Optimal mixed strategies in stochastic environments

Abstract

Environmental fluctuation between generations can lead to mixed optimal strategies (so-called “bet-hedging”). Due to mathematical intractability, however, optimality modelling has up to now largely ignored the effects of such fluctuations. The cases that have been considered so far are relatively simple. We show that the optimal strategy can be calculated explicitly for the case of non-structured populations. an environmental parameter which varies over generations according to an ergodic process and certain types of payoff functions (specifying the relationship between an individual′s trait value, the environment, and its expected contribution to the populations size in the next generation). Our results also lead to numerical solutions for other cases. Situations with and without information about the environment are considered. In both cases, there is a minimum environmental variability above which mixed strategies are optimal. Examination of the differences between long-term reproductive success of constrained purr strategies and optimal mixed strategies indicates that there is a high selection pressure for mixed strategies to evolve unless individuals can acquire highly accurate information about their environment. We show that the solution is robust in the sense that it has near to optimal long-term reproductive success under small perturbations of the payoff function and/or the distribution of the environmental parameter. © 1995 Academic Press. All rights reserved.