Convergent Evolution During Local Adaptation to Patchy Landscapes

Species often encounter, and adapt to, many patches of similar environmental conditions across their range. Such adaptation can occur through convergent evolution if different alleles arise in different patches, or through the spread of shared alleles by migration acting to synchronize adaptation across the species. The tension between the two reflects the constraint imposed on evolution by the underlying genetic architecture versus how effectively selection and geographic isolation act to inhibit the geographic spread of locally adapted alleles. This paper studies the balance between these two routes to adaptation in a model of continuous environments with patchy selection pressures. We address the following questions: How long does it take for a novel allele to appear in a patch where it is locally adapted through mutation? Or, through migration from another, already adapted patch? Which is more likely to occur, as a function of distance between the patches? What population genetic signal is left by the spread of migrant alleles? To answer these questions we examine the family structure underlying migration–selection equilibrium surrounding an already adapted patch, treating those rare families that reach new patches as spatial branching processes. A main result is that patches further apart than a critical distance will likely evolve independent locally adapted alleles; this distance is proportional to the spatial scale of selection (σ / s m, where σ is the dispersal distance and sm is the selective disadvantage of these alleles between patches), and depends linearly on log(sm/μ), where μ is the mutation rate. This provides a way to understand the role of geographic separation between patches in promoting convergent adaptation and the genomic signals it leaves behind. We illustrate these ideas using the convergent evolution of cryptic coloration in the rock pocket mouse, Chaetodipus intermedius, as an empirical example.Author Summary: Often, a large species range will include patches where the species differs because it has adapted to locally differing conditions. For instance, rock pocket mice are often found with a coat color that matches the rocks they live in, these color differences are controlled genetically, and mice that don’t match the local rock color are more likely to be eaten by predators. Sometimes, similar genetic changes have occurred independently in different patches, suggesting that there were few accessible ways to evolve the locally adaptive form. However, the genetic basis could also be shared if migrants carry the locally beneficial genotypes between nearby patches, despite being at a disadvantage between the patches. We use a mathematical model of random migration to determine how quickly adaptation is expected to occur through new mutation and through migration from other patches, and study in more detail what we would expect successful migrations between patches to look like. The results are useful for determining whether similar adaptations in different locations are likely to have the same genetic basis or not, and more generally in understanding how species adapt to patchy, heterogeneous landscapes.