John Wakeley

THE EFFECTS OF SUBDIVISION ON THE GENETIC DIVERGENCE OF POPULATIONS AND SPECIES

Abstract. An island model of migration is used to study the effects of subdivision within populations and species on sample genealogies and on between‐population or between‐species measures of genetic variation. The model assumes that the number of demes within each population or species is large. When populations (or species), connected either by gene flow or historical association, are themselves subdivided into demes, changes in the migration rate among demes alter both the structure of genealogies and the time scale of the coalescent process. The time scale of the coalescent is related to the effective size of the population, which depends on the migration rate among demes. When the migration rate among demes within populations is low, isolation (or speciation) events seem more recent and migration rates among populations seem higher because the effective size of each population is increased. This affects the probability of reciprocal monophyly of two samples, the chance that a gene tree of a sample matches the species tree, and relative likelihoods of different types of polymorphic sites. It can also have a profound effect on the estimation of divergence times.

The solitary wave of asexual evolution

Using a previously undescribed approach, we develop an analytic model that predicts whether an asexual population accumulates advantageous or deleterious mutations over time and the rate at which either process occurs. The model considers a large number of linked identical loci, or nucleotide sites; assumes that the selection coefficient per site is much less than the mutation rate per genome; and includes back and compensating mutations. Using analysis and Monte Carlo simulations, we demonstrate the accuracy of our results over almost the entire range of population sizes. Two limiting cases of our results, when either deleterious or advantageous mutations can be neglected, correspond to the Fisher–Muller effect and Mullers ratchet, respectively. By comparing predictions of our model (no recombination) to those of simple single-locus models (strong recombination), we show that the accumulation of advantageous mutations is slowed by linkage over a broad, finite range of population size. This supports the view of Fisher and Muller, who argued in the 1930s that progressive evolution of organisms is slowed because loci at which beneficial mutations can occur are often linked together on the same chromosome. These results follow from our main finding, that distribution of sequences over the mutation number evolves as a traveling wave whose speed and width depend on population size and other parameters. The model explains a logarithmic dependence of steady-state fitness on the population size reported recently for an RNA virus.

Coalescent processes when the distribution of offspring number among individuals is highly skewed.

We report a complex set of scaling relationships between mutation and reproduction in a simple model of a population. These follow from a consideration of patterns of genetic diversity in a sample of DNA sequences. Five different possible limit processes, each with a different scaled mutation parameter, can be used to describe genetic diversity in a large population. Only one of these corresponds to the usual population genetic model, and the others make drastically different predictions about genetic diversity. The complexity arises because individuals can potentially have very many offspring. To the extent that this occurs in a given species, our results imply that inferences from genetic data made under the usual assumptions are likely to be wrong. Our results also uncover a fundamental difference between populations in which generations are overlapping and those in which generations are discrete. We choose one of the five limit processes that appears to be appropriate for some marine organisms and use a sample of genetic data from a population of Pacific oysters to infer the parameters of the model. The data suggest the presence of rare reproduction events in which ∼8% of the population is replaced by the offspring of a single individual.

Evolutionary game dynamics in phenotype space

The emergence of cooperation in populations of selfish individuals is a fascinating topic that has inspired much work in theoretical biology. Here, we study the evolution of cooperation in a model where individuals are characterized by phenotypic properties that are visible to others. The population is well mixed in the sense that everyone is equally likely to interact with everyone else, but the behavioral strategies can depend on distance in phenotype space. We study the interaction of cooperators and defectors. In our model, cooperators cooperate with those who are similar and defect otherwise. Defectors always defect. Individuals mutate to nearby phenotypes, which generates a random walk of the population in phenotype space. Our analysis brings together ideas from coalescence theory and evolutionary game dynamics. We obtain a precise condition for natural selection to favor cooperators over defectors. Cooperation is favored when the phenotypic mutation rate is large and the strategy mutation rate is small. In the optimal case for cooperators, in a one-dimensional phenotype space and for large population size, the critical benefit-to-cost ratio is given by b/c=1+2/3. We also derive the fundamental condition for any two-strategy symmetric game and consider high-dimensional phenotype spaces.

Loss and Recovery of Genetic Diversity in Adapting Populations of HIV

The evolution of drug resistance in HIV occurs by the fixation of specific, well-known, drug-resistance mutations, but the underlying population genetic processes are not well understood. By analyzing within-patient longitudinal sequence data, we make four observations that shed a light on the underlying processes and allow us to infer the short-term effective population size of the viral population in a patient. Our first observation is that the evolution of drug resistance usually occurs by the fixation of one drug-resistance mutation at a time, as opposed to several changes simultaneously. Second, we find that these fixation events are accompanied by a reduction in genetic diversity in the region surrounding the fixed drug-resistance mutation, due to the hitchhiking effect. Third, we observe that the fixation of drug-resistance mutations involves both hard and soft selective sweeps. In a hard sweep, a resistance mutation arises in a single viral particle and drives all linked mutations with it when it spreads in the viral population, which dramatically reduces genetic diversity. On the other hand, in a soft sweep, a resistance mutation occurs multiple times on different genetic backgrounds, and the reduction of diversity is weak. Using the frequency of occurrence of hard and soft sweeps we estimate the effective population size of HIV to be ( confidence interval ). This number is much lower than the actual number of infected cells, but much larger than previous population size estimates based on synonymous diversity. We propose several explanations for the observed discrepancies. Finally, our fourth observation is that genetic diversity at non-synonymous sites recovers to its pre-fixation value within 18 months, whereas diversity at synonymous sites remains depressed after this time period. These results improve our understanding of HIV evolution and have potential implications for treatment strategies.

Metapopulation models for historical inference

The genealogical process for a sample from a metapopulation, in which local populations are connected by migration and can undergo extinction and subsequent recolonization, is shown to have a relatively simple structure in the limit as the number of populations in the metapopulation approaches infinity. The result, which is an approximation to the ancestral behaviour of samples from a metapopulation with a large number of populations, is the same as that previously described for other metapopulation models, namely that the genealogical process is closely related to Kingmans unstructured coalescent. The present work considers a more general class of models that includes two kinds of extinction and recolonization, and the possibility that gamete production precedes extinction. In addition, following other recent work, this result for a metapopulation divided into many populations is shown to hold both for finite population sizes and in the usual diffusion limit, which assumes that population sizes are large. Examples illustrate when the usual diffusion limit is appropriate and when it is not. Some shortcomings and extensions of the model are considered, and the relevance of such models to understanding human history is discussed.

Complex speciation of humans and chimpanzees

Arising from: N. Patterson, D. J. Richter, S. Gnerre, E. Lander & D. Reich 441, 1103–1108 (2006)10.1038/nature04789; Patterson et al. replyGenetic data from two or more species provide information about the process of speciation. In their analysis of DNA from humans, chimpanzees, gorillas, orangutans and macaques (HCGOM), Patterson et al. suggest that the apparently short divergence time between humans and chimpanzees on the X chromosome is explained by a massive interspecific hybridization event in the ancestry of these two species. However, Patterson et al. do not statistically test their own null model of simple speciation before concluding that speciation was complex, and—even if the null model could be rejected—they do not consider other explanations of a short divergence time on the X chromosome. These include natural selection on the X chromosome in the common ancestor of humans and chimpanzees, changes in the ratio of male-to-female mutation rates over time, and less extreme versions of divergence with gene flow (see ref. 2, for example). I therefore believe that their claim of hybridization is unwarranted.

Extensions of the Coalescent Effective Population Size

We suggest two extensions of the coalescent effective population size of Sjödin et al. (2005) and make a third, practical point. First, to bolster its relevance to data and allow comparisons between models, the coalescent effective size should be recast as a kind of mutation effective size. Second, the requirement that the coalescent effective population size must depend linearly on the actual population size should be lifted. Third, even if the coalescent effective population size does not exist in the mathematical sense, it may be difficult to reject Kingmans coalescent using genetic data.

GENOME STRUCTURE AND THE BENEFIT OF SEX

We examine the behavior of sexual and asexual populations in modular multipeaked fitness landscapes and show that sexuals can systematically reach different, higher fitness adaptive peaks than asexuals. Whereas asexuals must move against selection to escape local optima, sexuals reach higher fitness peaks reliably because they create specific genetic variants that “skip over” fitness valleys, moving from peak to peak in the fitness landscape. This occurs because recombination can supply combinations of mutations in functional composites or “modules,” that may include individually deleterious mutations. Thus when a beneficial module is substituted for another less‐fit module by sexual recombination it provides a genetic variant that would require either several specific simultaneous mutations in an asexual population or a sequence of individual mutations some of which would be selected against. This effect requires modular genomes, such that subsets of strongly epistatic mutations are tightly physically linked. We argue that such a structure is provided simply by virtue of the fact that genomes contain many genes each containing many strongly epistatic nucleotides. We briefly discuss the connections with “building blocks” in the evolutionary computation literature. We conclude that there are conditions in which sexuals can systematically evolve high‐fitness genotypes that are essentially unevolvable for asexuals.

Coalescence Times and FST Under a Skewed Offspring Distribution Among Individuals in a Population

Estimates of gene flow between subpopulations based on FST (or NST) are shown to be confounded by the reproduction parameters of a model of skewed offspring distribution. Genetic evidence of population subdivision can be observed even when gene flow is very high, if the offspring distribution is skewed. A skewed offspring distribution arises when individuals can have very many offspring with some probability. This leads to high probability of identity by descent within subpopulations and results in genetic heterogeneity between subpopulations even when Nm is very large. Thus, we consider a limiting model in which the rates of coalescence and migration can be much higher than for a Wright–Fisher population. We derive the densities of pairwise coalescence times and expressions for FST and other statistics under both the finite island model and a many-demes limit model. The results can explain the observed genetic heterogeneity among subpopulations of certain marine organisms despite substantial gene flow.