The Study of Diffusive Dispersal in Population Dynamics

Tuesday, June 15 at 07:45pm (PDT)
Wednesday, June 16 at 03:45am (BST)
Wednesday, June 16 11:45am (KST)

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

Seyyed Abbas Mohammadi

(Yasouj University, Iran)
"Optimal Chemotherapy for Brain Tumor Growth in a Reaction-Diffusion Model"
We address the question of determining optimal chemotherapy strategies to prevent the growth of brain tumor population. To do so, we consider a reaction-diffusion model which describes the diffusion and proliferation of tumor cells and a minimization problem corresponding to it. It is established that the optimization problem admits a solution and we obtain a necessary condition for the minimizer . In a specific case, the optimizer is calculated explicitly, and we prove that it is unique. Then, a gradient-based efficient numerical algorithm is developed in order to determine the optimizer. Our results suggest a bang-bang chemotherapy strategy in a cycle which starts at the maximum dose and terminates with a rest period. Numerical simulations based upon our algorithm on a real brain image show that this is in line with the maximum tolerated dose (MTD), a standard chemotherapy protocol.

Daozhou Gao

(Shanghai Normal University, China)
"Effects of asymmetric dispersal on total biomass in a two-patch logistic model"
The impact of animal dispersal on the total population abundance is one of the core issues in theoretical and applied ecology. In this talk, for the two-patch logistic model, we study how dispersal intensity and dispersal asymmetry affects the total population abundance. Two complete classifications of the model parameter space are given: one concerning when dispersal causes smaller or larger total biomass than no dispersal, and the other addressing how the total biomass changes with dispersal intensity and dispersal asymmetry. This improves some existing results, e.g., a recent work of Arditi et al. (Theor. Popul. Biol., 120: 11-15, 2018).

Alfonso Ruiz-Herrera

(University of Oviedo, Spain)
"Network Topology vs. Spatial Scale of Movement in Trophic Metacommunities"
A central question in spatial ecology is understanding the interplay between the different types of movement and (spatial) network topology in the dynamics of a metacommunity. However, this is not an easy task as most fragmented ecosystems have trophic interactions involving many species and complex path-way structures. Recent attempts to solve this challenge have introduced certain simplifying assumptions or focused on a limited set of examples. However, these results do not cover many real situations. The goal of the talk is to compare the influence of the different topologies for a given configuration of nodes on the population abundances of the species of a trophic metacommunity. In particular, we are able to describe optimal movements/topologies that maximize the total population size of a target species. Regarding methodology, we first distinguish between species with low and high mobility. In the first group, we analyze the role of each path in isolation. In the second, we study the kernel of a matrix obtained from the adjacency matrices. Our main result reveals that the influence of network topologies on the population abundances depends, to a great extent, on the movement time scale. Moreover, we will prove that some directed graphs are useful in maximising the population abundance of a target species. Our framework can be readily used with any metacommunity and, therefore, represents a unification of biological insights. Moreover, we shed light on some folkloric discussions such as the role of the symmetric movement or the number of paths of a landscape.

Xiaoqing He

(East China Normal University, China)
"On the effects of carrying capacity of intrinsic growth rate on single and multiple species in spatially heterogeneous environments"
We consider a diffusive logistic model of a single species in a heterogeneous environment, with two parameters, r(x) for intrinsic growth rate and K(x) for carrying capacity. When r(x) and K(x) are proportional, i.e., r=cK, it is proved by Prof. Lou Yuan that a population diffusing at any rate will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. In this talk, we study another case when r(x) is a constant, i.e., independent of K(x). In such case, a striking result is that for any dispersal rate, the logistic equation with spatially heterogeneous resources will always support a total population strictly smaller than the total carrying capacity at equilibrium, which is just opposite to the case r = cK. These two cases of single species models also lead to two different forms of Lotka-Volterra competition-diffusion systems. We then report the consequences of the aforementioned difference on the two corresponding forms of the competition systems. Our results indicate that in heterogeneous environments, the correlation between r(x) and K(x) has more profound impacts in population ecology then we had previously expected, at least from a mathematical point of view. This is joint work with Qian Guo and Prof. Wei-Ming Ni.

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