The genetics of adaptation to discrete heterogeneous environments: frequent mutation or large-effect alleles can allow range expansion.

Range expansions are complex evolutionary and ecological processes. From an evolutionary standpoint, a populations' adaptive capacity can determine the success or failure of expansion. Using individual-based simulations, we model range expansion over a two-dimensional, approximately continuous landscape. We investigate the ability of populations to adapt across patchy environmental gradients and examine how the effect sizes of mutations influence the ability to adapt to novel environments during range expansion. We find that genetic architecture and landscape patchiness both have the ability to change the outcome of adaptation and expansion over the landscape. Adaptation to new environments succeeds via many mutations of small effect or few of large effect, but not via the intermediate between these cases. Higher genetic variance contributes to increased ability to adapt, but an alternative route of successful adaptation can proceed from low genetic variance scenarios with alleles of sufficiently large effect. Steeper environmental gradients can prevent adaptation and range expansion on both linear and patchy landscapes. When the landscape is partitioned into local patches with sharp changes in phenotypic optimum, the local magnitude of change between subsequent patches in the environment determines the success of adaptation to new patches during expansion.