Long G E
Department of Zoology, Washington State University, 99163, Pullman, Washington.
Oecologia. 1974 Mar;17(1):65-85. doi: 10.1007/BF00345096.
A community model may be considered stable when, in the absence of exogenous variation, all population trajectories encircle or asymptotically approach equilibrium. In this paper, community models in which, in the absence of analytical indications of stability, all populations either 1. exhibit trajectories toward equilibrium or 2. possess properties such that departures from equilibrium are inhibited will be defined as resilient. The necessary properties include appropriate sensitivity (i.e., the total derivative, df /dV , of the i species function, f =dN /dt, with respect to the j variable) to exogenous variables. A real, though simplified, ecological system consisting of Daphnia galeata and its algal food source in an oligotrophic lake appears to be generally resilient in that changes in the exogenous factors nitrate concentration and temperature of the lake water consistently restrain the departure of predicted population densities from equilibrium.Each population in the community is represented by the Verhulst-Pearl logistic model of population growth augmented to include environmental effects on rate of increase, r; carrying capacity, K; and the effects of predation on population density, N; and therefore the population rate of change, dN/dt.It is suggested that such community submodels and sensitivity analysis represent logical and appropriate amplifications in the use of mathematical models in the management of populations.
当在没有外源变化的情况下，所有种群轨迹围绕或渐近趋近于平衡时，群落模型可被认为是稳定的。在本文中，在没有稳定性分析指标的情况下，所有种群要么1. 表现出趋向平衡的轨迹，要么2. 具有抑制偏离平衡特性的群落模型将被定义为有恢复力的。必要特性包括对外源变量具有适当的敏感性（即第i个物种函数f = dN/dt关于第j个变量的全导数df/dV）。一个由寡营养湖中的盔形溞及其藻类食物源组成的真实但简化的生态系统似乎总体上具有恢复力，因为外源因素湖水硝酸盐浓度和温度的变化持续抑制预测种群密度偏离平衡。群落中的每个种群都由Verhulst - Pearl种群增长逻辑模型表示，该模型进行了扩充，纳入了环境对增长率r、承载能力K以及捕食对种群密度N的影响，因此纳入了种群变化率dN/dt。有人提出，此类群落子模型和敏感性分析代表了在种群管理中使用数学模型的合理且恰当的扩展。
