Golubitsky Martin, Hao Wenrui, Lam King-Yeung, Lou Yuan
Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA.
Department of Mathematics, Pennsylvania State University, State College, PA, 16802, USA.
Bull Math Biol. 2017 May;79(5):1051-1069. doi: 10.1007/s11538-017-0268-3. Epub 2017 Mar 29.
Geritz, Gyllenberg, Jacobs, and Parvinen show that two similar species can coexist only if their strategies are in a sector of parameter space near a nondegenerate evolutionarily singular strategy. We show that the dimorphism region can be more general by using the unfolding theory of Wang and Golubitsky near a degenerate evolutionarily singular strategy. Specifically, we use a PDE model of river species as an example of this approach. Our finding shows that the dimorphism region can exhibit various different forms that are strikingly different from previously known results in adaptive dynamics.
杰里茨、吉伦贝格、雅各布斯和帕尔维宁表明，只有当两个相似物种的策略处于参数空间中靠近非退化进化奇异策略的一个区域时，它们才能共存。我们表明，通过在退化进化奇异策略附近使用王和戈卢布茨基的展开理论，双态区域可以更具一般性。具体而言，我们以河流物种的偏微分方程模型为例来说明这种方法。我们的发现表明，双态区域可以呈现出各种不同的形式，这些形式与自适应动力学中先前已知的结果显著不同。
