical research

Organized by: Amanda Laubmeier (Texas Tech University, United States), Kyle Dahlin (University of Georgia, United States)

  • Annabel Meade (North Carolina State University, United States)
    "Population model for the invasive insect Homalodisca vitripennis and the egg parasitoid Cosmocomoidea ashmeadi"
  • The glassy-winged sharpshooter, Homalodisca vitripennis, is an invasive pest which presents a major economic threat to the grape industries in California by spreading a disease-causing bacteria, Xylella fastidiosa. Recently a common enemy of H. vitripennis, certain mymarid parasitoid species including Cosmocomoidea ashmeadi and Cosmocomoidea morrilli, have been studied to use in place of insecticides as a control method. We create a time and temperature dependent mathematical model to analyze data and answer the question: Does the implementation of C. ashmeadi as a biological control method cause a significant decrease in the population of H. vitripennis?
  • Sofya Zaytseva (University of Georgia, United States)
    "Pattern Formation in Intertidal Oyster Reefs"
  • The Eastern oyster population has plummeted over the last century due to unregulated harvesting, effects of pollution and prevalence of disease, making reef restoration of critical importance. While various aspects of reef development have been studied in the past, the importance of water flow and geophysical processes on oyster reef development remains not well understood. This becomes particularly important in reef restoration and can help determine suitable locations and optimal configurations for the construction of artificial reefs. We use drone imagery of an extensive intertidal reef network to investigate the relationships between topography, flow, and reef geometry. This talk will focus on some recent results from our analysis exploring these relationships.
  • Shandelle Henson (Andrews University, United States)
    "Climate Change and Tipping Points for Seabird Colonies in the North American Pacific Northwest"
  • Changes in sea surface temperatures in the Pacific Northwest are associated with changes in reproductive and feeding tactics in colonial seabirds. Warm years in the El Niño–Southern Oscillation are associated with short-term “lifeboat” tactics such as egg cannibalism that are not sustainable over the long term. Mathematical models suggest that prolonged rises in SST can create tipping points that allow colony collapse.

Mathematical modeling of water resources

Organized by: Claudia Mazza Dias (UFFRJ - Universidade Federal Rural do Rio de Janeiro, Brazil), Anna Regina Corbo Costa (Cefet/RJ - Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Brazil), José Carlos Rubianes Silva (Cefet/RJ - Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Brazil), Kymie Karina S Saito (UFFRJ - Universidade Federal Rural do Rio de Janeiro, Brazil), Dayse Haime Pastore (CEFET-RJ)

  • Fernando Momo (Instituto de Ciencias. Universidad Nacional de General Sarmiento, Argentina)
    "How to convince policymakers that uncertainty exists: do mathematical models help or confuse?"
  • Policy makers have two problems when trying to make decisions about ecosystems, especially when these decisions involve aquatic resources: 1) They have problems to visualize the non-linear nature of ecological systems. This is important because the responses of aquatic ecosystems to exploitation or pollution can be abrupt and unpredictable. 2) They tend to think in terms of exact values and accurate predictions. This is serious because when we do not consider uncertainty and variability we do not adequately assess risks. I will show from two examples how these ideas can be corrected using mathematical models and how the results of those models should be adequately communicated to decision makers in order to clarify the concepts instead of confusing them even more.
  • João Frederico da Costa Azevedo Meyer (UNICAMP - Universidade Estadual de Campinas, Brazil)
    "Water quality and environmental and ecological risks"
  • My intention is that of presenting a situation which has been occurring in Brazil in recent years and which seriously affects water quality in hydrographic basins: tailings dams failures and their consequences both in immediate as well as long standing terms to the present and the future of nature and society. I will present the main results in terms of mathematically modeling aspects of dam failures and impact upon waterways undertaken by the Mathematical Engineering subgroup at the State University of Campinas the researching of which is part of a larger effort with two other subgroups: Society and Education, and Geophysical and Biotic Environments which form the Global Effort for Research and Action in Conflicts, Risks and Impacts associated to Tailings Dams (CRIAB).
  • Raquel Figueira (Hubz, Brazil)
    "Populacional Density Model of Limnoperna Fortunei for Três Irmãos Hydroelectric – São Paulo, Brasil"
  • The golden mussel is an invasive species in Brazil which causes great environmental and economic problems, including the displacement of native species, modification of natural habitats and damage to equipments in hydroelectric power plants and water treatment systems. The main objective of this research was to establish a method for the quick quantification of Golden Mussel populations in hydroelectric reservoirs in order to monitor the species and eventually employ control methods to combat this invasion. A hydrodynamic model of the area of the HPP Três Irmãos (São Paulo State) was created using Navier Stokes equations applied to a grid of triangular finite elements. The hydrodynamic model was then combined with a population growth model using a system of partial differential equations. The resulting map of population density clusters of the golden mussel matches field observations and shows the potential of this technique to control and monitor species in a large scale.
  • Renato Nascimento Elias (Civil Engineering Department at Federal University or Rio de Janeiro • PEC/COPPE/UFRJ, Brazil)
    "3D Numerical Modeling of Dambreak Problems using Finite Element Method"
  • Dams to store water, mud and mining sediments represent import civil engineering structures. Due to the scale of such large structures, any accident has severe social and ecconomical impacts in the surrouding areas. The simulation of dam break problems has emerged as an important tool to predict the impact of this kind of accidents. In this work, it is presented EdgeCFD: a numerical tool capable to simulate dam break problems. This tool employs a RB-VMS finite element formulation to simulate 3D incompressible fluid flow of Newtonian or non-Newtonian flows. In order to allows for high fidelity simulations, EdgeCFD is capable to run large scale parallel simulations using distributed and/or shared memory machines and state of art non-linear algorithms. Keywords: Navier-Stokes, Incompressible Fluid Flow, Dambreak, Volume-of-Fluid

Translational effects of trait changes in aquatic ecosystems

Organized by: Hanna Schenk (German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig; Leipzig University, Germany), Michael Raatz (Max Planck Institute for Evolutionary Biology, Germany)

  • Ken H. Andersen (Center for Ocean Life, Natl. Inst. of Aquatic Resources, Technical University of Denmark, Denmark)
    "Using size-spectrum models to address global food security"
  • Our assessments of the biomass, production, and future trajectory of fish communities on a global scale relies on process-based models calibrated to observations. The scarcity of observations in the vast oceanic regions places a large burden on the quality of the process descriptions that underpins model predictions. Here I review a novel class of trait-based “size spectrum” models that simulate fish communities and their response to fishing. Size spectrum models are based around predator-prey interactions between smaller prey and larger predators. The models resolve the growth of individuals from eggs, with a size of around 1 mg, to the size of adults. All physiological processes are parameterized with respect to the size of individuals. Differences between species are represented by the maximum size, which varies from 1 g for small meso-pelagic fish to 100’s of kg for large pelagic predators like tuna. The models are in the form of coupled partial differential-integro equations that can be solved efficiently with standard techniques. I will show examples of how size spectrum models simulates regional fish communities or the global biogeography of fish biomass, and how they are used for strategic fisheries management and climate change projections.
  • Andrea Campos Candela (The Leibniz-Institute of Freshwater Ecology and Inland Fisheries (IGB), Germany)
    "Towards a mechanistic understanding of phenotypic trait changes, adaptive behaviour and life history based on dynamic energy budgets"
  • Understanding phenotypic trait changes in spatial and temporal environmental gradients needs understanding the fitness consequences of phenotypic trait variation. This challenge requires connecting behavioural and physiological traits that mediate survivorship and reproductive success with the environmental context. Mechanistic frameworks such as the Dynamic Energy Budget (DEB) theory linking individual internal state dynamics with immediate changes in environmental conditions offer a new perspective to improve such understanding. Drawing on first bioenergetics principles informed by DEB theory, I present a dynamic state-dependent behavioural and life history model to explore the optimal strategies that maximize fitness in ecological contexts varying in food availability and predation risk. Novel contributions of this framework are manifold: 1) I encourage the use of DEB theory in the adaptive context to meet mortality payoff functions integrating ecological extrinsic risks as predation; and, specifically 2) explore the behavioural processes of energy acquisition and the bioenergetics processes of energy mobilization and energy allocation, that 3) together link emerging optimal phenotypic traits with individual internal and external states. Finally, 4) by assuming state-dependent dynamic trade-offs, DEB primary parameters can be dynamic during ontogeny, which breaks down the fixed rules within DEB while opening an interesting research line for future model developments. Results within the exploratory simulated scenarios support that processes related with energy mobilization and allocation can absorb more of the selective pressure driven by the extrinsic risk of mortality, while the process related with energy acquisition strongly correlates with food. I would like to motivate debate about feasible ways of extending this framework, with a physiological and mechanistic-based perspective, to more complex and meaningful scenarios.
  • Maite Erauskin-Extramiana (AZTI BRTA, Spain)
    "The influence of climate change and fishing pressure in global top predator abundance and body size in the future"
  • Tunas and billfishes are the main large pelagic commercial fished species. Tunas comprised around 5.5 million tonnes and USD 40 billion in 2018, being an economically important contribution to many nations. Tuna stocks are well covered by management assessments which estimate that 13% of the stocks are still overfished and 22% are at intermediate levels. Climate change studies and projections forecast that current global fish catches might decrease by the end of the century. However, there are sparse studies and projection for the higher trophic levels where tunas and billfishes belong. A combined Size-Spectrum and Dynamic Bioclimatic Envelope Model (SS-DBEM) was used to project the effects of climate change and fishing for 19 globally distributed large pelagic fishes under climate change (RCP 2.6 and 8.5) and fishing scenarios (0.8 to 1.2 times Maximum Sustainable Yield, MSY). The results suggest that high trophic level species will be more impacted by climate change than by fishing pressure if kept close to the Maximum Sustainable Yield. Projected impacts trends were more driven by species sizes than by the group they belong to. There are mixed responses of main commercial tuna stocks biomass by RFMOs with projections of decreases up to 43% and increases up to 68% by 2050, whereas some stocks can have higher increases up to 168% by 2100. Furthermore, their size is expected to decrease 15% on average by 2050 and 10% by 2100 except for the yellowfin East Pacific stock. Price and demand are often driven by body size, therefore this can reduce the revenue by the fishing industry due to climate change even in stocks that benefit from an increase of biomass. Industry can adopt adaptation strategies such as increase value of their products through added value processing to increase revenue with the same catches, or reduce fuel consumption and time at sea with higher digitalization and the use of decision support systems to reduce searching time and optimize routes considering environmental conditions, or through certified sustainability actions. Reducing fuel reduction would be also a mitigation measure to climate change since it reduces vessels emissions, i.e. a win-win for industry and the environment.
  • Hanna Schenk (German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig; Leipzig University, Germany)
    "Optimal harvest of evolving fish"
  • A side effect of targeting large fish is a strong selection pressure on a smaller size at maturation. This has resulted in fisheries-induced evolution of earlier maturation in several fish species. Due to life-history trade-offs fish that mature at a younger age also grow more slowly. The fisheries-induced evolution thus reduces the economic benefits for fisheries, especially as large fish are proportionally more valuable than small fish. We include these processes in an economic-ecological-evolutionary demographic fishery model to study economic implications of fisheries-induced evolution and to derive optimised fishing management strategies. Economic benefits of fishing depend on the size structure of catches, as prices depend on the size of the fish caught. Economic costs of fishing depend on the size of the fish population and the gear. We apply the model to the North Sea cod fishery and find that the optimal fishing strategy is sensitive to discounting. Whereas for a low discount rate the optimal strategy is to rebuild a population structure with late maturation and strong growth the optimal strategy for a high discount rate would not attempt to reverse the fisheries-induced evolution and rather continue to fish on the evolved population.

Population Dynamics Across Interacting Networks or Scales

Organized by: Necibe Tuncer (Florida Atlantic University, USA), Hayriye Gulbudak ( University of Louisiana at Lafayette, USA), Cameron Browne (University of Louisiana at Lafayette, USA)
Note: this minisymposia has multiple sessions. The second session is MS20-ECOP.

  • Glenn Webb (Vanderbilt University, USA)
    "A COVID-19 epidemic model predicting the effectiveness of vaccination in the US"
  • A model of a COVID-19 epidemic is used to predict the effectiveness of vaccination in the US. The model incorporates key features of COVID-19 epidemics: asymptomatic and symptomatic infectiousness, reported and unreported cases data, and social measures implemented to decrease infection transmission. The model analyzes the effectiveness of vaccination in terms of vaccination efficiency, vaccination scheduling, and relaxation of social measures that decrease disease transmission. The model demonstrates that the subsiding of the epidemic as vaccination is implemented depends strongly on the scale of relaxation of social measures that reduce disease transmission.
  • Cameron Browne (University of Louisiana at Lafayette, USA)
    "Connecting predator prey dynamics and population genetics in an evolving virus immune network"
  • Integrating population evolution and dynamics offers a promising avenue for understanding rapidly evolving pathogens. For example, during HIV infection, the virus can escape several immune response populations via resistance mutations at distinct epitopes (proteins coded in viral genome), precipitating a dynamic network of interacting virus and immune variants. Understanding the main factors shaping viral resistance pathways and immune dynamics is crucial for designing effective vaccines and immunotherapies. While the virus-immune interactions may be quite complex, I will talk about my recent work to link pathogen population genetics with dynamics theoretically and through data to characterize their evolution. We start with a general differential equation ecosystem model of multiple virus and immune populations, and then prove that different stable and persistent patterns emerge in the virus-immune network dependent on the virus fitness landscape. Next, I will present a collaborative project where the 'eco-evolutionary' modeling framework is connected to genomic and population data. We describe the interaction between several immune cell populations and viral 'quasi-species' sampled from experiments of the simian immunodeficiency virus (SIV)-infected macaque model of HIV infection. The mathematical models can recapitulate the data and shed light on pathogen evolution, along with motivating ongoing work on jointly deciphering the population genetics and dynamics of pathogens and their complex ecosystems.
  • Andrea Pugliese (University of Trento, Italy)
    "mmune memory build-up in models of repeated infections; how does this affect epidemic dynamics?"
  • It is well known that memory cells can help to build a quick immune response in case of a new infection with the same (or similar) pathogen. This is indeed the principle at the basis of vaccination. It is also known that for certain pathogens a single vaccine dose can be insufficient to achieve a complete control of an infection, and that a second dose may be necessary. On the other hand, in several models of virus-immune interactions, the lower is the immune level before an infection, the higher it will be afterwards. This property is an important feature of the immuno-epidemiological models developed recently by Diekmann and co-workers. Recently, Zarnitsyna et al. have proposed a realistic model for immune response to infection by influenza virus that results in a progressive build-up of immune memory. In the talk, I will discuss several simplifications of the model in order to assess which components of the model are essential for its qualitative behaviour. Furthermore I will show how these features can be incorporated in a consistent multi-scale epidemic models, where the susceptible population is stratified through the number of times it has been infected. Strain coexistence is then common, and potential evolutionary consequences are explored.
  • Lauren M Childs (Virginia Tech, USA)
    "Trade-offs in Malaria Population Dynamics Across Scales"
  • Malaria is a disease endemic in areas encompassing over half the world’s population and remains detrimental to the health and livelihood of millions of individuals. Plasmodium parasites, the causative agents of malaria, have a complex life cycle requiring two hosts – a vertebrate, such as a human, and the Anopheles mosquito. During the time in each of these hosts, the population dynamics of the parasite are quite variable in density and stage. In previous work using a stochastic model of malaria population dynamics, we showed how density of parasite stages alter the timing and probability of onward transmission at the mosquito to human interface. Here, we bridge within-host modeling of parasite dynamics in the mosquito and the human to investigate maintenance of parasite diversity at the population level.

Population Dynamics Across Interacting Networks or Scales

Organized by: Necibe Tuncer (Florida Atlantic University, USA), Hayriye Gulbudak ( University of Louisiana at Lafayette, USA), Cameron Browne (University of Louisiana at Lafayette, USA)
Note: this minisymposia has multiple sessions. The second session is MS19-ECOP.

  • Maia Martcheva (University of Florida, USA)
    "A Network Immuno-epidemiological Model of HIV and Opioid Epidemics"
  • We introduce a network immuno-epidemiological model of HIV and opoid epidemics where the jointly affected class is structured by the within-host dynamics. We fit the within-host model to data, collected in monkeys. We compute the reproduction numbers of the HIV and opiod epidemics. We show that the disease-free equilibrium is locally stable if both reproduction numbers are below one, and unstable if at least one of the reproduction numbers is above one. The HIV-only equilibrium exists if the reproduction number of HIV is larger than one. The opioid-use only equilibrium exists if the reproduction number of opioid use is larger than one. The HIV-only equilibrium is locally asymptotically stable if the invasion number of the opioid epidemic is below one and unstable if the invasion number of opoioid epidemic is above one. The opoioid-only equilibrium is locally asymptotically stable if the invasion number of the HIV epidemic is below one and unstable if the invasion number of HIV epidemic is above one. Simulation suggest that larger networks lead to higher reproduction numbers.
  • Stanca M. Ciupe (Virginia Tech, USA)
    "Neutrophil dynamics and their role in disease: a multi-scale investigation"
  • The highly controlled migration of neutrophils toward the site of an infection can be altered when they are challenged with competing external signals, leading to their dysregulation and oscillatory movement. In this talk, I will use mathematical models to evaluate the mechanistic interactions responsible for neutrophil migratory decision-making and to determine molecular and cellular contributions to disease pathogenesis. The results are applicable to sepsis and SARS-CoV-2 infections.
  • Michael Cortez (Florida State University, USA)
    "Using sensitivity analysis to explore the context dependent relationships between host species richness and disease prevalence"
  • In multi-host communities, the dilution effect is the phenomenon wherein focal host infection prevalence (i.e., the fraction of infected individuals in a focal host species) decreases with increases in host species richness. The opposite phenomenon is called an amplification effect. Empirical and theoretical studies show that relationships between host species richness and prevalence are likely to be context dependent, depending on the identity of the host species present in and added to a given community. However, current theory is limited in its ability to identify the context-dependent rules governing host species richness-prevalence relationships. This is due, in part, to modeling studies making different assumptions about the pathogen transmission mechanism, the presence/absence of interspecific interactions between host species, and the characteristics of the host species (e.g., competence and competitive ability). In this talk, I show how sensitivity analysis applied multihost-pathogen models can yield insight into how host characteristics, host density, and the pathogen transmission mechanism affect infection prevalence in a focal host. Specifically, I present an n-host model of an environmentally transmitted pathogen and show that it can unify common epidemiological ODE models for direct and environmental transmission under a single framework via fast-slow dynamical systems theory. I then use local sensitivity analysis applied to endemic equilibrium of the model to analytically derive the relationships between focal host infection prevalence and host densities and model parameters. This identifies how host competence, density, and the pathogen transmission mechanism jointly shape host richness-disease relationships. For example, the strength of interspecific host competition determines whether responses in focal host infection prevalence to increased density of a non-focal host are driven by the characteristics of the non-focal host or other host species in the community. I interpret these results in terms of factors promoting amplification and dilution of disease.
  • Juan B. Gutiérrez (University of Texas at San Antonio, USA)
    "Data, reality, and cognitive dissonance. On modeling what we don’t see with data we don’t have."
  • During the ongoing COVID-19 pandemic, the discrepancy between daily reports of cases and the trajectory of the disease has posed a substantial challenge to modeling efforts. In this talk, we will present the contrast between patient data and daily counts for the City of San Antonio, TX. We will demonstrate that a non-autonomous adjustment to data deficiencies can substantially improve forecasts. We present the extension of this method to multi-strain outbreaks. An exact data correction is possible with detailed patient data and genomic sequencing of the pathogen, which might not be available in all localities. To alleviate this problem, we propose a framework that incorporates information at multiple spatial and temporal scales to estimate the non-autonomous data correction. A derivation of classic quantities (R_o, R_e) is presented for a SEYAR model (Susceptible, Exposed, Symptomatic, Asymptomatic, Recovered) under this framework.

Sub-group contributed talks

ECOP Subgroup Contributed Talks

  • Abdennasser Chekroun University of Tlemcen
    "Traveling waves of a differential-difference diffusive Kermack-McKendrick epidemic model with age-structured protection phase"
  • We consider a general class of diffusive Kermack-McKendrick SIR epidemic models with an age-structured protection phase with limited duration, for example due to vaccination or drugs with temporary immunity. A saturated incidence rate is also considered which is more realistic than the bilinear rate. The characteristics method reduces the model to a coupled system of a reaction-diffusion equation and a continuous difference equation with a time-delay and a nonlocal spatial term caused by individuals moving during their protection phase. We study the existence and non-existence of non-trivial traveling wave solutions. We get almost complete information on the threshold and the minimal wave speed that describes the transition between the existence and non-existence of non-trivial traveling waves that indicate whether the epidemic can spread or not. We discuss how model parameters, such as protection rates, affect the minimal wave speed. The difficulty of our model is to combine a reaction-diffusion system with a continuous difference equation. We deal with our problem mainly by using Schauder's fixed point theorem. More precisely, we reduce the problem of the existence of non-trivial traveling wave solutions to the existence of an admissible pair of upper and lower solutions.
  • Laura Wadkin Newcastle University
    "Mathematical modelling of the spread of tree disease through forests"
  • The past decades have seen a dramatic rise in the number of emerging diseases of plants and trees across the world. These diseases threaten the survival of native trees and have huge social, economic, and environmental impacts. The Department for Environmental, Food and Rural Affairs have highlighted the importance of mathematical modelling in developing robust management policies to minimise the impacts of these threats. We are working to mathematically model the spread of tree diseases, using a combination of agent-based models, partial differential equations, and statistical inference techniques. The aim is to combine local lattice modelling approaches with global continuum models to perform systemic modelling and parameter inference of past and present tree epidemics in the mainland UK. The results can be used to deepen our understanding of the process of tree disease spread and crucially, explore intervention and management strategies to find the best methods of stopping the disease spread.
  • Laura Jimenez University of Hawaii
    "Statistical models to estimate the fundamental niche of a species using occurrence data"
  • The fundamental niche of a species is the set of environmental conditions that allow the species to survive in the absence of biotic interactions and dispersal limitations. Estimating the center (i.e., the optimal environmental conditions for the species) and extent of the fundamental niche is of great importance when the fitted models are used to predict the effects of climate change on the geographic distribution of the species. However, most of the existing approaches to estimate niches use occurrence samples that are biased, and often fit complex models that are not a biologically realistic representation of the fundamental niche' border. Occurrence samples come from the realized niche (a subset of the fundamental niche that includes biotic interactions and dispersal limitations) and may not represent the full environmental potentiality of a species; samples may be biased towards well-represented regions of niche space. I will present two new models to estimate the fundamental niche of a species that use occurrence data and assume a simple, biologically realistic shape for the fundamental niche. I will show how to incorporate known tolerance ranges for the species into the models and how to account for environmental biases in the samples.
  • Lee Altenberg University of Hawai`i at Mānoa
    "Going Against the Flow: Selection for Counter-Current Dispersal in Gyres"
  • Much attention has been given to the 'drift paradox' for river organisms: how populations in streams can maintain themselves despite being constantly swept downstream. Here we shall consider a different situation: where circular currents produce time-irreversible dispersal dynamics. We will see that when there is environmentally produced cyclical dispersal among habitats with spatial variability in quality, organisms that disperse against the cyclical flows will have an aggregate population growth advantage. These results are obtained by applying some classical results from spectral theory, including theorems by Karlin and Levinger. Temporal variation in habitat quality or dispersal is not addressed. Open problems for further work include the degree to which these result extend to dispersal that is only partially or approximately counter-current. The widespread occurrence of positive rheotaxis among ocean organisms may conceivably be a manifestation of these selection dynamics.

ECOP Subgroup Contributed Talks

  • William (Bill) Sherwin EERC, BEES. UNSW Sydney Australia
    "Can Bray-Curtis differentiation be meaningful in Molecular Ecology?"
  • A popular measure of differentiation in biodiversity is the Bray Curtis index of dissimilarity. It has recently also been proposed for use in molecular ecology. However, this measure currently cannot be predicted under specified conditions of population size, dispersal and speciation or mutation. Here I show forecasts for Bray-Curtis for two-variant systems such as single-nucleotide polymorphisms (SNPs) (or two species ecosystems). These are derived from well-known equations for population genetics, and shown to be appropriate by simulation. Thus, Bray-Curtis can now be used for assessment of differentiation, in order to understand natural or artificial processes, in addition to other measures such as Morisita-Horn/D_EST, G_ST and Shannon Mutual Information/Shannon Differentiation.
  • Tanveen Kaur Randhawa Indian Institute of Science, Bangalore
    "Role of trait variation in the dynamics of savanna-forest bistable system"
  • Over the last decade, several studies have discussed the importance of individual and trait variation in natural populations. However, trait variations are typically ignored in many theoretical studies of population dynamics, including those of bistable systems. In this talk, I present an analysis of a mean-field model of savanna-forest bistable dynamics -- modified from Staver and Levin, 2012, Am Nat to incorporate trait variation. Model parameters usually depend on trait values and distribution and are coupled to the state-variable in two ways: (i) as a coefficient to a state-variable or (ii) as a nonlinear function in which the trait variable and the state-variable cannot be separated as a product. Our model predicts that, in the first case, trait variation does not qualitatively affect the dynamics of the system, whereas, in the second case, it may change the dynamics. Within our model, we show that trait variation in the parameter sapling-to-adult recruitment rate affects bistability. We find that an increase in this trait variation shrinks the bistability region, or conversely, low trait variation allows the coexistence of the two stable states. Thus, we argue trait variation has important implications for the stability of ecosystems.
  • Ryo Oizumi National Institute of Population and Social Security Research
    "Sensitivity Analysis of The Declining Population: Effects of Prefecture Specific Fertility and Interregional Migration"
  • Interregional migration, as well as fertility and mortality, are essential ingredients of population dynamics. The general Leslie matrix is an essential tool in expressing a multi-regional population model and has been studied in demography since the 1970s. On the other hand, to study each effect of matrix entries on the eigenvalue, sensitivity analysis has also developed in ecology since the same age. Those two methodologies associate with each other via the eigensystem of the matrix model. This study reconstructs the eigensystem in the general Leslie matrix model from the perspective of the statistics for interregional migration pathways over a generation. Using this reconstructed eigensystem, we provide the sensitivity analysis consisting of the statistics of the interregional pathways. As an application of our framework, we use the latest data in Japan's declining birthrate for more than 40 years and clarify the interregional migration and the regional fertility rate that most influence population decline.
  • Nurdan Cabukoglu University of Wolverhampton
    "Kinesis movement impact on travelling waves"
  • In this study, we aim to introduce new models of purposeful kinesis with diffusion coefficient dependent on fitness. New models include one additional parameter, intensity of kinesis, and may be considered as the minimal models of purposeful kinesis. It is demonstrated how kinesis could be beneficial for assimilation of patches of food or periodic fluctuations. Nevertheless, kinesis is not always beneficial in the long-term and spatially global perspective: for example, for species with the Allee effect it can delay invasion and spreading. We will also present the impact of purposeful kinesis on travelling waves. Both monotonic and non-monotonic (Allee effect) dependence of the reproduction coefficient on the population density will be presented. The possible benefits of the purposeful kinesis are demonstrated: with the higher diffusion, while the population without kinesis ends up with extinction, with kinesis stays alive and has the travelling wave behaviour. While the kinesis of the prey population is decreasing, the wave amplitude gets smaller. On the other hand, for the lower kinesis of predators, they have a sharp increase.

ECOP Subgroup Contributed Talks

  • Eduardo Muñoz-Hernández Complutense University of Madrid
    "Minimal complexity of subharmonics in two classes of periodic Volterra predator-prey models"
  • This contribution analyzes the existence and minimal complexity of positive subharmonics of arbitrary order in the planar periodic Volterra predator-prey model. If the support of the birth rate of the prey intersects the support of the death rate of the predator, then the existence of positive subharmonics can be derived with a refinement of the Poincaré-Birkhoff theorem. However, in the “degenerate” case when these supports do not intersect, then, the last Poincaré theorem can fails. Still in these degenerate situations, some local and global bifurcations techniques combined with a refinement of the Poincaré-Birkhoff theorem provide us with the existence of positive subharmonics of arbitrary order.
  • Thomas Woolley Cardiff University
    "Locating bat roosts through the coupling of motion modelling and microphone data"
  • Bats play an important role in the UK ecosystem, but their populations are declining due to many reasons, including loss of habitat from human activity. As a result, ecological surveys are legally required when undertaking large-scale building work to locate breeding, or resting places (roosts). However, locating roosts is generally a difficult task, requiring many hours of manual searching. In collaboration with ecological experts we propose a novel approach for modelling bat motion dynamics and use it to predict roost locations using data from static acoustic detectors. Specifically, radio tracking studies of Greater Horseshoe bats demonstrate that bat movement can be split into two phases: dispersion and return. Dispersion is easily understood and can be modelled as simple random motion. The return phase is much more complex, as it requires intelligent directed motion and results in all agents returning home in a stereotypical manner. Critically, combining reaction-diffusion theory and domain shrinking we deterministically and stochastically model a ``leap-frogging'' motion, which fits favourably with the observed tracking data.
  • Christopher Kribs University of Texas at Arlington
    "Competition between obligate & facultative scavengers & infection: vulture-jackal-anthrax dynamics in Etosha National Park"
  • Different species of scavengers may compete for the same food in an ecosystem. This case study considers the competition between jackals, vultures and anthrax outbreaks in Etosha National Park in Namibia. While jackals are facultative scavengers, able to hunt for food if necessary, vultures are obligate scavengers wholly dependent on carcasses of animals like zebras for persistence. This competition is further affected by outbreaks of infections such as anthrax, which temporarily increase the number of carcasses but lower the zebra population, acting in some ways as a third competitor. We use a dynamical system to model the interplay between competition dynamics and infection dynamics, and how it is affected by the nature of the competition: indirect (exploitative) or direct (interference). A bifurcation analysis using reproduction numbers shows how vultures' survival may depend on their direct competitive edge in reaching carcasses faster than jackals, and how the infection and the scavengers complicate each other's persistence.
  • Lukas Eigentler University of Dundee
    "Spatial dynamics underpin competitive interactions within bacterial biofilms"
  • Bacterial biofilms are surface-adhering multicellular collectives embedded in a self-produced extracellular matrix. They can have both beneficial and detrimental effects on the surrounding environment. For example, the soil-dwelling bacterium Bacillus subtilis forms biofilms on the roots of plants, where some strains promote the growth of plants. However, to fully realise their potential as biocontrol agents, strains need to be capable of coexisting with (or outcompeting) other biofilm-forming strains in the rhizosphere. Many antagonistic interaction mechanisms require spatial colocation of competing strains. In this talk, we discuss the crucial role of spatial dynamics on competitive interactions within biofilms using an interdisciplinary approach. Mathematical modelling using a continuum approach predicts that the density of biofilm founder cells has a profound impact on competitive outcome and that randomly allocated cell locations in the biofilm inoculum significantly affect competitive dynamics. We define a predictor for competitive outcome that quantifies a strain's “access to free space” in the initial condition and show that a favourable initial cell placement can lead to domination of a weaker strain (in the sense of interactions of well-mixed populations) in the biofilm. Finally, we present validation of model hypotheses through biofilm assays using strains of B. subtilis.

ECOP Subgroup Contributed Talks

  • Arwa Baabdulla University of Alberta
    "Homogenization of a Reaction Diffusion Equation can Explain Influenza A Virus Load Data"
  • We study the influence of spatial heterogeneity on the antiviral activity of mouse embryonic fibroblasts (MEF) infected with influenza A. MEF of type Ube1L^-/- are composed of two distinct sub-populations, the strong type that sustains a strong viral infection and the weak type, sustaining a weak viral load. These show different antiviral activity. When arranged in a checker board pattern, the total viral load significantly depends on the spatial arrangement of the cells. We explain this observation by using a reaction diffusion model and we show that mathematical homogenization can explain the observed inhomogeneities.
  • Emil Frølich Ph.D. Student at Technical University of Denmark
    "A new approach to multispecies population games in continuous space and time"
  • Population dynamics are generally modelled without taking behaviour into account. This in spite of the largest daily feeding times for predators, namely at dawn and dusk, being driven by behaviour. This is usually explained by prey avoiding visual predators, and visual predators seeking to find prey. We develop a game-theoretical model of predator-prey interactions in continuous time and space, finding the Nash equilibrium at every instant. By using the general resolution of polymatrix games, and an efficient discretization, we solve the spatial game nearly instantaneously. Our approach allows a unified model for the slow time-scale of population dynamics, and the fast time-scale of behaviour. We use the diel vertical migration as a case, examining emergent phenomena from the introduction of the fast dynamics. On the behavioural time-scale, we see the emergence of a deep scattering layer from the game dynamics. On the longer time-scale of population dynamics, the introduction of optimal behaviour has a strong stabilizing effect. In a seasonal environment, we observe a change in daily migration patterns throughout the seasons, driven by changes in population and light levels. The framework we propose can easily be adapted to population games in inhomogeneous terrestrial environments, and more complex food-webs.
  • Abdel Halloway University of Illinois -- Urbana Champaign
    "Unstable Population Dynamics in Obligate Cooperators"
  • Cooperation significantly impacts a species' population dynamics as individuals choose with whom to associate based upon fitness opportunities. Models of these dynamics typically assume that individuals can freely disperse between groups which works well for facultative co-operators like flocking birds, schooling fish, and swarming locusts. However, obligate co-operators like canids, cetaceans, and primates may be more discerning and selective over their associations, rejecting new members and even removing current members, thereby limiting dispersal. Incorporating such aspects into population models may better reflect the population dynamics of obligately cooperative species. We created and analyzed a model of the population dynamics of obligate co-operators where a behavioral game determines within-group population dynamics that then spill over into between-group dynamics. We identify a fundamental mismatch between the stability of the behavioral dynamics and the stability of the population dynamics; when one is stable, the other is not. Our results suggest that group turnover may be inherent to the population dynamics of obligate co-operators. If our model is true. the instability arises from a non-chaotic deterministic process, and such dynamics should be predictable and testable. Furthermore, we identify four key features that impact the conservation of obligate cooperative species and make recommendations on such.
  • Peter Thompson University of Alberta Department of Biological Sciences
    "Using movement models to identify spatial memory in animals"
  • Spatial memory, the storage and recovery of the locations of important landmarks on the landscape, plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in their environments allows for an increased understanding of animal cognition. We developed a model that accounts for the memory of seasonal or ephemeral qualities of an animal's environment. The model builds on existing research to test hypotheses about the mechanisms driving animal movement behavior. Our model allows for comparison of four different hypotheses that detail the important of resource selection and spatial memory in animal movement. We used simulation analyses to verify that our model appropriately identifies memory and resource selection in simulated movement data, and these analyses have been informative about the data required to use the model properly. This model has potential to identify cognitive mechanisms for memory in a variety of ecological systems where periodic or seasonal revisitation patterns within a home range may take place.

ECOP Subgroup Contributed Talks

  • Maksim Mazuryn Technical University of Denmark
    "Mean Field Game Model for Diel Vertical Migration"
  • Diel vertical migration is the largest daily movement of marine species where animals remain in deep, dark water during daylight hours to avoid visual predators and migrate to upper levels at dusk to feed. The migration of each organism can be rationalized as a trade-off between growth and survival with strategies as spatial distributions of the populations. The dynamics driving vertical migration have broad implications for fluxes through the food-web predator-pray interactions; for vertical transport of carbon in ocean with implications for global climate.I will present ongoing work on a framework for expressing diel vertical migration as a game in terms of partial differential equations. In the base model setup we consider a population of animals distributed in the water column. It is assumed that each animal moves optimally, seeking regions with high growth rate and small mortality, avoiding regions with high population density. The Nash equilibrium for this mean field game is characterized by a system of partial differential equations, which governs the population distribution and migration velocities of animals. I will talk about extension of the base model with added diffusion to cover deep water case.
  • Jasper Croll IBED, University of Amsterdam
    "The effect of growth plasticity on the population dynamics of structured populations"
  • Population structure is an important aspect of natural populations and has a large impact on population dynamics. In theoretical models, populations are generally structured by age or size. As long as individuals follow a fixed growth curve, age- and size structured models are virtually similar, but if individual growth rates become plastic (e.g. depend on the environment), age- and size structured models start to differ. In nature, individuals of various species differ strongly in the plasticity of their somatic growth rate as well. To explore the effect of plasticity in somatic growth we formulated a physiologically structured population model in which growth plasticity can be varied from entirely plastic to entirely non-plastic. The life history rates in this model were based on a Dynamic energy budget model to ensure closed individual energy dynamics. From the analysis of our model it became clear that changes in growth plasticity provoke a complex trade-off between energy allocation to somatic growth and reproduction. This tradeoff results in two distinct parameter regions which differ in their ecological and evolutionary dynamics. These results can gain insight in the different ways a population can respond to human impact and the different ways population structure can be modelled.
  • Subekshya Bidari University of Colorado Boulder
    "Evidence accumulation models of social foraging"
  • Foraging is often modeled as a sequence of patch-leaving decisions. An animal enters a patch of food, harvests resources, and then decides when to leave and search for other patches. Foraging strategies shape experimental observables like patch residence time, inter-patch travel time, as well as rate of energy intake. Models of foraging as an evidence accumulation process accounts for learning processes involved in determining resource availability within and across patches by associating evidence for leaving a patch with a deterministic drift term and the stochasticity of food encounters and memory with diffusive noise (Davidson & El Hady A, 2019). My work extends these individual evidence accumulation models to consider patch foraging decisions of multi-agent systems sharing social information.
  • Samuel Dijoux Dept. of Ecosystem Biology, Faculty of Science, University of South Bohemia, České Budejovice, Czech Republic
    "Invasions in simple food webs along environmental and size structure gradients: insights on exploitative competition."
  • 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.

ECOP Subgroup Contributed Talks

  • Nazanin Zaker University of Ottawa
    "The effect landscape fragmentation on Turing pattern formation"
  • Many biological populations reside in increasingly fragmented landscapes, which arise from human activities and natural causes. Landscape characteristics may change abruptly in space and create sharp transitions (interfaces) in landscape quality. We study how interactions between individuals and populations in a predator-prey system are affected by habitat fragmentation.We model population dynamics with a predator-prey system in a coupled ecological reaction-diffusion equation in a homogeneous landscape to study Turing patterns that emerge from diffusion driven instability (DDI). We derive the DDI conditions and then we use a finite difference scheme method to numerically explore the general conditions using the May model and we present numerical simulations to illustrate our results. Then we extend our studies on Turing pattern formation by considering a predator-prey system on an infinite patchy periodic landscape. The movement between patches is incorporated into the interface conditions that link the reaction-diffusion system between patches. We use a homogenization technique to obtain an analytically tractable approximate model and determine Turing pattern formation conditions. We use numerical simulation to present our results from this approximation method for this model to explore how differential movement and habitat preference of both species in this model, prey and predator, affect DDI.
  • Wencel Valega-Mackenzie University of Tennessee Knoxville
    "Resource Allocation in a PDE Ecosystem Model"
  • The importance of habitat heterogeneity on a diffusing population is crucial to understand population dynamics. In this talk, we formulate a reaction-diffusion population model to study the effect of resource allocation in an ecosystem with resources having their own dynamics in space and time. This approach is more realistic than simply assuming the resource level is not changing as the population changes. Furthermore, we solve an optimal control problem of our ecosystem model to maximize the abundance of a single species while minimizing the cost of inflow resource allocation.
  • Lucas dos Anjos National Laboratory for Scientific Computing
    "Rapid spread agents may impair biological control in a tritrophic food web with intraguild predation"
  • The augmentation of natural enemies against agricultural pests is a common tactic undertaken to minimize crop damage without the use of chemical pesticides. Failures of this strategy may result from (i) Allee effects acting on biological control agent; (ii) trophic interactions between the released control agent and native species in the local ecosystem; (iii) excessively rapid spreading agents. To investigate the interplay of these mechanisms in pest biocontrol efficiency in the context of intraguild predation (IGP), we develop a one-dimensional dynamical model of a spatial, tritrophic food web with intraguild predation. We show that the agent's diffusivity (i.e., agent's dispersal speed), and intraguild predator's addition of alternative food sources are important factors in determining the success or failure of pest biocontrol. These results are obtained for spatially explicit models by considering the speed of dispersal of the control agent and the pest. Feedback from theoretical models as the one constructed in this work can provide useful guidelines for practitioners in biological control.
  • Shadi Sadat Esmaeili-Wellman University of California Davis
    "Noise-Induced vs. Noisy Intrinsic Oscillations in Ecological Systems"
  • Cyclic and oscillatory behaviors are ubiquitous in ecological systems. These oscillations can be noise-induced or due to intrinsic ecological interactions. Due to the stochastic nature of ecological systems, these types of oscillations appear to be very similar and distinguishing between them using ecological data is a topic of active research. Intrinsic oscillations, unlike noise-induced oscillations, are known to be readily synchronized by local coupling. We propose that spatial patterns in spatially extended systems may contain indirect information about whether cycles are noise-induced or intrinsic. We explore this idea using an ecological model with a period-doubling route to chaos, comparing noise-induced cycles in the stable regime to intrinsic oscillations in the 2-cycle regime, on a lattice with nearest neighbor coupling. Such models implemented on the lattice undergoes a second order phase transition from disordered to synchrony. Our results show that although noise-induced and intrinsic oscillations are effectively indistinguishable in the disordered state, the onset of synchrony allows us to differentiate between these two causes of cycles, across a range of spatial scales of observation.

ECOP Subgroup Contributed Talks

  • Prince Harvim University of Ottawa
    "Transmission Dynamics and Control Mechanisms of Vector-Borne Diseases with Active and Passive Movements Between Urban and Satellite Cities"
  • We formulate a metapopulation model to investigate the role of active and passive mobility on the spread of an epidemic between an urban center connected to a satellite city. The epidemic disease considered is transmitted via both sexual and vector mode (eg Zika virus). The basic reproduction number of the disease is explicitly determined as a combination of sexual and vector-borne transmission parameters. The sensitivity analysis reveals that the disease is primarily transmitted via the vector-borne mode, rather than via sexual transmission, and that sexual transmission by itself may not initiate or sustain an outbreak. Furthermore, increasing the mobility of the population from urban center to the satellite city leads to an increase in the basic reproduction number of the satellite city but a decrease in the basic reproduction number in the urban center. We explore the potential effects of optimal control strategies relying upon several distinct restrictions on population movement. We find that although travel restrictions from the urban center to the satellite city may reduce the prevalence of the disease in the satellite city, significant control measures targeting the densely populated cities are required in order to eradicate the disease in the entire region.
  • Qianying Lin University of Michigan, Ann Arbor
    "Viral Phylodynamics and A Class of Markov Genealogy Processes"
  • Phylodynamic studies aim to extract information on the population process of pathogens from genome sequences. In this talk, I focus on the relationship between genealogies or phylogenies reconstructed from sampled virus genomes and the population processes that generate them. I show how the problem is naturally formulated in terms of a class of interrelated Markov processes that are built on the stochastic dynamics of births and deaths in the population. For interesting transmission models, the exact likelihood is intractable, but I show how to construct an efficient sequential Monte Carlo algorithm to estimate it with high accuracy.
  • Sipkaduwa Arachchige Sashika Sureni Wickramasooriya Clarkson University
    "Biological Control via Alternative Food to Predator"
  • Biological control is a means by which pest/invasive populations are kept in check by the use ofnatural enemies of the pest, or perhaps even parasites, pathogens or a combination thereof. The classic work ofSrinivasu et. al. demonstrates how such a process can be facilitated, by providing additional food to an introducedpredator to control a target pest. A critical assumption in the literature is that the additional food is constant.Theoretical studies carried out previously in this direction indicate that incorporating mutual interference betweenpredators can stabilize the system. In this work, Beddington–DeAngelis type functional response has been used tomodel the mutual interference between predators. The conditions for eradication of pest is derived and the mainconcern is to determine whether the model exhibit different bifurcation. Various biological implications of ourmathematical results are drawn in conclusion.

ECOP Subgroup Contributed Talks

  • Eduardo Colombo Princeton Univeristy
    "Taxis-induced mesoscale patchiness in plankton communities"
  • A fundamental problem in ecology is how individual-level behavior affects emergent macro-ecological patterns. In marine ecosystems, this issue is intimately related to the interaction between physical and biological forces. For example, while being advected by the turbulent ocean, plankton can actively move in search for resources, establishing a tug-of-war between behavior and turbulence. The spatial structures that emerge from this interplay, especially at small scales, are key to community diversity and stability. To further the understanding about this issue, we developed an agent-based model that keeps track of a grazer-resource community advected by a turbulent flow. Our model accounts for this flow by using the “seeded-eddy” model to generate a velocity vector field that mimics the main hydrodynamic signatures of turbulence. The ecological dynamics include reproduction, grazing, natural mortality, as well as grazer capabilities of swimming and sensing resources' hydrodynamic and chemical cues. We observe that, as the grazer shifts from a purely planktonic to an active behavior, mesoscale patchiness and a new phase portrait for the population dynamics emerge. In detail, we investigate how the grazer swimming velocity affects these outcomes.
  • Paulo Amorim Federal University of Rio de Janeiro
    "Predator-prey models with hunger structure"
  • We present, analyse and simulate a model for predator-prey interaction structured by hunger. The model consists of a nonlocal transport equation for the predator, coupled to an ordinary differential equation for the prey. We deduce a system of 3 ODEs for integral quantities of the transport equation, which generalises some classical Lotka-Volterra systems. By taking an asymptotic regime of fast hunger variation, we find that this system provides new interpretations and derivations of several variations of the classical Lotka-Volterra system, including the Holling-type functional responses. We next establish a well-posedness result for the nonlocal transport equation. Finally, we show that in the basin of attraction of the nontrivial equilibrium, the asymptotic behaviour of the original coupled PDE-ODE system is completely described by solutions of the ODE system.
  • Anna Sisk University of Tennessee
    "Linking Immuno-Epidemiology Principles to Violence"
  • Societies have always struggled with violence, but recently there has been a push to understand violence as a disease and public health issue. This idea has unified professionals in medicine, epidemiology, and psychology with a goal to end violence and help heal those exposed to it. Recently, analogies have been made between community-level infectious disease epidemiology and how violence spreads within a community. Experts in public health and medicine suggest an epidemiological framework could be used to study violence. Since mathematical modeling plays an important role in epidemiology and community level organizations have previously shown success in addressing violence using disease mitigating-like techniques, we see that mathematical modeling could be useful tool in violence prevention. In this talk I will expand on the analogy of violence as an infectious disease and show how mathematical epidemiology is a useful framework for understanding the dynamics of violence. Then we will examine a susceptible-exposed-infected mathematical model for violence spread in a community and explore its usefulness by looking at some example numerical simulations. To end we will explore some of the primary insight these simulations offer on the effectiveness of different potential violence prevention strategies that have been considered for deployment.
  • Adam Lampert Arizona State University, Tempe, AZ, USA
    "Combining multiple tactics over time for cost-effective eradication of invading insect populations"
  • Because of the profound ecological and economic impacts of many non-native insect species, early detection and eradication of newly founded, isolated populations is a high priority for preventing damages. Though successful eradication is often challenging, the effectiveness of several treatment methods/tactics is enhanced by the existence of Allee dynamics in target populations. Historically, successful eradication has often relied on the application of several tactics. We ask how to combine three treatment tactics in the most cost-effective manner, either simultaneously or sequentially in a multiple-annum process. We construct an optimal-control model that describes the population dynamics of the invading insect population and how it is affected by three types of treatments: pesticide cation, mating disruption, and sterile male release. Then, we use stochastic programming to find the optimal treatment over time. We show that each of the three tactics is most efficient across a specific range of population densities. Furthermore, we show that mating disruption and sterile male release inhibit the efficiency of each other, and therefore, they should not be used simultaneously. However, since each tactic is effective at different population densities, different combinations of tactics should be applied sequentially through time when a multiple-annum eradication program is needed.

Sub-group poster presentations

ECOP(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.