Evolution of social learning: a mathematical analysis.

Social learning is an important ability seen in a wide range of animals including humans. It has been argued that individual learning, social learning, and innate determination of behavior are favored by natural selection when environmental changes occur at short, intermediate, and long intervals, respectively. Only recently, however, has the hypothesis been examined by means of mathematical models. In this paper, we construct a simple model in which each organism uses one of three genetically determined strategies--it is an individual learner, a social learner or an "innate"--and the three types of organisms are in direct competition with each other. A reduced model, involving only the individual learners and innates, is effectively linear, and we show that by solving the eigenvalue problem of this reduced system we arrive at a good approximation to the global dynamics of the full model. We also study the effect of stochastic environmental changes and reversible mutations among the three strategies. Our results are consistent with the predictions of previous studies. In addition, we identify a critical level of environmental constancy below which only individual and social learners are present.