Cushing J M
a Department of Mathematics, Interdisciplinary Program in Applied Mathematics , University of Arizona , Tucson, AZ , USA.
J Biol Dyn. 2019 Dec;13(1):103-127. doi: 10.1080/17513758.2019.1574034.
We describe the evolutionary game theoretic methodology for extending a difference equation population dynamic model in a way so as to account for the Darwinian evolution of model coefficients. We give a general theorem that describes the familiar transcritical bifurcation that occurs in non-evolutionary models when theextinction equilibrium destabilizes. This bifurcation results in survival (positive) equilibria whose stability depends on the direction of bifurcation. We give several applications based on evolutionary versions of some classic equations, such as the discrete logistic (Beverton-Holt) and Ricker equations. In addition to illustrating our theorems, these examples also illustrate other biological phenomena, such as strong Allee effects, time-dependent adaptive landscapes, and evolutionary stable strategies.
我们描述了一种演化博弈论方法，用于以一种考虑模型系数的达尔文式演化的方式扩展差分方程种群动态模型。我们给出了一个一般性定理，该定理描述了在非演化模型中当灭绝平衡点失稳时出现的常见跨临界分岔。这种分岔会导致生存（正）平衡点，其稳定性取决于分岔方向。我们基于一些经典方程的演化版本给出了几个应用，例如离散逻辑斯蒂（贝弗顿 - 霍尔特）方程和里克方程。除了阐明我们的定理外，这些例子还阐明了其他生物学现象，如强阿利效应、时间依赖的适应度景观和演化稳定策略。
