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The Other Side of the Nearly Neutral Theory, Evidence of Slightly Advantageous Back-Mutations

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The Other Side of the Nearly Neutral Theory, Evidence of Slightly Advantageous Back-Mutations The other side of the nearly neutral theory, evidence of slightly advantageous back-mutations Jane Charlesworth and Adam Eyre-Walker* Centre for the Study of Evolution, School of Life Sciences, University of Sussex, Brighton BN1 9QG, United Kingdom Edited by Tomoko Ohta, National Institute of Genetics, Mishima, Japan, and approved September 5, 2007 (received for review June 13, 2007) We argue that if there is a category of slightly deleterious muta- deleterious with a disadvantage of Ϫs. Let us imagine that this tions, then there should be a category of slightly advantageous T mutation spreads through the population and becomes fixed. back-mutations. We show that when there are both slightly del- If a new C mutation then occurs at this site, it will be slightly eterious and advantageous back-mutations, there is likely to be an advantageous with an advantage of ϩs, unless the relative increase in the rate of evolution after a population size expansion. fitnesses of the C and T alleles have changed. Such a change in This increase in the rate of evolution is short-lived. However, we fitness could occur because of a change in the environment or the show how its signature can be captured by comparing the rate of fixation of mutations at other sites which have epistatic inter- evolution in species that have undergone population size expan- actions with the alleles at a site of interest. However, it seems sion versus contraction. We test our model by comparing the likely that fitnesses will remain approximately constant, at least pattern of evolution in pairs of island and mainland species in over moderate time scales. Models of evolution in which there which the colonization event was either island-to-mainland (pop- are slightly deleterious mutations and slightly advantageous ulation size expansion) or mainland-to-island (contraction). We mutations are familiar in the study of synonymous codon evo- show that the predicted pattern of evolution is observed. lution (27, 28), but they have rarely been considered in studies of protein evolution (although see refs. 24–26 and 29–31). t is now well established that there is a category of mutations Although we expect slightly advantageous mutations to exist, Ithat are slightly deleterious; these are deleterious mutations currently there is only limited evidence for their existence in real whose fate is determined by a combination of random genetic populations; analyses of McDonald–Kreitman (32) type data drift and selection. Four lines of evidence suggest that these within the context of the selection models proposed by Sawyer mutations exist. First, in many species, nonsynonymous muta- and Hartl (33) and Sawyer et al. (34) suggest that there are tions segregate at lower allelic frequencies on average than silent weakly selected advantageous mutations (34–37). However, mutations; this has been observed in humans (1), Drosophila (2, these data are also always consistent with strongly advantageous 3), and various bacteria (4, 5). There is also evidence that some mutations. mutations in noncoding DNA are slightly deleterious; in Dro- Here, we undertake to test for the presence of slightly sophila, mutations in introns and intergenic DNA tend to advantageous mutations by exploiting a property of models of segregate at lower frequencies than synonymous mutations (6), molecular evolution that contain both slightly deleterious and and, in humans, mutations in conserved noncoding sequences slightly advantageous mutations. Under the ‘‘classic’’ nearly (7) or sites (8) segregate at lower frequencies than mutations neutral model of molecular evolution (38), all mutations are outside these sequences or sites. Second, species that are ex- assumed to be neutral, slightly deleterious, or strongly deleteri- pected to have small effective population sizes have higher ratios ous, leading to the prediction that the rate of substitution will be of nonsynonymous to synonymous substitutions (9–15). A sim- higher for species and genomic regions with small effective ilar effect is apparent in the sequences upstream and down- population sizes. This prediction arises from the idea that stream of protein-coding sequences (16), and within conserved purifying selection is less efficient against slightly deleterious nongenic sequences in mammals (17); in both cases, these mutations in small populations than in large ones, allowing some sequences appear to be much less well conserved, relative to proportion of mildly deleterious mutations to drift to fixation in intron sequences, in hominids, which have small effective pop- small populations. However, as Gillespie (24) first noted, this ulation sizes, than in rodents, which probably have large effective simple pattern is not always predicted if the distribution of fitness population sizes. Third, regions of the genome with small effects allows some proportion of mutations to be advantageous. effective population sizes tend to show a higher ratio of non- If there is an expansion in effective population size, there will be synonymous to synonymous substitutions; this is particularly a temporary increase in the rate of substitution because of the apparent on the sex-specific chromosomes (18–20). Finally, in fixation of advantageous mutations that were previously effec- some species the ratio of nonsynonymous to synonymous poly- tively neutral. As a result, the rate of substitution is higher in the morphism is greater than the ratio of nonsynonymous to syn- population that has the larger effective population size for some onymous substitution. This is particularly evident in the mito- time after the expansion. Gillespie (24) did not formally dem- chondrial genome (21–23). Such a pattern is consistent with the onstrate this behavior, but Takano-Shimizu (39) has shown presence of slightly deleterious nonsynonymous mutations, be- theoretically that this increase in the rate of substitution occurs cause these contribute to polymorphism but rarely become fixed. in a model in which there are slightly deleterious and slightly There is, therefore, considerable evidence that slightly dele- advantageous back-mutations. terious mutations exist. However, models of molecular evolution in which all mutations are deleterious predict a decline in fitness, which is unrealistic, and one might reasonably expect there to be Author contributions: A.E.-W. designed research; J.C. and A.E.-W. performed research; J.C. slightly advantageous mutations if there are slightly deleterious and A.E.-W. analyzed data; and J.C. and A.E.-W. wrote the paper. mutations for two reasons. First, models of molecular evolution The authors declare no conflict of interest. that contain advantageous mutations generally predict there to This article is a PNAS Direct Submission. be a class of mutations that are slightly advantageous (24–26). *To whom correspondence should be addressed. E-mail: [email protected]. Second, simple back-mutation is expected to generate slightly This article contains supporting information online at www.pnas.org/cgi/content/full/ advantageous mutations. For example, let us imagine that a site 0705456104/DC1. is fixed for C, and that a new T mutation occurs that is slightly © 2007 by The National Academy of Sciences of the USA 16992–16997 ͉ PNAS ͉ October 23, 2007 ͉ vol. 104 ͉ no. 43 www.pnas.org͞cgi͞doi͞10.1073͞pnas.0705456104 Downloaded by guest on September 27, 2021 There are potentially many different models we could con- 2uSeS RЈ͑u, S͒ ϭ . [4] sider in which there are both slightly deleterious and advanta- ͑eS ϩ 1͒͑eS Ϫ 1͒ geous mutations (24). Here, we choose the simplest model, which has the clearest biological basis, a model in which each slightly Now, let us consider the dynamics of the system after the change deleterious mutation has a corresponding slightly advantageous in population size. Let us assume that the effective population back-mutation: i.e., if an A mutation at a site fixed for G is size becomes ␣ times larger than it was before the change in the deleterious, the G mutation at the same site fixed for A is population size t generations in the past. Solving Eq. 1, and advantageous with the same absolute strength of selection. This noting that we are assuming that the population was at equilib- model was previously considered by Takano-Shimizu (39). We rium before the increase/decrease in population size, we have confirm his result that there is an instantaneous increase in the Ϫ␶␾͑␣ ͒ ͑␾͑␣S ͒fЈ͑S͒ Ϫ Q͑␣S ͒͒e S0 ϩ Q͑␣S ͒ rate of substitution after an increase in effective population size ͑␣ ␶͒ ϭ 0 0 0 f , S0, ␾͑␣ ͒ , [5] and show that this increase can be substantial but that it is S0 relatively short-lived. However this pattern is seen only if some ␾ ␣ ϭ ␣ ϩ Ϫ␣ ␶ ϭ mutations are allowed to be slightly advantageous; if all muta- where ( S0) Q( S0) Q( S0), ut, and S0 is the value tions are assumed to be deleterious the rate of substitution is of S before the change in the population size. Substituting the always predicted to correlate negatively with effective popula- proportion of sites fixed for the A1 allele after the change in 5 3 tion size, regardless of whether an expansion in effective pop- population size given by Eq. into Eq. , we derive an expression for the rate of substitution after a population size change ulation size has occurred or not. We use a comparative frame- work to examine cases where there has been an expansion in ͑ ␣ ␶͒ ϭ ͑␣ ␶͒ ͑Ϫ␣ ͒ R u, , S0, f , S0, uQ S0 population size and those where there has been a contraction, by ϩ ͑ Ϫ ͑␣ ␶͒͒ ͑␣ ͒ choosing pairs of island and mainland species and classifying 1 f , S0, uQ S0 . [6] them according to the direction of colonization, island-to- mainland or mainland-to-island. We demonstrate statistically We have so far derived expressions for the rates of substitution significant support for models of molecular evolution that allow at equilibrium and after a population size change, for the case adaptive evolution through back-mutation.
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