title: Demographic noise can reverse the direction of deterministic selection.
abstract: 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 [Formula: see text] theory, by which small populations can evolve to higher densities in the absence of disturbance.
authors.affiliation: Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544; constabl@princeton.edu ctarnita@princeton.edu.
authors.forename: George W A
authors.initials: GW
authors.lastname: Constable
authors.affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom;
authors.forename: Tim
authors.initials: T
authors.lastname: Rogers
authors.affiliation: School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Alan J
authors.initials: AJ
authors.lastname: McKane
authors.affiliation: Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544; constabl@princeton.edu ctarnita@princeton.edu.
authors.forename: Corina E
authors.initials: CE
authors.lastname: Tarnita
mesh_terms: D005075:Biological Evolution; D003299:Cooperative Behavior; D003710:Demography; D005716:Game Theory; D006801:Humans; D011156:Population Density; D012641:Selection, Genetic; D013269:Stochastic Processes
keywords: cooperation; nonfixed population size; public goods; stochastic dynamics; timescale separation