Evolution of social versus individual learning in an infinite island model

We model the evolution of learning in a population composed of infinitely many, finite-sized islands connected by migration. We assume that there are two discrete strategies, social and individual learning, and that the environment is spatially homogeneous but varies temporally in a periodic or stochastic manner. Using a population-genetic approximation technique, we derive a mathematical condition for the two strategies to coexist stably and the equilibrium frequency of social learners under stable coexistence. Analytical and numerical results both reveal that social learners are favored when island size is large or migration rate between islands is high, suggesting that spatial subdivision disfavors social learners. We also show that the average fecundity of the population under stable coexistence of the two strategies is in general lower than that in the absence of social learners and is minimized at an intermediate migration rate.