Emergent Ecological Phenomena in Evolving and Migrating Populations

Evolution is a ubiquitous feature of systems of interacting organisms. However, ecological models that neglect evolution often provide an adequate description of systems composed of distinct species. Even in cases where only one species is considered, evolutionary dynamics can lead to the emergence of multiple strains that interact in ways resembling distinct species. For example, a recent study of gut microbiota showed that several strains of a single species coexist and obey simple ecological laws. A theoretical understanding of how and when ecological laws emerge from evolutionary dynamics may be critical for understanding such systems. We study a model of an evolving population that migrates through a spatially heterogeneous environment. We give precise criteria for when distinct strains emerge, and we analyze how they interact. We show that extinction of strains corresponds to a phase transition characterized by slow relaxation to steady state. This slow relaxation may provide a signal to detect impending extinction. Our results may apply to a variety of systems including human microbiomes, antibodies undergoing affinity maturation, and bacteria acquiring antibiotic resistance.