The Study of Diffusive Dispersal in Population Dynamics

Tuesday, June 15 at 11:30am (PDT)
Tuesday, June 15 at 07:30pm (BST)
Wednesday, June 16 03:30am (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS08" time block.
Note: this minisymposia has multiple sessions. The second session is MS09-EVOP (click here). The third session is MS10-EVOP (click here).

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Chiu-Yen Kao (Claremont McKenna College, United States), Bo Zhang (Oklahoma State University, United States)


The study of diffusive dispersal plays an important role in population dynamics, especially under the changing environment and anthropogenic disturbance. Recently, there are many studies which explore the effect of diffusive dispersal in different aspects. These include mathematical modeling, analytical and numerical techniques, and experimental studies. This mini-symposium brings together mathematicians and biologists to share their diverse perspectives from theoretical, numerical, and experimental study in diffusive dispersal and their related optimization problems. Mathematicians will introduce the new theories they have developed in recent years while biologists and epidemiologists will show how to apply these theories to solving real problems. Applications to optimization problems in translational sciences such as invasion control, population management, optimal chemotherapy will be discussed. This minisymposium will provide a forum for recent scientific developments, discussions, exchange ideas, and open problems. Topics will be discussed include but not limited to the following: * the difference between homogeneous and heterogeneous environments, * the effects of population movement on disease spread and control, * the diffusive competition network system for multiple species, * concentration and fragmentation of resources in spatial ecology, * the optimal allocation of resources to maximize the total population size.

Suzanne Lenhart

(University of Tennessee, United States)
"Optimal control for management of an invasive population model with diffusion in a river"
Invasive species in rivers may be managed by changing flow rates. Using a partial differential equation model with diffusion representing an invasive population in a river, we consider optimal control of the time-varying water discharge rate to keep the population downstream. We will present some numerical results with varying parameters to illustrate the movement of the invasive population.

Idriss Mazari

(Institute of Analysis and Scientific Computing, TU Wien, Austria)
"Fragmenting and concentrating resources to optimise the total population size: a qualitative analysis"
In this talk, we investigate the optimal way to spread resources inside a domain in order to maximise the total population size. More specifically, we will explain why, when the individuals disperse quickly, it is much better to concentrate resources while, when they disperse slowly, it is more relevant to scatter the resources throughout the domain. The talk will mostly be descriptive, and is based on collaborations with G. Nadin, Y. Privat and D. Ruiz-Balet.

Yun Kang

(Arizona State University, United States)
"Dynamics of a Diffusion Reaction Prey-Predator Model with Delay in Prey: Effects of Delay and Spatial Components"
We study the complex dynamics of a Monod-Haldane-type predator-prey interaction model that incorporates: (1) A constant time delay in the prey growth; and (2) diffusion in both prey and predator. We provide the rigorous results of our system including the asymptotic stability of a positive equilibrium; Hopf bifurcation; and the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. We also perform numerical simulations on the effects of diffusion or/and delay when the corresponding ODE model has either a unique interior equilibrium with two interior attractors or two interior equilibria. Our theoretical and numerical results show that diffusion can either stabilize or destabilize the system; large delay could destabilize the system; and the combination of diffusion and delay could intensify the instability of the system. Moreover, when the corresponding ODE system has two interior equilibria, diffusion or time delay in prey or both could lead to the extinction of predator. Our results may provide us useful biological insights on population managements for prey-predator interaction systems.

Noelle Beckman

(Biology Department & Ecology Center, Utah State University, United States)
"Population persistence of plants under global change"
Climate change and habitat loss are two of the primary causes of global biodiversity loss. Habitats gradually become unsuitable as temperature, rainfall, and related climatic variables change. In addition to climate change, 75% of the land surface around the world has been converted by humans. As habitats shift, species must adapt to the new conditions, move to stay within their suitable habitat, or die. We examine the global distribution of species’ vulnerabilities to climate change and habitat loss using integrodifference equations. With information on demography and dispersal, we can quantify a population’s spreading speed -- the ability of a population to shift its range -- and its critical patch size – the size of habitat where population growth due to reproduction balances population loss through dispersal. We analyze the distributions of spreading speeds and critical patch sizes across a defined set of species within a system (e.g., community or taxonomic group). We use a range of distributions for population growth rates and dispersal. We analyzed the distributions for spreading speeds and critical patch sizes when dispersal variance and the geometric growth rates are independent and either fixed or distributed according to an exponential, gamma, modified gamma, or log-normal. We can use these distributions to estimate the proportion of species that can shift their ranges in response to climate change or persist based on a minimum critical patch size. This approach allows us to predict responses to environmental change across a broad range of species for which data may be lacking, and this is particularly important for developing indicators of biodiversity loss and planning of remedial actions.

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Virtual conference of the Society for Mathematical Biology, 2021.