Learning in a game context: strategy choice by some keeps learning from evolving in others

Behavioural decisions in a social context commonly have frequency-dependent outcomes and so require analysis using evolutionary game theory. Learning provides a mechanism for tracking changing conditions and it has frequently been predicted to supplant fixed behaviour in shifting environments; yet few studies have examined the evolution of learning specifically in a game-theoretic context. We present a model that examines the evolution of learning in a frequency-dependent context created by a producer-scrounger game, where producers search for their own resources and scroungers usurp the discoveries of producers. We ask whether a learning mutant that can optimize its use of producer and scrounger to local conditions can invade a population of non-learning individuals that play producer and scrounger with fixed probabilities. We find that learning provides an initial advantage but never evolves to fixation. Once a stable equilibrium is attained, the population is always made up of a majority of fixed players and a minority of learning individuals. This result is robust to variation in the initial proportion of fixed individuals, the rate of within-and between-generation environmental change, and population size. Such learning polymorphisms will manifest themselves in a wide range of contexts, providing an important element leading to behavioural syndromes.