The expected time to cross extended fitness plateaus

For a population to acquire a complex adaptation requiring multiple individually neutral mutations, it must cross a plateau in the fitness landscape. We consider plateaus involving three mutations, and show that large populations can cross them rapidly via lineages that acquire multiple mutations while remaining at low frequency. Plateau-crossing is fastest for very large populations. At intermediate population sizes, recombination can greatly accelerate adaptation by combining independent mutant lineages to form triple-mutants. For more frequent recombination, such that the population is kept near linkage equilibrium, we extend our analysis to find simple expressions for the expected time to cross plateaus of arbitrary width.