Saloniemi I
Am Nat. 1993 Jun;141(6):880-96. doi: 10.1086/285514.
A new model for coevolution in generalized predator-prey systems is presented by incorporating quantitative characters relevant to predation in both prey and predator. Malthusian fitnesses are derived from ecological models, and they include interspecific frequency and density dependence. Both prey and predator characters are under stabilizing selection even without predation, and predation adds an additional linear selection component to both characters. The nonlinear system of differential equations is studied analytically by using local linearization near the equilibrium points. Parameters related to intrinsic growth and death rates and stabilizing selection determine whether there are zero, one, or two equilibria. Additive genetic variances do not have an effect on the equilibrium points, but genetic variability is crucial for determining their stability. Analysis of the linearized model shows that at most one equilibrium can be stable, and stability is achieved when additive genetic variance is high enough in both the prey and predator populations. The stability properties are illustrated by numerical examples of the full dynamics of the original nonlinear model.
通过纳入与猎物和捕食者的捕食相关的定量特征，提出了一种广义捕食 - 猎物系统中共进化的新模型。马尔萨斯适合度源自生态模型，且包括种间频率和密度依赖性。即使没有捕食，猎物和捕食者的特征都处于稳定选择之下，而捕食会给这两个特征都增加一个额外的线性选择成分。通过在平衡点附近使用局部线性化方法对非线性微分方程组进行了分析研究。与内在增长率和死亡率以及稳定选择相关的参数决定了是否存在零个、一个或两个平衡点。加性遗传方差对平衡点没有影响，但遗传变异性对于确定它们的稳定性至关重要。对线性化模型的分析表明，最多只有一个平衡点可以是稳定的，并且当猎物和捕食者种群中的加性遗传方差都足够高时可实现稳定性。通过原始非线性模型完整动态的数值示例说明了稳定性特性。
