Bet-hedging in stochastically switching environments

• Published in: Journal of theoretical biology Vol. 336; pp. 144 - 157
• Main Authors: Müller, J., Hense, B.A., Fuchs, T.M., Utz, M., Pötzsche, Ch
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 07-11-2013
• Subjects: Adaptive dynamics; Bet-hedging; Computer Simulation; Environment; environmental factors; evolutionarily stable strategy; evolutionary adaptation; Lyapunov exponent; Models, Biological; Phenotype; Population Density; Stochastic Processes; Stochastic switching systems; Bet-hedging; Stochastic switching systems; Adaptive dynamics; Lyapunov exponent
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2013.07.017

We investigate the evolution of bet-hedging in a population that experiences a stochastically switching environment by means of adaptive dynamics. The aim is to extend known results to the situation at hand, and to deepen the understanding of the range of validity of these results. We find three different types of evolutionarily stable strategies (ESSs) depending on the frequency at which the environment changes: for a rapid change, a monomorphic phenotype adapted to the mean environment; for an intermediate range, a bimorphic bet-hedging phenotype; for slowly changing environments, a monomorphic phenotype adapted to the current environment. While the last result is only obtained by means of heuristic arguments and simulations, the first two results are based on the analysis of Lyapunov exponents for stochastically switching systems.
•Bet-hedging in stochastically switching envionments is analzed via adaptive dynamics.•Expansions of Lyapunoc exponents for linear 2-dim. systems and different time scales are derived.•Fast time-scale: homogeneous phenotype, adapted to the average environment is optimal.•Middle range time scale: bet-hedging is optimal.•Slow time scale: phenotype adapted to one environment only is optimal.