Abstract
Locally adapted traits can exhibit a wide range of genetic architectures, from pronounced divergence at a few loci to small frequency divergence at many loci. The type of architecture that evolves depends strongly on the migration rate, as weakly selected loci experience swamping and do not make lasting contributions to divergence. Simulations from previous studies showed that even when mutations are strongly selected and should resist migration swamping, the architecture of adaptation can collapse and become transient at high mutation rates. Here, we use an analytical two-population model to study how this transition in genetic architecture depends upon population size, strength of selection, and parameters describing the mutation process. To do this, we develop a mathematical theory based on the diffusion approximation to predict the threshold mutation rate above which the transition occurs. We find that this performs well across a wide range of parameter space, based on comparisons with individual-based simulations. The threshold mutation rate depends most strongly on the average effect size of mutations, weakly on the strength of selection, and marginally on the population size. Across a wide range of the parameter space, we observe that the transition to a transient architecture occurs when the trait-wide mutation rate is 10-3-10-2, suggesting that this phenomenon is potentially relevant to complex traits with a large mutational target. On the other hand, based on the apparent stability of genetic architecture in many classic examples of local adaptation, our theory suggests that per-trait mutation rates are often relatively low.