Stationary stability for evolutionary dynamics in finite populations [electronic resource]

• Ngôn ngữ: eng
• Ký hiệu phân loại: 577.82 +Ecological communities
• Thông tin xuất bản: Washington, D.C. : Oak Ridge, Tenn. : United States. Dept. of Energy. Office of Science ; Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2016
• Mô tả vật lý: Size: Article No. 316 : , digital, PDF file.
• Bộ sưu tập: Metadata
• ID: 262023
• Chủ đề: 1. 60 applied life sciences; 2. 97 mathematics and computing; 3. Evolutionary stability; 4. Finite populations; 5. Information entropy; 6. Stationary distributions

Tóm tắt

Here, we demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We define the notion of stationary stability for the Moran process with mutation and generalizations, as well as a generalized notion of evolutionary stability that includes mutation called an incentive stable state (ISS) candidate. For sufficiently large populations, extrema of the stationary distribution are ISS candidates and we give a family of Lyapunov quantities that are locally minimized at the stationary extrema and at ISS candidates. In various examples, including for the Moran andWright?Fisher processes, we show that the local maxima of the stationary distribution capture the traditionally-defined evolutionarily stable states. The classical stability theory of the replicator dynamic is recovered in the large population limit. Finally we include descriptions of possible extensions to populations of variable size and populations evolving on graphs.