Droz M, Pekalski A
Département de Physique Théorique, Université de Genève, quai E. Ansermet 24, 1211 Genève 4, Switzerland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 May;63(5 Pt 1):051909. doi: 10.1103/PhysRevE.63.051909. Epub 2001 Apr 23.
We propose a lattice model of two populations, predators and prey. The model is solved via Monte Carlo simulations. Each species moves randomly on the lattice and can live only a certain time without eating. The lattice cells are either grass (eaten by prey) or tree (giving cover for prey). Each animal has a reserve of food that is increased by eating (prey or grass) and decreased after each Monte Carlo step. To breed, a pair of animals must be adjacent and have a certain minimum of food supply. The number of offspring produced depends on the number of available empty sites. We show that such a predator-prey system may finally reach one of the following three steady states: coexisting, with predators and prey; pure prey; or an empty one, in which both populations become extinct. We demonstrate that the probability of arriving at one of the above states depends on the initial densities of the prey and predator populations, the amount of cover, and the way it is spatially distributed.
我们提出了一个关于捕食者和猎物两个种群的晶格模型。该模型通过蒙特卡罗模拟求解。每个物种在晶格上随机移动，并且如果不进食只能存活一定时间。晶格单元格要么是草（被猎物食用），要么是树（为猎物提供掩护）。每只动物都有食物储备，通过进食（猎物或草）增加，在每个蒙特卡罗步骤后减少。为了繁殖，一对动物必须相邻且有一定的最低食物供应。产生的后代数量取决于可用空位点的数量。我们表明，这样的捕食者 - 猎物系统最终可能达到以下三种稳态之一：捕食者和猎物共存；只有猎物；或者为空态，即两个种群都灭绝。我们证明，达到上述状态之一的概率取决于猎物和捕食者种群的初始密度、掩护量以及其空间分布方式。
