Cosner Chris, Winkler Michael
Department of Mathematics, University of Miami Coral Gables, Florida, USA,
J Math Biol. 2014 Dec;69(6-7):1343-82. doi: 10.1007/s00285-013-0733-z. Epub 2013 Oct 30.
Understanding the spatial distribution of populations in heterogeneous environments is an important problem in ecology. In the case of a population of organisms that can sense the quality of their environment and move to increase their fitness, one theoretical description of the expected distribution of the population is the ideal free distribution, where individuals locate themselves to optimize fitness. A model for a dynamical process that allows a population to achieve an ideal free distribution was proposed by the Cosner (Theor Popul Biol 67:101-108, 2005). The model is based on a reaction-diffusion-advection equation with nonlinear diffusion which is similar to a porous medium equation with additional advection and population growth terms. We establish that the model is well-posed, show that solutions stabilize, determine the stationary states, discuss their stability, and describe the biological interpretation of the results.
了解异质环境中种群的空间分布是生态学中的一个重要问题。对于能够感知环境质量并通过移动来提高自身适应性的生物种群而言，种群预期分布的一种理论描述是理想自由分布，即个体通过自我定位来优化适应性。科斯纳（《理论种群生物学》67卷：101 - 108页，2005年）提出了一个动态过程模型，该模型能使种群实现理想自由分布。该模型基于一个具有非线性扩散的反应 - 扩散 - 对流方程，它类似于带有额外对流和种群增长项的多孔介质方程。我们证明了该模型是适定的，表明解是稳定的，确定了稳态，讨论了它们的稳定性，并描述了结果的生物学解释。
