The rate of establishment of Complex Adaptations

A central problem in evolutionary theory concerns the mechanisms by which adaptations requiring multiple mutations emerge in natural populations.We develop a series of expressions that clarify the scaling of the time to establishment of com-plex adaptations with population size, mutation rate, magnitude of the selective disadvantage of intermediate-state alleles, and the complexity of the adaptation. In general, even in the face of deleterious intermediate steps, the time to establishment isminimized in populationswith very large size. Under a broad range of conditions, the time to establishmentalso scales by no more than the square of themutation rate, regardless of the number of sites contributing to the adaptive change, demonstrat-ing that the emergence of complex adaptations is only weakly constrained by the independent acquisition of mutations at the underlying sites. Mutator alleleswith deleterious side effects have onlymoderate effects on the rate of adaptation in large populations but can cause a quantum decrease in the time to establishment of some adaptive alleles in small populations, although probably not at a high enough rate to offset the increased deleterious mutation load. Transient hypermutability, whereby a subset of gamete-producing cells mutate at an elevated rate in a nonheritablemanner, may also elevate the rate of adaptation, although the effect ismodest and appears to result from a simple increase in the rate of transitionsbetween inter-mediate states rather than from the saltational production of doublet mutations. Taken together, these results illustrate the plausibility of the relatively rapid emergence of specific complex adaptations by conventional population geneticmechanisms and provide insight into the relative incidences of various paths of allelic adaptation in organisms with different population genetic features. Key words: adaptation, adaptive evolution, evolutionary rate, genome evolution, molecular evolution, mutation rate, mutator, fixation time, transient hypermutability. Research articl