Demographic noise can reverse the direction of deterministic selection

George W.A. Constable, Tim Rogers, Alan J. McKane, Corina E. Tarnita

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


Deterministic evolutionary theory robustly predicts that populations displaying altruistic behaviors will be driven to extinction by mutant cheats that absorb common benefits but do not themselves contribute. Here we show that when demographic stochasticity is accounted for, selection can in fact act in the reverse direction to that predicted deterministically, instead favoring cooperative behaviors that appreciably increase the carrying capacity of the population. Populations that exist in larger numbers experience a selective advantage by being more stochastically robust to invasions than smaller populations, and this advantage can persist even in the presence of reproductive costs. We investigate this general effect in the specific context of public goods production and find conditions for stochastic selection reversal leading to the success of public good producers. This insight, developed here analytically, is missed by the deterministic analysis as well as by standard game theoretic models that enforce a fixed population size. The effect is found to be amplified by space; in this scenario we find that selection reversal occurs within biologically reasonable parameter regimes for microbial populations. Beyond the public good problem, we formulate a general mathematical framework for models that may exhibit stochastic selection reversal. In this context, we describe a stochastic analog to r - K theory, by which small populations can evolve to higher densities in the absence of disturbance.

Original languageEnglish (US)
Pages (from-to)E4745-E4754
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number32
StatePublished - Aug 9 2016

All Science Journal Classification (ASJC) codes

  • General


  • Cooperation
  • Nonfixed population size
  • Public goods
  • Stochastic dynamics
  • Timescale separation


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