The Rate of Establishment of Complex AdaptationsMichael Lynch*,1and Adam Abegg21Department of Biology, Indiana University2Department of Mathematics, St Louis University*Corresponding author: E-mail: [email protected] editor: Yoko SattaAbstractA central problem in evolutionary theory concerns the mechanisms by which adaptations requiring multiple mutationsemerge 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 establishmentis minimized in populationswithvery large size. Under a broad range of conditions,the time to establishmentalso scales by nomore than the square of the mutation rate, regardless of the number of sites contributing to the adaptivechange, demonstrat-ing that the emergence of complex adaptations is only weakly constrained by the independent acquisition of mutations atthe underlying sites. Mutator alleles with deleterious side effects have only moderate effectson the rate of adaptation in largepopulations 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 nonheritable manner, may also elevate the rate ofadaptation,although the effect is modest and appears to result from a simple increase in the rate of transitionsbetween inter-mediate states rather than from the saltationalproduction of doublet mutations. Taken together, these results illustrate theplausibility of the relatively rapid emergence of specific complex adaptations by conventional population genetic mechanismsand provide insight into the relative incidences of various p aths of allelic adaptation in organisms with different populationgenetic features.Key words: adaptation, adaptive evolution, evolutionary rate, genome evolution, molecular evolution, mutation rate,mutator, fixation time, transient hypermutability.Research articleIntroductionUnderstanding the mechanistic origins of complex adapta-tions (here defined as character alterations requiring morethan one novel mutation to yield a functional advantage)remains a cent ral challenge for evolutionary bi ology (Hartland Taubes 1998; Orr 2002; DePristo et al. 2005; Dean andThornton 2007). Some have even questioned whether con-ventional mutational mechanisms and current principlesof population genetics are capable of explaining the emer-gence of complex adaptations on reasonable evolutionarytime scales (e.g., Behe and Snoke 2004; Pigliucci 2008). Be-causemutationsarerareevents,theoriginofcomplexadap-tations is often expected to occur a t very low rates in smallpopulations, owing to the long cumulative time span nec-essary for the independent arrival and sequential fixationof multiple mutations. In contrast, whereas large p opula-tions provide more individual targets f or mutational origin,should the intermediate steps toward a complex adaptationbe disadvantageous, the increased efficiency of selectionagainst intermediate mutants in large populations might in-hibit adaptational advance.A number of factors may facilitate the rate of emergenceof complex adaptations in ways that defy these simpleexpectations. First, despite the short persistence times ofdeleterious intermediate-stage mutations in large popu-lations, the steady input of new mutations results i n themaintenance of a small stable reservoir of intermediatealleles poised to take the next step(s) in the path towardadaptation (Gillespie 1984). Likewise, even though nearlyall neutral intermediate-step alleles are destined to be lostby drift, their accumulation by mutation pressure can pro-vide a growing resource for secondary adaptive mutations.Second, owing to the reduced ef ficiency of n atural selec-tion, p opulations with small effective sizes are vulnerableto the accumulation of mutations with mild effects on theefficiency of DNA replication and repair loci (Lynch 2008).The predicted increase in the per capita mutation rate isconsistent with the known gradient in the per-generationmutation rate from prokaryotes to multicellular eukaryotes(Lynch 2007) and could offset the decline in the number ofindividual mutational targets i n species with relatively smallpopulation sizes. Third, because the principle of selection–mutation balance extends to the loci that define the mu-tation rate, even large populations will always contain apool of in dividuals with mutation rates elevated above thepopulation norm. Although maladapted at the individuallevel, this small segment of the population might be a majorsource of evolutionary novelties.In the following sections, we attempt to incorporatethe above-mentioned issues into a more comprehensiveframework for understanding the population genetic envi-ronments in which complex adaptations are most likely toemerge by alternative routes. A series of analytical ap p rox-imations, supportedby computer simulations, demonstrate© The Author 2010. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, pleasee-mail: [email protected] Mol. Biol. Evol. 27(6):1404–1414. 2010 doi:10.1093/molbev/msq020 Advance Access publication January 29, 2010Rate of Establishment of Complex Adaptations · doi:10.1093/molbev/msq020 MBEthe existence of many plausible pathways by which com-plex adaptations can emerge much more rapidly than ex-pected when mutations at independent sites are assumedto proceed to fixation in a sequential manner. Our resultsalso reveal several scaling properties for the time to estab-lishment of complex adaptations with respect to popula-tion size, mutation rate, and degree of adaptive complexity,providing t he seeds for a general theory f or the contexts inwhich adaptiveevolution is most likely to proceed in organ-isms residing at differentpositionsalong these fundamentalpopulation genetic axes.BackgroundThe focus throughout will be on diploid sexual populations,with segregation of chromosomes occurring each genera-tion, but complete linkage between the sites at the locusunder