E. J. Collins, J. M. McNamara and D. M. Ramsey

The quality of a chosen partner can be one of the most significant factors affecting an animal's long-term reproductive success. We investigate optimal mate choice rules in an environment where there is both local variation in the quality of potential mates within each local mating pool and spatial (or temporal) variation in the average quality of the pools themselves. In such a situation, a robust rule that works well across a variety of environments will confer a significant reproductive advantage. We formulate a full Bayesian model for updating information in such a varying environment and derive the form of the rule that maximizes expected reward in a spatially varying environment. We compare the theoretical performance of our optimal learning rule against both fixed threshold rules and simpler near-optimal learning rules and show that learning is most advantageous when both the local and environmental variances are large. We consider how optimal simple learning rules might evolve and compare their evolution with that of fixed threshold rules using genetic algorithms as minimal models of the relevant genetics. Our analysis points up the variety of ways in which a near-optimal rule can be expressed. Finally, we describe how our results extend to the case of temporally varying environments.

*Some key words:*

sexual selection, sequential search, spatially varying environment,
Bayesian model, genetic algorithm, evolution of learning rules