The Study of Diffusive Dispersal in Population Dynamics

Tuesday, June 15 at 05:45pm (PDT)
Wednesday, June 16 at 01:45am (BST)
Wednesday, June 16 09:45am (KST)

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

Rachidi Salako

(University of Nevada at LasVegas, United States)
"Study of a diffusive multiple-strains epidemic model"
Infectious diseases are one of the leading causes of many deaths around the world. As a result, health officials and the World Health Organization have devoted several resources to educate populations on safety measures which prevent the spread of infectious diseases. Hence restricting population’s movement has been widely used in an effort to limit the outbreak of an infectious disease. In this talk, we will study a multiple-strains PDE infectious disease epidemic model and discuss how population movement can affect the dynamics of the disease.

Kurt Anderson

(Department of Evolution, Ecology, and Organismal Biology, University of California, Riverside, United States)
"Body size dependent dispersal influences stability in heterogeneous metacommunities"
Body size affects key biological processes across the tree of life, with particular importance for food web dynamics and stability. Traits influencing movement capabilities depend strongly on body size, yet the effects of allometrically-structured dispersal on food web stability are less well understood than other demographic processes. Here we study the stability properties of spatially-arranged model food webs in which larger bodied species occupy higher trophic positions, while species' body sizes also determine the rates at which they traverse spatial networks of heterogeneous habitat patches. Our analysis shows an apparent stabilizing effect of positive dispersal rate scaling with body size compared to negative scaling relationships or uniform dispersal. However, as the global coupling strength among patches increases, the benefits of positive body size-dispersal scaling disappear. A permutational analysis shows that breaking allometric dispersal hierarchies while preserving dispersal rate distributions rarely alters qualitative aspects of metacommunity stability. Taken together, these results suggest that the oft-predicted stabilizing effects of large mobile predators may, for some dimensions of ecological stability, be attributed to increased patch coupling per se, and not necessarily coupling by top trophic levels in particular.

Harunori Monobe

(Okayama University, Japan)
"Singular limit of a mathematical model related to controlling invasive alien species"
In this talk, we suppose simple PDE models related to controlling invasive alien species. Also we consider the singular limit of the PDE and show that solutions of the PDE problem converge to that of free boundary problems called Fisher-Stefan problem.

King-Yeung Lam

(Department of Mathematics, The Ohio State University, United States)
"Defining the Ideal Free Distribution in Spatio-temporally Heterogeneous Environments."
A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing for the effects of crowding. In this paper, we extend the idea of individual fitness associated with a specific location in space to account for the full path that an individual organism takes in space and time over a periodic cycle, and extend the mathematical formulation of an ideal free distribution to general time periodic environments. We find that, as in many other cases, populations using dispersal strategies that can produce a generalized ideal free distribution have a competitive advantage relative to populations using strategies that do not produce an ideal free distribution. A sharp criterion on the environmental functions is found to be necessary and sufficient for such ideal free distribution to be feasible. In the case the criterion is met, we showed that there exist dispersal strategies that can be identified as producing a time-periodic version of an ideal free distribution, and such strategies are evolutionarily steady and are neighborhood invaders from the viewpoint of adaptive dynamics.

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Virtual conference of the Society for Mathematical Biology, 2021.