Exact Calculation of the Joint Allele Frequency Spectrum for Isolation with Migration Models

Conditional frequency spectra as a tool for studying selection on complex traits in biobanks

Natural selection on complex traits is difficult to study in part due to the ascertainment inherent to genome-wide association studies (GWAS). The power to detect a trait-associated variant in GWAS is a function of frequency and effect size - but for traits under selection, the effect size of a variant determines the strength of selection against it, constraining its frequency. To account for GWAS ascertainment, we propose studying the joint distribution of allele frequencies across populations, conditional on the frequencies in the GWAS cohort. Before considering these conditional frequency spectra, we first characterized the impact of selection and non-equilibrium demography on allele frequency dynamics forwards and backwards in time. We then used these results to understand conditional frequency spectra under realistic human demography. Finally, we investigated empirical conditional frequency spectra for GWAS variants associated with 106 complex traits, finding compelling evidence for either stabilizing or purifying selection. Our results provide insight into polygenic score portability and other properties of variants ascertained with GWAS, highlighting the utility of conditional frequency spectra.

Computationally Efficient Demographic History Inference from Allele Frequencies with Supervised Machine Learning

Inferring past demographic history of natural populations from genomic data is of central concern in many studies across research fields. Previously, our group had developed dadi, a widely used demographic history inference method based on the allele frequency spectrum (AFS) and maximum composite-likelihood optimization. However, dadi's optimization procedure can be computationally expensive. Here, we present donni (demography optimization via neural network inference), a new inference method based on dadi that is more efficient while maintaining comparable inference accuracy. For each dadi-supported demographic model, donni simulates the expected AFS for a range of model parameters then trains a set of Mean Variance Estimation neural networks using the simulated AFS. Trained networks can then be used to instantaneously infer the model parameters from future genomic data summarized by an AFS. We demonstrate that for many demographic models, donni can infer some parameters, such as population size changes, very well and other parameters, such as migration rates and times of demographic events, fairly well. Importantly, donni provides both parameter and confidence interval estimates from input AFS with accuracy comparable to parameters inferred by dadi's likelihood optimization while bypassing its long and computationally intensive evaluation process. donni's performance demonstrates that supervised machine learning algorithms may be a promising avenue for developing more sustainable and computationally efficient demographic history inference methods.

Computationally efficient demographic history inference from allele frequencies with supervised machine learning

Inferring past demographic history of natural populations from genomic data is of central concern in many studies across research fields. Previously, our group had developed dadi, a widely used demographic history inference method based on the allele frequency spectrum (AFS) and maximum composite likelihood optimization. However, dadi's optimization procedure can be computationally expensive. Here, we developed donni (demography optimization via neural network inference), a new inference method based on dadi that is more efficient while maintaining comparable inference accuracy. For each dadi-supported demographic model, donni simulates the expected AFS for a range of model parameters then trains a set of Mean Variance Estimation neural networks using the simulated AFS. Trained networks can then be used to instantaneously infer the model parameters from future input data AFS. We demonstrated that for many demographic models, donni can infer some parameters, such as population size changes, very well and other parameters, such as migration rates and times of demographic events, fairly well. Importantly, donni provides both parameter and confidence interval estimates from input AFS with accuracy comparable to parameters inferred by dadi's likelihood optimization while bypassing its long and computationally intensive evaluation process. donni's performance demonstrates that supervised machine learning algorithms may be a promising avenue for developing more sustainable and computationally efficient demographic history inference methods.

Recurrent mutation in the ancestry of a rare variant

Recurrent mutation produces multiple copies of the same allele which may be co-segregating in a population. Yet, most analyses of allele-frequency or site-frequency spectra assume that all observed copies of an allele trace back to a single mutation. We develop a sampling theory for the number of latent mutations in the ancestry of a rare variant, specifically a variant observed in relatively small count in a large sample. Our results follow from the statistical independence of low-count mutations, which we show to hold for the standard neutral coalescent or diffusion model of population genetics as well as for more general coalescent trees. For populations of constant size, these counts are distributed like the number of alleles in the Ewens sampling formula. We develop a Poisson sampling model for populations of varying size and illustrate it using new results for site-frequency spectra in an exponentially growing population. We apply our model to a large data set of human SNPs and use it to explain dramatic differences in site-frequency spectra across the range of mutation rates in the human genome.

Patterns of Population Structure and Introgression Among Recently Differentiated Drosophila melanogaster Populations

Despite a century of genetic analysis, the evolutionary processes that have generated the patterns of exceptional genetic and phenotypic variation in the model organism Drosophila melanogaster remains poorly understood. In particular, how genetic variation is partitioned within its putative ancestral range in Southern Africa remains unresolved. Here, we study patterns of population genetic structure, admixture, and the spatial structuring of candidate incompatibility alleles across a global sample, including 223 new accessions, predominantly from remote regions in Southern Africa. We identify nine major ancestries, six that primarily occur in Africa and one that has not been previously described. We find evidence for both contemporary and historical admixture between ancestries, with admixture rates varying both within and between continents. For example, while previous work has highlighted an admixture zone between broadly defined African and European ancestries in the Caribbean and southeastern USA, we identify West African ancestry as the most likely African contributor. Moreover, loci showing the strongest signal of introgression between West Africa and the Caribbean/southeastern USA include several genes relating to neurological development and male courtship behavior, in line with previous work showing shared mating behaviors between these regions. Finally, while we hypothesized that potential incompatibility loci may contribute to population genetic structure across the range of D. melanogaster; these loci are, on average, not highly differentiated between ancestries. This work contributes to our understanding of the evolutionary history of a key model system, and provides insight into the partitioning of diversity across its range.

Effects of the neo-X chromosome on genomic signatures of hybridization in Rumex hastatulus

Natural hybrid zones provide opportunities for studies of the evolution of reproductive isolation in wild populations. Although recent investigations have found that the formation of neo-sex chromosomes is associated with reproductive isolation, the mechanisms remain unclear in most cases. Here, we assess the contemporary structure of gene flow in the contact zone between largely allopatric cytotypes of the dioecious plant Rumex hastatulus, a species with evidence of sex chromosome turn-over. Males to the west of the Mississippi river, USA, have an X and a single Y chromosome, whereas populations to the east of the river have undergone a chromosomal rearrangement giving rise to a larger X and two Y chromosomes. Using reduced-representation sequencing, we provide evidence that hybrids form readily and survive multiple backcross generations in the field, demonstrating the potential for ongoing gene flow between the cytotypes. Cline analysis of each chromosome separately captured no signals of difference in cline shape between chromosomes. However, principal component regression revealed a significant increase in the contribution of individual SNPs to inter-cytotype differentiation on the neo-X chromosome, but no correlation with recombination rate. Cline analysis revealed that the only SNPs with significantly steeper clines than the genome average were located on the neo-X. Our data are consistent with a role for neo-sex chromosomes in reproductive isolation between R. hastatulus cytotypes. Our investigation highlights the importance of studying plant hybrid zones for understanding the evolution of sex chromosomes.

Multispecies coalescent and its applications to infer species phylogenies and cross-species gene flow

Multispecies coalescent (MSC) is the extension of the single-population coalescent model to multiple species. It integrates the phylogenetic process of species divergences and the population genetic process of coalescent, and provides a powerful framework for a number of inference problems using genomic sequence data from multiple species, including estimation of species divergence times and population sizes, estimation of species trees accommodating discordant gene trees, inference of cross-species gene flow and species delimitation. In this review, we introduce the major features of the MSC model, discuss full-likelihood and heuristic methods of species tree estimation and summarize recent methodological advances in inference of cross-species gene flow. We discuss the statistical and computational challenges in the field and research directions where breakthroughs may be likely in the next few years.

Studying models of balancing selection using phase-type theory

Balancing selection (BLS) is the evolutionary force that maintains high levels of genetic variability in many important genes. To further our understanding of its evolutionary significance, we analyze models with BLS acting on a biallelic locus: an equilibrium model with long-term BLS, a model with long-term BLS and recent changes in population size, and a model of recent BLS. Using phase-type theory, a mathematical tool for analyzing continuous time Markov chains with an absorbing state, we examine how BLS affects polymorphism patterns in linked neutral regions, as summarized by nucleotide diversity, the expected number of segregating sites, the site frequency spectrum, and the level of linkage disequilibrium (LD). Long-term BLS affects polymorphism patterns in a relatively small genomic neighborhood, and such selection targets are easier to detect when the equilibrium frequencies of the selected variants are close to 50%, or when there has been a population size reduction. For a new mutation subject to BLS, its initial increase in frequency in the population causes linked neutral regions to have reduced diversity, an excess of both high and low frequency derived variants, and elevated LD with the selected locus. These patterns are similar to those produced by selective sweeps, but the effects of recent BLS are weaker. Nonetheless, compared to selective sweeps, nonequilibrium polymorphism and LD patterns persist for a much longer period under recent BLS, which may increase the chance of detecting such selection targets. An R package for analyzing these models, among others (e.g., isolation with migration), is available.

Inference of gene flow in the process of speciation: Efficient maximum-likelihood implementation of a generalised isolation-with-migration model

The 'isolation with migration' (IM) model has been extensively used in the literature to detect gene flow during the process of speciation. In this model, an ancestral population split into two or more descendant populations which subsequently exchanged migrants at a constant rate until the present. Of course, the assumption of constant gene flow until the present is often over-simplistic in the context of speciation. In this paper, we consider a 'generalised IM' (GIM) model: a two-population IM model in which migration rates and population sizes are allowed to change at some point in the past. By developing a maximum-likelihood implementation of this model, we enable inference on both historical and contemporary rates of gene flow between two closely related populations or species. The GIM model encompasses both the standard two-population IM model and the 'isolation with initial migration' (IIM) model as special cases, as well as a model of secondary contact. We examine for simulated data how our method can be used, by means of likelihood ratio tests or AIC scores, to distinguish between the following scenarios of population divergence: (a) divergence in complete isolation; (b) divergence with a period of gene flow followed by isolation; (c) divergence with a period of isolation followed by secondary contact; (d) divergence with ongoing gene flow. Our method is based on the coalescent and is suitable for data sets consisting of the number of nucleotide differences between one pair of DNA sequences at each of a large number of independent loci. As our method relies on an explicit expression for the likelihood, it is computationally very fast.

Recurrent Collection of Drosophila melanogaster from Wild African Environments and Genomic Insights into Species History

A long-standing enigma concerns the geographic and ecological origins of the intensively studied vinegar fly, Drosophila melanogaster. This globally distributed human commensal is thought to originate from sub-Saharan Africa, yet until recently, it had never been reported from undisturbed wilderness environments that could reflect its precommensal niche. Here, we document the collection of 288 D. melanogaster individuals from multiple African wilderness areas in Zambia, Zimbabwe, and Namibia. The presence of D. melanogaster in these remote woodland environments is consistent with an ancestral range in southern-central Africa, as opposed to equatorial regions. After sequencing the genomes of 17 wilderness-collected flies collected from Kafue National Park in Zambia, we found reduced genetic diversity relative to town populations, elevated chromosomal inversion frequencies, and strong differences at specific genes including known insecticide targets. Combining these genomes with existing data, we probed the history of this species' geographic expansion. Demographic estimates indicated that expansion from southern-central Africa began ∼10,000 years ago, with a Saharan crossing soon after, but expansion from the Middle East into Europe did not begin until roughly 1,400 years ago. This improved model of demographic history will provide an important resource for future evolutionary and genomic studies of this key model organism. Our findings add context to the history of D. melanogaster, while opening the door for future studies on the biological basis of adaptation to human environments.

Ancestral and neo-sex chromosomes contribute to population divergence in a dioecious plant

Empirical evidence from several animal groups suggests sex chromosomes disproportionately contribute to reproductive isolation. This effect may be enhanced when sex chromosomes are associated with turnover of sex determination systems resulting from structural rearrangements to the chromosomes. We investigated these predictions in the dioecious plant Rumex hastatulus, which is composed of populations of two different sex chromosome cytotypes caused by an X-autosome fusion. Using population genomic analyses, we investigated the demographic history of R. hastatulus and explored the contributions of ancestral and neo-sex chromosomes to population genetic divergence. Our study revealed that the cytotypes represent genetically divergent populations with evidence for historical but not contemporary gene flow between them. In agreement with classical predictions, we found that the ancestral X chromosome was disproportionately divergent compared with the rest of the genome. Excess differentiation was also observed on the Y chromosome, even when we used measures of differentiation that control for differences in effective population size. Our estimates of the timing of the origin of neo-sex chromosomes in R. hastatulus are coincident with cessation of gene flow, suggesting that the chromosomal fusion event that gave rise to the origin of the XYY cytotype may have also contributed to reproductive isolation.

Wild African Drosophila melanogaster Are Seasonal Specialists on Marula Fruit

Although the vinegar fly Drosophila melanogaster is arguably the most studied organism on the planet, fundamental aspects of this species' natural ecology have remained enigmatic [1]. We have here investigated a wild population of D. melanogaster from a mopane forest in Zimbabwe. We find that these flies are closely associated with marula fruit (Sclerocarya birrea) and propose that this seasonally abundant and predominantly Southern African fruit is a key ancestral host of D. melanogaster. Moreover, when fruiting, marula is nearly exclusively used by D. melanogaster, suggesting that these forest-dwelling D. melanogaster are seasonal specialists, in a similar manner to, e.g., Drosophila erecta on screw pine cones [2]. We further demonstrate that the main chemicals released by marula activate odorant receptors that mediate species-specific host choice (Or22a) [3, 4] and oviposition site selection (Or19a) [5]. The Or22a-expressing neurons-ab3A-respond strongly to the marula ester ethyl isovalerate, a volatile rarely encountered in high amounts in other fruit. We also show that Or22a differs among African populations sampled from a wide range of habitats, in line with a function associated with host fruit usage. Flies from Southern Africa, most of which carry a distinct allele at the Or22a/Or22b locus, have ab3A neurons that are more sensitive to ethyl isovalerate than, e.g., European flies. Finally, we discuss the possibility that marula, which is also a culturally and nutritionally important resource to humans, may have helped the transition to commensalism in D. melanogaster.

Estimating the Timing of Multiple Admixture Pulses During Local Ancestry Inference

Admixture, the mixing of genetically distinct populations, is increasingly recognized as a fundamental biological process. One major goal of admixture analyses is to estimate the timing of admixture events. Whereas most methods today can only detect the most recent admixture event, here, we present coalescent theory and associated software that can be used to estimate the timing of multiple admixture events in an admixed population. We extensively validate this approach and evaluate the conditions under which it can successfully distinguish one- from two-pulse admixture models. We apply our approach to real and simulated data of Drosophila melanogaster We find evidence of a single very recent pulse of cosmopolitan ancestry contributing to African populations, as well as evidence for more ancient admixture among genetically differentiated populations in sub-Saharan Africa. These results suggest our method can quantify complex admixture histories involving genetic material introduced by multiple discrete admixture pulses. The new method facilitates the exploration of admixture and its contribution to adaptation, ecological divergence, and speciation.

Impacts of Recurrent Hitchhiking on Divergence and Demographic Inference in Drosophila

In species with large population sizes such as Drosophila, natural selection may have substantial effects on genetic diversity and divergence. However, the implications of this widespread nonneutrality for standard population genetic assumptions and practices remain poorly resolved. Here, we assess the consequences of recurrent hitchhiking (RHH), in which selective sweeps occur at a given rate randomly across the genome. We use forward simulations to examine two published RHH models for D. melanogaster, reflecting relatively common/weak and rare/strong selection. We find that unlike the rare/strong RHH model, the common/weak model entails a slight degree of Hill-Robertson interference in high recombination regions. We also find that the common/weak RHH model is more consistent with our genome-wide estimate of the proportion of substitutions fixed by natural selection between D. melanogaster and D. simulans (19%). Finally, we examine how these models of RHH might bias demographic inference. We find that these RHH scenarios can bias demographic parameter estimation, but such biases are weaker for parameters relating recently diverged populations, and for the common/weak RHH model in general. Thus, even for species with important genome-wide impacts of selective sweeps, neutralist demographic inference can have some utility in understanding the histories of recently diverged populations.