Adaptations may require multiple mutations that are beneficial only in combination. To adapt, a lineage must acquire mutations that are individually neutral or deleterious before gaining the beneficial combination, thereby crossing a plateau or valley, respectively, in the mapping from genotype to fitness. Spatial population structure can facilitate plateau and valley crossing by allowing neutral and deleterious lineages to survive longer and produce more beneficial mutants. Here, we analyze adaptation across a two-mutation plateau or valley in an asexual population that is subdivided into discrete subpopulations, or demes, connected by migration. We describe how subdivision alters the dynamics of adaptation from those in an equally sized unstructured population and give a complete quantitative description of these dynamics for the island migration model. Subdivision can significantly decrease the waiting time for the adaptation if demes and migration rates are small enough that single-mutant lineages fix in one or more demes before producing the beneficial double mutant. But, the potential decrease is small in very large populations and may also be limited by the slow spread of the beneficial mutant in extremely subdivided populations. Subdivision has a smaller effect on the probability that the population adapts very quickly than on the mean time to adapt, which has important consequences in some applications, such as the development of cancer. Our results provide a general and intuitive framework for predicting the effects of spatial structure in other models and in natural populations.

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