Conditional persistence in logistic models via nonlinear diffusion

Author:

Cantrell Robert Stephen,Cosner Chris

Abstract

A nonlinear diffusion process modelling aggregative dispersal is combined with local (in space) population dynamics given by a logistic equation and the resulting growth-dispersal model is analysed. The nonlinear diffusion process models aggregation via a diffusion coefficient, which is decreasing with respect to the population density at low densities. This mechanism is similar to area-restricted search, but it is applied to conspecifics rather than prey. The analysis shows that in some cases the models predict a threshold effect similar to an Allee effect. That is, for some parameter ranges, the models predict a form of conditional persistence where small populations go extinct but large populations persist. This is somewhat surprising because logistic equations without diffusion or with non-aggregative diffusion predict either unconditional persistence or unconditional extinction. Furthermore, in the aggregative models, the minimum patch size needed to sustain an existing population at moderate to high densities may be smaller than the minimum patch size needed for invasibility by a small population. The tradeoff is that if a population is inhabiting a large patch whose size is reduced below the size needed to sustain any population, then the population on the patch can be expected to experience a sudden crash rather than a steady decline.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 16 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the Allee effect and directed movement on the whole space;Mathematical Biosciences and Engineering;2023

2. Fractional diffusion with Neumann boundary conditions: The logistic equation;Discrete & Continuous Dynamical Systems - B;2013

3. Population models with diffusion, strong Allee effect, and nonlinear boundary conditions;Nonlinear Analysis: Theory, Methods & Applications;2011-12

4. Diffusive logistic equation with non-linear boundary conditions;Journal of Mathematical Analysis and Applications;2011-03

5. Eigenvalue Problems of a Degenerate Quasilinear Elliptic Equation;Rocky Mountain Journal of Mathematics;2010-02-01

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