The genetic architecture of polygenic local adaptation and its role in shaping barriers to gene flow

We consider how the genetic architecture underlying locally adaptive traits determines the strength of a barrier to gene flow in a mainland-island model. Assuming a general life cycle, we derive an expression for the effective migration rate when local adaptation is due to genetic variation at many loci under directional selection on the island, allowing for arbitrary fitness and dominance effects across loci. We show how the effective migration rate can be combined with classical single-locus diffusion theory to accurately predict multilocus differentiation between the mainland and island at migration-selection-drift equilibrium and determine the migration rate beyond which local adaptation collapses, while accounting for genetic drift and weak linkage. Using our efficient numerical tools, we then present a detailed study of the effects of dominance on barriers to gene flow, showing that when total selection is sufficiently strong, more recessive local adaptation generates stronger barriers to gene flow. We then study how heterogeneous genetic architectures of local adaptation affect barriers to gene flow, characterizing adaptive differentiation at migration-selection balance for different distributions of fitness effects. We find that a more heterogeneous genetic architecture generally yields a stronger genome-wide barrier to gene flow and that the detailed genetic architecture underlying locally adaptive traits can have an important effect on observable differentiation when divergence is not too large. Lastly, we study the limits of our approach as loci become more tightly linked, showing that our predictions remain accurate over a large biologically relevant domain.