NDLI: Measures of success in a class of evolutionary models with fixed population size and structure

Content Provider	Springer Nature Link
Author	Tarnita, Corina E. Allen, Benjamin
Copyright Year	2012
Abstract	We investigate a class of evolutionary models, encompassing many established models of well-mixed and spatially structured populations. Models in this class have fixed population size and structure. Evolution proceeds as a Markov chain, with birth and death probabilities dependent on the current population state. Starting from basic assumptions, we show how the asymptotic (long-term) behavior of the evolutionary process can be characterized by probability distributions over the set of possible states. We then define and compare three quantities characterizing evolutionary success: fixation probability, expected frequency, and expected change due to selection. We show that these quantities yield the same conditions for success in the limit of low mutation rate, but may disagree when mutation is present. As part of our analysis, we derive versions of the Price equation and the replicator equation that describe the asymptotic behavior of the entire evolutionary process, rather than the change from a single state. We illustrate our results using the frequency-dependent Moran process and the birth–death process on graphs as examples. Our broader aim is to spearhead a new approach to evolutionary theory, in which general principles of evolution are proven as mathematical theorems from axioms.
Ending Page	143
Page Count	35
Starting Page	109
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	1-2
Volume Number	68
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2012-11-20
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Axioms Evolutionary success Mathematical and Computational Biology Evolution Stochastic Price equation Applications of Mathematics Fixation probability Problems related to evolution
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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