Shigesada N
J Math Biol. 1980 Mar;9(1):85-96. doi: 10.1007/BF00276037.
A mathematical model for the dispersal of an animal population is presented for a system in which animals are initially released in the central region of a uniform field and migrate randomly, exerting mutually repulsive influences (population pressure) until they eventually become sedentary. The effect of the population pressure, which acts to enhance the dispersal of animals as their density becomes high, is modeled in terms of a nonlinear-diffusion equation. From this model, the density distribution of animals is obtained as a function of time and the initial number of released animals. The analysis of this function shows that the population ultimately reaches a nonzero stationary distribution which is confined to a finite region if both the sedentary effect and the population pressure are present. Our results are in good agreement with the experimental data on ant lions reported by Morisita, and we can also interpret some general features known for the spatial distribution of dispersing insects.
针对这样一个系统，提出了一种动物种群扩散的数学模型。在该系统中，动物最初被释放到一个均匀区域的中心，然后随机迁移，相互施加排斥影响（种群压力），直到它们最终定居下来。种群压力在动物密度较高时会促进其扩散，这种效应通过一个非线性扩散方程进行建模。从这个模型中，可以得到动物的密度分布作为时间和初始释放动物数量的函数。对该函数的分析表明，如果同时存在定居效应和种群压力，种群最终会达到一个非零的稳态分布，且该分布局限于一个有限区域。我们的结果与森下报道的蚁狮实验数据高度吻合，并且我们还可以解释一些已知的扩散昆虫空间分布的一般特征。
