Specialization and evolutionary branching within migratory populations

Understanding the mechanisms that drive specialization and speciation within initially homogeneous populations is a fundamental challenge for evolutionary theory. It is an issue of relevance for significant open questions in biology concerning the generation and maintenance of biodiversity, the origins of reciprocal cooperation, and the efficient division of labor in social or colonial organisms. Several mathematical frameworks have been developed to address this question and models based on evolutionary game theory or the adaptive dynamics of phenotypic mutation have demonstrated the emergence of polymorphic, specialized populations. Here we focus on a ubiquitous biological phenomenon, migration. Individuals in our model may evolve the capacity to detect and follow an environmental cue that indicates a preferred migration route. The strategy space is defined by the level of investment in acquiring personal information about this route or the alternative tendency to follow the direction choice of others. The result is a relation between the migratory process and a game theoretic dynamic that is generally applicable to situations where information may be considered a public good. Through the use of an approximation of social interactions, we demonstrate the emergence of a stable, polymorphic population consisting of an uninformed subpopulation that is dependent upon a specialized group of leaders. The branching process is classified using the techniques of adaptive dynamics.