Spatial soft sweeps: Patterns of adaptation in populations with long-range dispersal

Adaptation in extended populations often occurs through multiple independent mutations responding in parallel to a common selection pressure. As the mutations spread concurrently through the population, they leave behind characteristic patterns of polymorphism near selected lociso-called soft sweepswhich remain visible after adaptation is complete. These patterns are well-understood in two limits of the spreading dynamics of beneficial mutations: the panmictic case with complete absence of spatial structure, and spreading via short-ranged or diffusive dispersal events, which tessellates space into distinct compact regions each descended from a unique mutation. However, spreading behaviour in most natural populations is not exclusively panmictic or diffusive, but incorporates both short-range and long-range dispersal events. Here, we characterize the spatial patterns of soft sweeps driven by dispersal events whose jump distances are broadly distributed, using lattice-based simulations and scaling arguments. We find that mutant clones adopt a distinctive structure consisting of compact cores surrounded by fragmented haloes which mingle with haloes from other clones. As long-range dispersal becomes more prominent, the progression from diffusive to panmictic behaviour is marked by two transitions separating regimes with differing relative sizes of halo to core. We analyze the implications of the core-halo structure for the statistics of soft sweep detection in small genomic samples from the population, and find opposing effects of long-range dispersal on the expected diversity in global samples compared to local samples from geographic subregions of the range. We also discuss consequences of the standing genetic variation induced by the soft sweep on future adaptation and mixing. Author summary When a species is spread out over a large geographic range, different regions may adapt to the same selection pressure by acquiring distinct beneficial mutations. The resulting pattern of genetic variation in the population is called a soft sweep. Dispersal strongly influences soft sweep patterns, as it determines how a mutation that arose in one region might spread to others. Although most plant and animal populations experience some amount of dispersal over very long distances, the impact of such long-range dispersal events on soft sweep patterns remains poorly understood. We use computer simulations and mathematical analysis to study patterns of genetic variation in a model of soft sweeps including long-range dispersal. We show that long-range dispersal leaves distinct signatures in the genetic makeup of the population, which can be detected in genetic samples from individuals across the range. Our results are important for correctly interpreting patterns of genetic diversity in populations that have undergone recent adaptation.