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

Benjamin Allen, Corina E. Tarnita

Research output: Contribution to journalArticle

35 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)109-143
Number of pages35
JournalJournal of mathematical biology
Volume68
Issue number1-2
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Keywords

  • Axioms
  • Evolution
  • Evolutionary success
  • Fixation probability
  • Price equation
  • Stochastic

Fingerprint Dive into the research topics of 'Measures of success in a class of evolutionary models with fixed population size and structure'. Together they form a unique fingerprint.

  • Cite this