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Natural selection drives populations towards higher fitness, but crossingfitness valleys or plateaus may facilitate progress up a rugged fitnesslandscape involving epistasis. We investigate quantitatively the effect ofsubdividing an asexual population on the time it takes to cross a fitnessvalley or plateau. We focus on a generic and minimal model that includes onlypopulation subdivision into equivalent demes connected by global migration, anddoes not require significant size changes of the demes, environmentalheterogeneity or specific geographic structure. We determine the optimalspeedup of valley or plateau crossing that can be gained by subdivision, if theprocess is driven by the deme that crosses fastest. We show that isolated demeshave to be in the sequential fixation regime for subdivision to significantlyaccelerate crossing. Using Markov chain theory, we obtain analyticalexpressions for the conditions under which optimal speedup is achieved: valleyor plateau crossing by the subdivided population is then as fast as that of itsfastest deme. We verify our analytical predictions through stochasticsimulations. We demonstrate that subdivision can substantially accelerate thecrossing of fitness valleys and plateaus in a wide range of parametersextending beyond the optimal window. We study the effect of varying the degreeof subdivision of a population, and investigate the trade-off between themagnitude of the optimal speedup and the width of the parameter range overwhich it occurs. Our results also hold for weakly beneficial intermediatemutations. We extend our work to the case of a population connected bymigration to one or several smaller islands. Our results demonstrate thatsubdivision with migration alone can significantly accelerate the crossing offitness valleys and plateaus, and shed light onto the quantitative conditionsnecessary for this to occur.

Quantifying the role of population subdivision in evolution on rugged fitness landscapes