Rogers' paradox recast and resolved: population structure and the evolution of social learning strategies.

We explore the evolution of reliance on social and asocial learning using a spatially explicit stochastic model. Our analysis considers the relative merits of four evolved strategies, two pure strategies (asocial and social learning) and two conditional strategies (the "critical social learner," which learns asocially only when copying fails, and the "conditional social learner," which copies only when asocial learning fails). We find that spatial structure generates outcomes that do not always conform to the finding of earlier theoretical analyses that social learning does not enhance average individual fitness at equilibrium (Rogers' paradox). Although we describe circumstances under which the strategy of pure social learning increases the average fitness of individuals, we find that spatial structure introduces a new paradox, which is that social learning can spread even when it decreases the average fitness of individuals below that of asocial learners. We also show that the critical social learner and conditional social learner both provide solutions to the aforementioned paradoxes, although we find some conditions in which pure (random) social learning out-competes both conditional strategies. Finally, we consider the relative merits of critical and conditional social learning under various conditions.