OPTIMAL MIXED STRATEGIES IN STOCHASTIC ENVIRONMENTS

Environmental fluctuation between generations can lead to mixed optima l strategies (so-called ''bet-hedging''). Due to mathematical intracta bility, however, optimality modelling has up to now largely ignored th e effects of such fluctuations. The cases that have been considered so far are relatively simple. We show that the optimal strategy can be c alculated explicitly for the case of non-structured populations. an en vironmental parameter which varies over generations according to an er godic process and certain types of payoff functions (specifying the re lationship between an individual's trait value, the environment, and i ts expected contribution to the populations size in the next generatio n). Our results also lead to numerical solutions for other cases. Situ ations with and without information about the environment are consider ed. In both cases, there is a minimum environmental variability above which mixed strategies are optimal. Examination of the differences bet ween long-term reproductive success of constrained purr strategies and optimal mixed strategies indicates that there is a high selection pre ssure for mixed strategies to evolve unless individuals can acquire hi ghly accurate information about their environment. We show that the so lution is robust in the sense that it has near to optimal long-term re productive success under small perturbations of the payoff function an d/or the distribution of the environmental parameter. (C) 1995 Academi c Press, Inc.