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Title: Stationary stability for evolutionary dynamics in finite populations

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.
 [1] ;  [2]
  1. Independent, Playa del Rey, CA (United States)
  2. San Jose State Univ., San Jose, CA (United States)
Publication Date:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Additional Journal Information:
Journal Volume: 18; Journal Issue: 9; Journal ID: ISSN 1099-4300
Research Org:
San Jose State Univ., San Jose, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
60 APPLIED LIFE SCIENCES; 97 MATHEMATICS AND COMPUTING; evolutionary stability; finite populations; information entropy; stationary distributions
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