Scaling expectations for the time to establishment of complex adaptations

Abstract

Although the vast majority of research in evolutionary biology is focused on adaption, a general theory for the population-genetic mechanisms by which complex adaptations are acquired remains to be developed. The issue explored here is the procurement of novel traits that specifically require multiple mutations to achieve a fitness advantage. By highlighting the roles played by the forces of mutation, recombination, and random genetic drift, and drawing from observations on the joint constraints on these factors, the ways in which rates of acquisition of specific types of adaptations scale with population size are explored. These general results provide insight into a number of ongoing controversies regarding the molecular basis of adaptation, including the adaptive utility of recombination and the role of drift in the passage through adaptive valleys.adaptive evolution | complex traits | evolutionary rate | molecular evolution | recombination R ecent empirical observations imply that approximate scaling laws exist for several fundamental evolutionary forces (1-3). First, across the full domain of life, there is an inverse relationship between population density and organism size. This relationship bears importantly on the power of random genetic drift, which is expected to scale negatively (although not necessarily linearly) with total population size (4). Second, the recombination rate per physical distance on chromosomes scales inversely with genome size. This feature is a simple consequence of an apparent structural constraint across all sexually reproducing eukaryotes-the occurrence of approximately one crossover event per chromosome arm per meiosis, and the fact that most variation in genome size is associated with variation in chromosome size rather than chromosome number. Finally, the mutation rate per nucleotide site per generation scales negatively with the genetic effective size of a population, possibly because lineages more vulnerable to random genetic drift are less efficient at maintaining high-fidelity replication/repair machinery (3, 5). The fact that all three of these nonadaptive forces of evolution influence the efficiency of selection raises the question as to whether general scaling laws also exist for the exploitation of various pathways to adaptive evolution.The development of theory in this area is rendered difficult by the multidimensional nature of the problem. One strategy has been to ignore all deleterious mutations and to assume that selection is strong enough and mutation weak enough relative to the power of random genetic drift and recombination that evolution always proceeds by the sequential fixation of single mutations (e.g., refs. 6-11). Such an approach provides a useful entree into the evolutionary dynamics of rare adaptive mutations with large effects. Under these conditions, the expectations are clear-with larger numbers of mutational targets and a reduced power of random genetic drift, the rate of adaptation will increase with population size, although more slowly than ex...

The Resolution of Sexual Antagonism by Gene Duplication

“…The mean waiting time until a male-beneficial duplicate becomes established by either process is T ¼ 1/(1/T drift 1 1/T res ) (see Weinreich and Chao 2005;Lynch 2010;Lynch and Abegg 2010), which is negatively correlated with the population size (N e ), the proportion of male-beneficial relative to null mutations (u b /u n ), and the strength of selection in males (s m ; Figure 1a; supporting information, Figure S1). Each parameterization set yields a long waiting time until duplicate invasion.…”

“…This represents a special case of ''stochastic tunneling'' (Komarova et al 2003). Modifying the results of several previous studies (Iwasa et al 2004;Weissman et al 2009;Lynch 2010;Lynch and Abegg 2010), the mean waiting time until a male-beneficial duplicate becomes fixed by the tunneling process is…”

“…Several prior studies (e.g., Iwasa et al 2004;Weissman et al 2009;Lynch 2010;Lynch and Abegg 2010) have modeled adaptation in a two-locus system (A and B), where the population is currently two mutation steps away from a higher fitness state, and intermediate genotypes are neutral (i.e., the fixed wild-type haplotype is A 1 B 1 , the most fit haplotype is A 2 B 2 , and A 1 B 2 and A 2 B 1 have the same fitness as A 1 B 1 ). Our gene duplication scenario is very similar, in that a transition from B 0 (no duplicate) to B m (male-beneficial duplicate) requires two mutation steps: with A f A f ancestral, the first mutation is from B 0 to B f , and the second one is from B f to B m .…”

Stochastic Tunneling and Metastable States During the Somatic Evolution of Cancer

“…These studies were concerned with computing fixation times of the advantageous type 2 cells and rely on the assumption that the number of type 1 cells is small. Finally, the horizontal striped region approximately corresponds to the literature of crossing fitness valleys, notably Weinreich and Chao (2005), Weissman et al (2009), Lynch (2010, and Altland et al (2011). These studies are concerned with 1=N , r 2 2 r 0 ( 1.…”

“…Using this process, Weinreich and Chao (2005) determined the critical population sizes for sequential fixation or stochastic tunneling, and Weissman et al (2009) calculated the rate of tunneling as a function of the mutation rates, population size, and relative fitness of cells harboring one mutation. Finally, these results were extended to investigate the effects of recombination, or sexual reproduction, on the rate of stochastic tunneling (Weissman et al 2010;Lynch 2010;Altland et al 2011). These authors found that the time to establishment of the double-mutant cells can be reduced by several orders of magnitude when sexual reproduction is considered (Weissman et al 2010).…”