A Coalescent Model for a Sweep of a Unique Standing Variant

The use of genetic polymorphism data to understand the dynamics of adaptation and identify the loci that are involved has become a major pursuit of modern evolutionary genetics. In addition to the classical “hard sweep” hitchhiking model, recent research has drawn attention to the fact that the dynamics of adaptation can play out in a variety of different ways and that the specific signatures left behind in population genetic data may depend somewhat strongly on these dynamics. One particular model for which a large number of empirical examples are already known is that in which a single derived mutation arises and drifts to some low frequency before an environmental change causes the allele to become beneficial and sweeps to fixation. Here, we pursue an analytical investigation of this model, bolstered and extended via simulation study. We use coalescent theory to develop an analytical approximation for the effect of a sweep from standing variation on the genealogy at the locus of the selected allele and sites tightly linked to it. We show that the distribution of haplotypes that the selected allele is present on at the time of the environmental change can be approximated by considering recombinant haplotypes as alleles in the infinite-alleles model. We show that this approximation can be leveraged to make accurate predictions regarding patterns of genetic polymorphism following such a sweep. We then use simulations to highlight which sources of haplotypic information are likely to be most useful in distinguishing this model from neutrality, as well as from other sweep models, such as the classic hard sweep and multiple-mutation soft sweeps. We find that in general, adaptation from a unique standing variant will likely be difficult to detect on the basis of genetic polymorphism data from a single population time point alone, and when it can be detected, it will be difficult to distinguish from other varieties of selective sweeps. Samples from multiple populations and/or time points have the potential to ease this difficulty.     

Coalescent patterns for chromosomal inversions in divergent populations

Chromosomal inversions allow genetic divergence of locally adapted populations by reducing recombination between chromosomes with different arrangements. Divergence between populations (or hybridization between species) is expected to leave signatures in the neutral genetic diversity of the inverted region. Quantitative expectations for these patterns, however, have not been obtained. Here, we develop coalescent models of neutral sites linked to an inversion polymorphism in two locally adapted populations. We consider two scenarios of local adaptation: selection on the inversion breakpoints and selection on alleles inside the inversion. We find that ancient inversion polymorphisms cause genetic diversity to depart dramatically from neutral expectations. Other situations, however, lead to patterns that may be difficult to detect; important determinants are the age of the inversion and the rate of gene flux between arrangements. We also study inversions under genetic drift, finding that they produce patterns similar to locally adapted inversions of intermediate age. Our results are consistent with empirical observations, and provide the foundation for quantitative analyses of the roles that inversions have played in speciation.     

The evolution of genetic architecture under frequency-dependent disruptive selection

We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.     

The evolution of genetic canalization under fluctuating selection

Abstract.— If the direction of selection changes from generation to generation, the ability to respond to selection is maladaptive: the response to selection in one generation leads to reduced fitness in the next. Because the response is determined by the amount of genetic variance expressed at the phenotypic level, rapidly fluctuating selection should favor modifier genes that reduce the phenotypic effect of alleles segregating at structural loci underlying the trait. Such reduction in phenotypic expression of genetic variation has been named "genetic canalization." I support this argument with a series of two- and multilocus models with alternating linear selection and Gaussian selection with fluctuating optimum. A canalizing modifier gene affects the fitness of its carriers in three ways: (1) it reduces the phenotypic consequences of genetic response to previous selection; (2) it reduces the genetic response to selection, which is manifested as linkage disequilibrium between the modifier and structural loci; and (3) it reduces the phenotypic variance. The first two effects reduce fitness under directional selection sustained for several generations, but improve fitness when the direction of selection has just been reversed. The net effect tends to favor a canalizing modifier under rapidly fluctuating selection regimes (period of eight generations or less). The third effect improves fitness of the modifier allele if the fitness function is convex and reduces it if the function is concave. Under fluctuating Gaussian selection, the population is more likely to experience the concave portion of the fitness function when selection is stronger. Therefore, only weak to moderately strong fluctuating Gaussian selection favors genetic canalization. This paper considerably broadens the conditions that favor genetic canalization, which so far has only been postulated to evolve under long-term stabilizing selection.     

Parallel evolutionary forces influence the evolution of male and female songs in a tropical songbird

Given the important role that animal vocalizations play in mate attraction and resource defence, acoustic signals are expected to play a significant role in speciation. Most studies, however, have focused on the acoustic traits of male animals living in the temperate zone. In contrast to temperate environments, in the tropics, it is commonplace for both sexes to produce complex acoustic signals. Therefore, tropical birds offer the opportunity to compare the sexes and provide a more comprehensive understanding of the evolution of animal signals. In this study, we quantified patterns of acoustic variation in Rufous‐and‐white Wrens (Thryophilus rufalbus) from five populations in Central America. We quantified similarities and differences between male and female songs by comparing the role that acoustic adaptation, cultural isolation and neutral genetic divergence have played in shaping acoustic divergence. We found that males and females showed considerable acoustic variation across populations, although females exhibited greater population divergence than males. Redundancy analysis and partial‐redundancy analysis revealed significant relationships between acoustic variation and ecological variables, genetic distance, and geographic distance. Both ambient background noise and geographic distance explained a high proportion of variance for both males and females, suggesting that both acoustic adaptation and cultural isolation influence song. Overall, our results indicate that parallel evolutionary forces act on male and female acoustic signals and highlight the important role that cultural drift and selection play in the evolution of both male and female songs.     

Social heterosis and the maintenance of genetic diversity at the genome level

Social heterosis is when individuals in groups or neighbourhoods receive a mutualistic benefit from across‐individual genetic diversity. Although it can be a viable evolutionary mechanism to maintain allelic diversity at a given locus, its efficacy at maintaining genome‐wide diversity is in question when multiple loci are being simultaneously selected. Therefore, we modelled social heterosis in a population of haploid genomes of two‐ or three‐linked loci. With such linkages, social heterosis decreases gametic diversity, but maintains allelic diversity. Genomes tend to survive as complimentary pairs, with alternate alleles at each locus (e.g. the pair AbC and aBc). The outcomes of selection appear similar to fitness epistasis but are novel in the sense that phenotypic interactions occur across rather than within individuals. The model’s results strongly suggest that strong linkage across gene loci actually increases the probability that social heterosis maintains significant genetic diversity at the level of the genome.     

The Coalescent Time in the Presence of Background Fertility Selection

Selection ultimately entails differential reproductive success over several generations. This can be measured as a correlation of the number of progeny an individual has with the number of progeny its parent had. This correlation could have a genetic or a cultural basis. The effect of such a correlation is to multiply the single generation sampling variance (Vdeltap) in the diffusion approximation for fixation time by (1-b)+bx(1+r)/(1-r), where bxrn is the correlation between the number of progeny of an individual and its ancestor n generations ago (e.g., b is the heritability and br is the resultant parent-offspring progeny number correlation if the progeny number is genetically determined). This results in a reduction of the fixation or coalescent time by division by this factor. Sex differences in this correlation have been observed, and this provides an explanation for the difference of coalescent times of y-chromosomes and mitochondria.     

Coalescent analyses support multiple mainland-to-island dispersals in the evolution of Malagasy Triaenops bats (Chiroptera: Hipposideridae)

Aim We investigate the directionality of mainland‐to‐island dispersals, focusing on a case study of an African‐Malagasy bat genus, Triaenops (Hipposideridae). Taxa include T. persicus from east Africa and three Triaenops species from Madagascar (T. auritus, T. furculus, and T. rufus). The evolution of this bat family considerably post‐dated the tectonic division of Madagascar from Africa, excluding vicariance as a viable hypothesis. Therefore, we consider three biogeographical scenarios to explain these species' current ranges: (A) a single dispersal from Africa to Madagascar with subsequent speciation of the Malagasy species; (B) multiple, unidirectional dispersals from Africa to Madagascar resulting in multiple, independent Malagasy lineages; or (C) early dispersal of a proto‐species from Africa to Madagascar, with later back‐dispersal of a descendant Malagasy taxon to Africa. Location East Africa, Madagascar, and the Mozambique Channel. Methods We compare the utility of phylogenetic and coalescent methodologies to address the question of directionality in a mainland‐to‐island dispersal event for recently diverged taxa. We also emphasize the application of biologically explicit demographic systems, such as the non‐equilibrium isolation‐with‐migration model. Here, these methods are applied to a four‐species haploid genetic data set, with simulation analyses being applied to validate this approach. Results Coalescent simulations favour scenario B: multiple, unidirectional dispersals from Africa to Madagascar resulting in multiple, independent Malagasy bat lineages. From coalescent dating, we estimate that the genus Triaenops was still a single taxon approximately 2.25 Ma. The most recent Africa to Madagascar dispersal occurred much more recently (c. 660 ka), and led to the formation of the extant Malagasy species, T. rufus. Main conclusions Haploid genetic data from four species of Triaenops are statistically most consistent with multiple, unidirectional dispersals from mainland Africa to Madagascar during the late Pleistocene.     

Genetic Variability Under the Seedbank Coalescent

We analyze patterns of genetic variability of populations in the presence of a large seedbank with the help of a new coalescent structure called the seedbank coalescent. This ancestral process appears naturally as a scaling limit of the genealogy of large populations that sustain seedbanks, if the seedbank size and individual dormancy times are of the same order as those of the active population. Mutations appear as Poisson processes on the active lineages and potentially at reduced rate also on the dormant lineages. The presence of “dormant” lineages leads to qualitatively altered times to the most recent common ancestor and nonclassical patterns of genetic diversity. To illustrate this we provide a Wright–Fisher model with a seedbank component and mutation, motivated from recent models of microbial dormancy, whose genealogy can be described by the seedbank coalescent. Based on our coalescent model, we derive recursions for the expectation and variance of the time to most recent common ancestor, number of segregating sites, pairwise differences, and singletons. Estimates (obtained by simulations) of the distributions of commonly employed distance statistics, in the presence and absence of a seedbank, are compared. The effect of a seedbank on the expected site-frequency spectrum is also investigated using simulations. Our results indicate that the presence of a large seedbank considerably alters the distribution of some distance statistics, as well as the site-frequency spectrum. Thus, one should be able to detect from genetic data the presence of a large seedbank in natural populations.     

Coalescent simulations of Yakut mtDNA variation suggest small founding population

The Yakuts are a Turkic‐speaking population from northeastern Siberia who are believed to have originated from ancient Turkic populations in South Siberia, based on archaeological and ethnohistorical evidence. In order to better understand Yakut origins, we modeled 25 demographic scenarios and tested by coalescent simulation whether any are consistent with the patterns of mtDNA diversity observed in present‐day Yakuts. The models consist of either two simulated demes that represent Yakuts and a South Siberian ancestral population, or three demes that also include a regional Northeast Siberian population that served as a source of local gene flow into the Yakut deme. The model that produced the best fit to the observed data defined a founder group with an effective female population size of only 150 individuals that migrated northwards approximately 1,000 years BP and who experienced significant admixture with neighboring populations in Northeastern Siberia. These simulation results indicate a pronounced founder effect that was primarily kin‐structured and reconcile reported discrepancies between Yakut mtDNA and Y chromosome diversity levels. Am J Phys Anthropol, 2009. © 2009 Wiley‐Liss, Inc.     

Bayesian Phylogenetic Inference using Relaxed-clocks and the Multispecies Coalescent

The multispecies coalescent (MSC) model accommodates both species divergences and within-species coalescent and provides a natural framework for phylogenetic analysis of genomic data when the gene trees vary across the genome. The MSC model implemented in the program bpp assumes a molecular clock and the Jukes–Cantor model, and is suitable for analyzing genomic data from closely related species. Here we extend our implementation to more general substitution models and relaxed clocks to allow the rate to vary among species. The MSC-with-relaxed-clock model allows the estimation of species divergence times and ancestral population sizes using genomic sequences sampled from contemporary species when the strict clock assumption is violated, and provides a simulation framework for evaluating species tree estimation methods. We conducted simulations and analyzed two real datasets to evaluate the utility of the new models. We confirm that the clock-JC model is adequate for inference of shallow trees with closely related species, but it is important to account for clock violation for distant species. Our simulation suggests that there is valuable phylogenetic information in the gene-tree branch lengths even if the molecular clock assumption is seriously violated, and the relaxed-clock models implemented in bpp are able to extract such information. Our Markov chain Monte Carlo algorithms suffer from mixing problems when used for species tree estimation under the relaxed clock and we discuss possible improvements. We conclude that the new models are currently most effective for estimating population parameters such as species divergence times when the species tree is fixed.     

Parallel plumage colour evolution and introgressive hybridization in wheatears

Genetic and phenotypic mosaics, in which various phenotypes and different genomic regions show discordant patterns of species or population divergence, offer unique opportunities to study the role of ancestral and introgressed genetic variation in phenotypic evolution. Here, we investigated the evolution of discordant phenotypic and genetic divergence in a monophyletic clade of four songbird taxa—pied wheatear (O. pleschanka), Cyprus wheatear (Oenanthe cypriaca), and western and eastern subspecies of black‐eared wheatear (O. h. hispanica and O. h. melanoleuca). Phenotypically, black back and neck sides distinguish pied and Cyprus wheatears from the white‐backed/necked black‐eared wheatears. Meanwhile, mitochondrial variation only distinguishes western black‐eared wheatear. In the absence of nuclear genetic data, and given frequent hybridization among eastern black‐eared and pied wheatear, it remains unclear whether introgression is responsible for discordance between mitochondrial divergence patterns and phenotypic similarities, or whether plumage coloration evolved in parallel. Multispecies coalescent analyses of about 20,000 SNPs obtained from RAD data mapped to a draft genome assembly resolve the species tree, provide evidence for the parallel evolution of colour phenotypes and establish western and eastern black‐eared wheatears as independent taxa that should be recognized as full species. The presence of the entire admixture spectrum in the Iranian hybrid zone and the detection of footprints of introgression from pied into eastern black‐eared wheatear beyond the hybrid zone despite strong geographic structure of ancestry proportions furthermore suggest a potential role for introgression in parallel plumage colour evolution. Our results support the importance of standing heterospecific and/or ancestral variation in phenotypic evolution.     

Coalescent inference for infectious disease: meta-analysis of hepatitis C

Genetic analysis of pathogen genomes is a powerful approach to investigating the population dynamics and epidemic history of infectious diseases. However, the theoretical underpinnings of the most widely used, coalescent methods have been questioned, casting doubt on their interpretation. The aim of this study is to develop robust population genetic inference for compartmental models in epidemiology. Using a general approach based on the theory of metapopulations, we derive coalescent models under susceptible–infectious (SI), susceptible–infectious–susceptible (SIS) and susceptible–infectious–recovered (SIR) dynamics. We show that exponential and logistic growth models are equivalent to SI and SIS models, respectively, when co-infection is negligible. Implementing SI, SIS and SIR models in BEAST, we conduct a meta-analysis of hepatitis C epidemics, and show that we can directly estimate the basic reproductive number (R₀) and prevalence under SIR dynamics. We find that differences in genetic diversity between epidemics can be explained by differences in underlying epidemiology (age of the epidemic and local population density) and viral subtype. Model comparison reveals SIR dynamics in three globally restricted epidemics, but most are better fit by the simpler SI dynamics. In summary, metapopulation models provide a general and practical framework for integrating epidemiology and population genetics for the purposes of joint inference.     

Efficient Strategies for Calculating Blockwise Likelihoods Under the Coalescent

The inference of demographic history from genome data is hindered by a lack of efficient computational approaches. In particular, it has proved difficult to exploit the information contained in the distribution of genealogies across the genome. We have previously shown that the generating function (GF) of genealogies can be used to analytically compute likelihoods of demographic models from configurations of mutations in short sequence blocks (Lohse et al. 2011). Although the GF has a simple, recursive form, the size of such likelihood calculations explodes quickly with the number of individuals and applications of this framework have so far been mainly limited to small samples (pairs and triplets) for which the GF can be written by hand. Here we investigate several strategies for exploiting the inherent symmetries of the coalescent. In particular, we show that the GF of genealogies can be decomposed into a set of equivalence classes that allows likelihood calculations from nontrivial samples. Using this strategy, we automated blockwise likelihood calculations for a general set of demographic scenarios in Mathematica. These histories may involve population size changes, continuous migration, discrete divergence, and admixture between multiple populations. To give a concrete example, we calculate the likelihood for a model of isolation with migration (IM), assuming two diploid samples without phase and outgroup information. We demonstrate the new inference scheme with an analysis of two individual butterfly genomes from the sister species Heliconius melpomene rosina and H. cydno.     

Evolution of coadaptation in a two-locus epistatic system

Although recent advances in genome biology have dramatically increased our understanding of the contribution of gene interactions to the development of complex phenotypes, we still lack general agreement on the process and mechanisms responsible for the evolution of epistatic systems. Even if genes in a species are indeed integrated into coadapted complexes of interacting components, simple additive evolution may eventually result in epistatic differentiation of populations. Consequently, the prevalence of epistatic gene action does not tell us anything about the role of epistatic selection in the history of population divergence. To elucidate the contribution of epistatic selection in the evolution of coadaptation, we investigate the fixation process of two mutations that interact synergistically to enhance fitness. We show by diffusion analysis and simulations that epistatic selection on cosegregating variants does not by itself promote the evolution of epistatic systems; rather, accumulation of neutral mutations may play a crucial role, creating an appropriate genetic milieu for adaptive evolution in the future generations.     

Epigenetic epistatic interactions constrain the evolution of gene expression

Reduced activity of two genes in combination often has a more detrimental effect than expected. Such epistatic interactions not only occur when genes are mutated but also due to variation in gene expression, including among isogenic individuals in a controlled environment. We hypothesized that these ‘epigenetic’ epistatic interactions could place important constraints on the evolution of gene expression. Consistent with this, we show here that yeast genes with many epistatic interaction partners typically show low expression variation among isogenic individuals and low variation across different conditions. In addition, their expression tends to remain stable in response to the accumulation of mutations and only diverges slowly between strains and species. Yeast promoter architectures, the retention of gene duplicates, and the divergence of expression between humans and chimps are also consistent with selective pressure to reduce the likelihood of harmful epigenetic epistatic interactions. Based on these and previous analyses, we propose that the tight regulation of epistatic interaction network hubs makes an important contribution to the maintenance of a robust, ‘canalized’ phenotype. Moreover, that epigenetic epistatic interactions may contribute substantially to fitness defects when single genes are deleted.     

Coalescent methods for estimating species trees from phylogenomic data

Genome-scale sequence data have become increasingly available in the phylogenetic studies for understanding the evolutionary histories of species. However, it is challenging to develop probabilistic models to account for heterogeneity of phylogenomic data. The multispecies coalescent model describes gene trees as independent random variables generated from a coalescence process occurring along the lineages of the species tree. Since the multispecies coalescent model allows gene trees to vary across genes, coalescent-based methods have been popularly used to account for heterogeneous gene trees in phylogenomic data analysis. In this paper, we summarize and evaluate the performance of coalescent-based methods for estimating species trees from genome-scale sequence data. We investigate the effects of deep coalescence and mutation on the performance of species tree estimation methods. We found that the coalescent-based methods perform well in estimating species trees for a large number of genes, regardless of the degree of deep coalescence and mutation. The performance of the coalescent methods is negatively correlated with the lengths of internal branches of the species tree.     

Epistasis can accelerate adaptive diversification in haploid asexual populations

A fundamental goal of the biological sciences is to determine processes that facilitate the evolution of diversity. These processes can be separated into ecological, physiological, developmental and genetic. An ecological process that facilitates diversification is frequency-dependent selection caused by competition. Models of frequency-dependent adaptive diversification have generally assumed a genetic basis of phenotype that is non-epistatic. Here, we present a model that indicates diversification is accelerated by an epistatic basis of phenotype in combination with a competition model that invokes frequency-dependent selection. Our model makes use of a genealogical model of epistasis and insights into the effects of balancing selection on the genealogical structure of a population to understand how epistasis can facilitate diversification. The finding that epistasis facilitates diversification may be informative with respect to empirical results that indicate an epistatic basis of phenotype in experimental bacterial populations that experienced adaptive diversification.     

The evolution of genetic architecture. I. Diversification of genetic backgrounds by genetic drift

The genetic architecture of a phenotype plays a critical role in determining phenotypic evolution through its effects on patterns of genetic variation. Genetic architecture is often considered to be constant in evolutionary quantitative genetic models. However, genetic architecture may be variable and itself evolve when there are dominance and epistatic interactions among alleles at the same and different loci, respectively. The evolution of genetic architecture by genetic drift is examined here by testing the breeding value of four standard inbred mouse strains mated across a set of 26 related recombinant quasi-inbred (RqI) lines generated from the intercross of the Large (LG/J) and Small (SM/J) inbred mouse strains. Phenotypes of interest include age-specific body weights, growth, and adult body composition. If the genetic architecture of these traits has differentiated by genetic drift during the production of the RqI strains, we should observe interactions between tester strain and RqI strain. The breeding values of the tester strains will change relative to one another depending on which RqI strain they are crossed to. The study included an average of 15.1 offspring per cross, over a total of 100 different crosses. Multivariate and univariate analyses of variance indicate that there is strongly significant interaction for all traits. Interaction is more pronounced in males than in females and accounted for an average of about 40% of the explained variation in males and 30% in females. These results indicate that the genetic architecture of these traits has differentiated by genetic drift in the RqI strains since their isolation from a common founder population. Further analysis indicates that this differentiation results in changes in the order of tester strain effects so that common patterns of selection in these differentiated populations could result in the fixation of different alleles.