Nonlinear dispersal and growth change the phylogenetic structure of expanding populations

Range expansions have shaped the evolutionary history of many organisms, from microbes to humans. Here, we study how the specifics of growth and dispersal affect the genealogical structure of expanding populations. The genealogical structure plays an important role in fixation of alleles, maintenance of genetic diversity, and genomic inference. Previous studies suggest that genealogies of expanding populations could be nontrivial because organisms at the expansion edge are expected to have an unusually large number of descendants. Indeed, we find these structures can be described by a family of Λ-coalescents, controlled by a single parameter: the ratio between the expansion velocity and the geometric mean of the dispersal and growth rates at low densities. For high values of this ratio, which occur when populations grow or disperse cooperatively, the genealogies are described by a Kingman coalescent. For low values—when the velocity is determined by growth and dispersal at the edge—we find a family of coalescents in which many lineages can merge simultaneously, including the Bolthausen-Sznitman coalescent at one end. These findings show that genealogies in expanding populations have a much richer structure than previously thought.