Statistical Inference in the Wright-Fisher Model Using Allele Frequency Data

Limits on the evolutionary rates of biological traits

This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These rate limits link the variability in a population to evolutionary rates. In particular, high variances in the fitness of a population and of a quantitative trait allow for fast changes in the trait's average. In contrast, low variability makes a trait less susceptible to random changes due to genetic drift. The results in this article generalize Fisher's fundamental theorem of natural selection to dynamics that allow for mutations and genetic drift, via trade-off relations that constrain the evolutionary rates of arbitrary traits. The rate limits can be used to probe questions in various evolutionary biology and ecology settings. They apply, for instance, to trait dynamics within or across species or to the evolution of bacteria strains. They apply to any quantitative trait, e.g., from species' weights to the lengths of DNA strands.

A mechanistic model of gossip, reputations, and cooperation

Social reputations facilitate cooperation: those who help others gain a good reputation, making them more likely to receive help themselves. But when people hold private views of one another, this cycle of indirect reciprocity breaks down, as disagreements lead to the perception of unjustified behavior that ultimately undermines cooperation. Theoretical studies often assume population-wide agreement about reputations, invoking rapid gossip as an endogenous mechanism for reaching consensus. However, the theory of indirect reciprocity lacks a mechanistic description of how gossip actually generates consensus. Here, we develop a mechanistic model of gossip-based indirect reciprocity that incorporates two alternative forms of gossip: exchanging information with randomly selected peers or consulting a single gossip source. We show that these two forms of gossip are mathematically equivalent under an appropriate transformation of parameters. We derive an analytical expression for the minimum amount of gossip required to reach sufficient consensus and stabilize cooperation. We analyze how the amount of gossip necessary for cooperation depends on the benefits and costs of cooperation, the assessment rule (social norm), and errors in reputation assessment, strategy execution, and gossip transmission. Finally, we show that biased gossip can either facilitate or hinder cooperation, depending on the direction and magnitude of the bias. Our results contribute to the growing literature on cooperation facilitated by communication, and they highlight the need to study strategic interactions coupled with the spread of social information.

A novel expectation-maximization approach to infer general diploid selection from time-series genetic data

Detecting and quantifying the strength of selection is a main objective in population genetics. Since selection acts over multiple generations, many approaches have been developed to detect and quantify selection using genetic data sampled at multiple points in time. Such time series genetic data is commonly analyzed using Hidden Markov Models, but in most cases, under the assumption of additive selection. However, many examples of genetic variation exhibiting non-additive mechanisms exist, making it critical to develop methods that can characterize selection in more general scenarios. Thus, we extend a previously introduced expectation-maximization algorithm for the inference of additive selection coefficients to the case of general diploid selection, in which heterozygote and homozygote fitnesses are parameterized independently. We furthermore introduce a framework to identify bespoke modes of diploid selection from given data, as well as a procedure for aggregating data across linked loci to increase power and robustness. Using extensive simulation studies, we find that our method accurately and efficiently estimates selection coefficients for different modes of diploid selection across a wide range of scenarios; however, power to classify the mode of selection is low unless selection is very strong. We apply our method to ancient DNA samples from Great Britain in the last 4,450 years, and detect evidence for selection in six genomic regions, including the well-characterized LCT locus. Our work is the first genome-wide scan characterizing signals of general diploid selection.

Self-contained Beta-with-Spikes approximation for inference under a Wright-Fisher model

We construct a reliable estimation method for evolutionary parameters within the Wright-Fisher model, which describes changes in allele frequencies due to selection and genetic drift, from time-series data. Such data exist for biological populations, for example via artificial evolution experiments, and for the cultural evolution of behavior, such as linguistic corpora that document historical usage of different words with similar meanings. Our method of analysis builds on a Beta-with-Spikes approximation to the distribution of allele frequencies predicted by the Wright-Fisher model. We introduce a self-contained scheme for estimating parameters in the approximation, and demonstrate its robustness with synthetic data, especially in the strong-selection and near-extinction regimes where previous approaches fail. We further apply the method to allele frequency data for baker's yeast (Saccharomyces cerevisiae), finding a significant signal of selection in cases where independent evidence supports such a conclusion. We further demonstrate the possibility of detecting time points at which evolutionary parameters change in the context of a historical spelling reform in the Spanish language.

Reversions mask the contribution of adaptive evolution in microbiomes

When examining bacterial genomes for evidence of past selection, the results obtained depend heavily on the mutational distance between chosen genomes. Even within a bacterial species, genomes separated by larger mutational distances exhibit stronger evidence of purifying selection as assessed by d N / d S , the normalized ratio of nonsynonymous to synonymous mutations. This dependence on mutational distance, and thus time, has been proposed to arise from the inefficiency of purifying selection at removing weakly deleterious mutations. Here, we revisit this assumption in light of abundant genomes from gut microbiomes and show that a model of weak purifying selection that fits the data leads to problematic mutation accumulation. We propose an alternative model to explain the timescale dependence of d N / d S , in which constantly changing environmental pressures select for revertants of previously adaptive mutations. Reversions that sweep within-host populations are nearly guaranteed in microbiomes due to large population sizes, short generation times, and variable environments. Using analytical and simulation approaches, we fit the adaptive reversion model to d N / d S decay curves and obtain estimates of local adaptation that are realistic in the context of bacterial genomes. These results argue for interpreting low values of d N / d S with caution, as they may emerge even when adaptive sweeps are frequent. This work reframes an old observation in bacterial evolution, illustrates the potential of mutation reversions to shape genomic landscapes over time, and highlights the need for additional research on bacterial genomic evolution on short time scales.

Bézier interpolation improves the inference of dynamical models from data

Many dynamical systems, from quantum many-body systems to evolving populations to financial markets, are described by stochastic processes. Parameters characterizing such processes can often be inferred using information integrated over stochastic paths. However, estimating time-integrated quantities from real data with limited time resolution is challenging. Here, we propose a framework for accurately estimating time-integrated quantities using Bézier interpolation. We applied our approach to two dynamical inference problems: Determining fitness parameters for evolving populations and inferring forces driving Ornstein-Uhlenbeck processes. We found that Bézier interpolation reduces the estimation bias for both dynamical inference problems. This improvement was especially noticeable for data sets with limited time resolution. Our method could be broadly applied to improve accuracy for other dynamical inference problems using finitely sampled data.

Large-effect loci mediate rapid adaptation of salmon body size after river regulation

Understanding the potential of natural populations to adapt to altered environments is becoming increasingly relevant in evolutionary research. Currently, our understanding of adaptation to human alteration of the environment is hampered by lack of knowledge on the genetic basis of traits, lack of time series, and little or no information on changes in optimal trait values. Here, we used time series data spanning nearly a century to investigate how the body mass of Atlantic salmon (Salmo salar) adapts to river regulation. We found that the change in body mass followed the change in waterflow, both decreasing to ∼1/3 of their original values. Allele frequency changes at two loci in the regions of vgll3 and six6 predicted more than 80% of the observed body mass reduction. Modeling the adaptive dynamics revealed that the population mean lagged behind its optimum before catching up approximately six salmon generations after the initial waterflow reduction. Our results demonstrate rapid adaptation mediated by large-effect loci and provide insight into the temporal dynamics of evolutionary rescue following human disturbance.

Inferring Epistasis from Genetic Time-series Data

Epistasis refers to fitness or functional effects of mutations that depend on the sequence background in which these mutations arise. Epistasis is prevalent in nature, including populations of viruses, bacteria, and cancers, and can contribute to the evolution of drug resistance and immune escape. However, it is difficult to directly estimate epistatic effects from sampled observations of a population. At present, there are very few methods that can disentangle the effects of selection (including epistasis), mutation, recombination, genetic drift, and genetic linkage in evolving populations. Here we develop a method to infer epistasis, along with the fitness effects of individual mutations, from observed evolutionary histories. Simulations show that we can accurately infer pairwise epistatic interactions provided that there is sufficient genetic diversity in the data. Our method also allows us to identify which fitness parameters can be reliably inferred from a particular data set and which ones are unidentifiable. Our approach therefore allows for the inference of more complex models of selection from time-series genetic data, while also quantifying uncertainty in the inferred parameters.

Direct detection of natural selection in Bronze Age Britain

We developed a novel method for efficiently estimating time-varying selection coefficients from genome-wide ancient DNA data. In simulations, our method accurately recovers selective trajectories and is robust to misspecification of population size. We applied it to a large data set of ancient and present-day human genomes from Britain and identified seven loci with genome-wide significant evidence of selection in the past 4500 yr. Almost all of them can be related to increased vitamin D or calcium levels, suggesting strong selective pressure on these or related phenotypes. However, the strength of selection on individual loci varied substantially over time, suggesting that cultural or environmental factors moderated the genetic response. Of 28 complex anthropometric and metabolic traits, skin pigmentation was the only one with significant evidence of polygenic selection, further underscoring the importance of phenotypes related to vitamin D. Our approach illustrates the power of ancient DNA to characterize selection in human populations and illuminates the recent evolutionary history of Britain.

Dynamic sampling bias and overdispersion induced by skewed offspring distributions

Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population expansions. The resulting allele-frequency fluctuations are large and, therefore, challenge standard models of population genetics, which assume sufficiently narrow offspring distributions. While the neutral dynamics backward in time can be readily analyzed using coalescent approaches, we still know little about the effect of broad offspring distributions on the forward-in-time dynamics, especially with selection. Here, we employ an asymptotic analysis combined with a scaling hypothesis to demonstrate that over-dispersed frequency trajectories emerge from the competition of conventional forces, such as selection or mutations, with an emerging time-dependent sampling bias against the minor allele. The sampling bias arises from the characteristic time-dependence of the largest sampled family size within each allelic type. Using this insight, we establish simple scaling relations for allele-frequency fluctuations, fixation probabilities, extinction times, and the site frequency spectra that arise when offspring numbers are distributed according to a power law.

Characterizing Amino Acid Substitution with Complete Linkage of Sites on a Lineage

Amino acid substitution models are commonly used for phylogenetic inference, for ancestral sequence reconstruction, and for the inference of positive selection. All commonly used models explicitly assume that each site evolves independently, an assumption that is violated by both linkage and protein structural and functional constraints. We introduce two new models for amino acid substitution which incorporate linkage between sites, each based on the (population-genetic) Moran model. The first model is a generalized population process tracking arbitrarily many sites which undergo mutation, with individuals replaced according to their fitnesses. This model provides a reasonably complete framework for simulations but is numerically and analytically intractable. We also introduce a second model which includes several simplifying assumptions but for which some theoretical results can be derived. We analyze the simplified model to determine conditions where linkage is likely to have meaningful effects on sitewise substitution probabilities, as well as conditions under which the effects are likely to be negligible. These findings are an important step in the generation of tractable phylogenetic models that parameterize selective coefficients for amino acid substitution while accounting for linkage of sites leading to both hitchhiking and background selection.

Clonal fitness inferred from time-series modelling of single-cell cancer genomes

Progress in defining genomic fitness landscapes in cancer, especially those defined by copy number alterations (CNAs), has been impeded by lack of time-series single-cell sampling of polyclonal populations and temporal statistical models1-7. Here we generated 42,000 genomes from multi-year time-series single-cell whole-genome sequencing of breast epithelium and primary triple-negative breast cancer (TNBC) patient-derived xenografts (PDXs), revealing the nature of CNA-defined clonal fitness dynamics induced by TP53 mutation and cisplatin chemotherapy. Using a new Wright-Fisher population genetics model8,9 to infer clonal fitness, we found that TP53 mutation alters the fitness landscape, reproducibly distributing fitness over a larger number of clones associated with distinct CNAs. Furthermore, in TNBC PDX models with mutated TP53, inferred fitness coefficients from CNA-based genotypes accurately forecast experimentally enforced clonal competition dynamics. Drug treatment in three long-term serially passaged TNBC PDXs resulted in cisplatin-resistant clones emerging from low-fitness phylogenetic lineages in the untreated setting. Conversely, high-fitness clones from treatment-naive controls were eradicated, signalling an inversion of the fitness landscape. Finally, upon release of drug, selection pressure dynamics were reversed, indicating a fitness cost of treatment resistance. Together, our findings define clonal fitness linked to both CNA and therapeutic resistance in polyclonal tumours.

MPL resolves genetic linkage in fitness inference from complex evolutionary histories

Genetic linkage causes the fate of new mutations in a population to be contingent on the genetic background on which they appear. This makes it challenging to identify how individual mutations affect fitness. To overcome this challenge, we developed marginal path likelihood (MPL), a method to infer selection from evolutionary histories that resolves genetic linkage. Validation on real and simulated data sets shows that MPL is fast and accurate, outperforming existing inference approaches. We found that resolving linkage is crucial for accurately quantifying selection in complex evolving populations, which we demonstrate through a quantitative analysis of intrahost HIV-1 evolution using multiple patient data sets. Linkage effects generated by variants that sweep rapidly through the population are particularly strong, extending far across the genome. Taken together, our results argue for the importance of resolving linkage in studies of natural selection.

Optimal prediction with resource constraints using the information bottleneck

Responding to stimuli requires that organisms encode information about the external world. Not all parts of the input are important for behavior, and resource limitations demand that signals be compressed. Prediction of the future input is widely beneficial in many biological systems. We compute the trade-offs between representing the past faithfully and predicting the future using the information bottleneck approach, for input dynamics with different levels of complexity. For motion prediction, we show that, depending on the parameters in the input dynamics, velocity or position information is more useful for accurate prediction. We show which motion representations are easiest to re-use for accurate prediction in other motion contexts, and identify and quantify those with the highest transferability. For non-Markovian dynamics, we explore the role of long-term memory in shaping the internal representation. Lastly, we show that prediction in evolutionary population dynamics is linked to clustering allele frequencies into non-overlapping memories.

Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games

This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection-as a result of competition fashioned by game-theoretic consideration-into the Wright-Fisher process, a stochastic birth-death process. The process is further considered to be active in a generation-wise nonoverlapping finite population where individuals play a two-strategy bimatrix population game. Subsequently, connections among the corresponding master equation, the Fokker-Planck equation, and the Langevin equation are exploited to arrive at the deterministic discrete replicator maps in the limit of infinite population size.

Detecting and Quantifying Natural Selection at Two Linked Loci from Time Series Data of Allele Frequencies with Forward-in-Time Simulations

Recent advances in DNA sequencing techniques have made it possible to monitor genomes in great detail over time. This improvement provides an opportunity for us to study natural selection based on time serial samples of genomes while accounting for genetic recombination effect and local linkage information. Such time series genomic data allow for more accurate estimation of population genetic parameters and hypothesis testing on the recent action of natural selection. In this work, we develop a novel Bayesian statistical framework for inferring natural selection at a pair of linked loci by capitalising on the temporal aspect of DNA data with the additional flexibility of modeling the sampled chromosomes that contain unknown alleles. Our approach is built on a hidden Markov model where the underlying process is a two-locus Wright-Fisher diffusion with selection, which enables us to explicitly model genetic recombination and local linkage. The posterior probability distribution for selection coefficients is computed by applying the particle marginal Metropolis-Hastings algorithm, which allows us to efficiently calculate the likelihood. We evaluate the performance of our Bayesian inference procedure through extensive simulations, showing that our approach can deliver accurate estimates of selection coefficients, and the addition of genetic recombination and local linkage brings about significant improvement in the inference of natural selection. We also illustrate the utility of our method on real data with an application to ancient DNA data associated with white spotting patterns in horses.

Postadmixture Selection on Chileans Targets Haplotype Involved in Pigmentation, Thermogenesis and Immune Defense against Pathogens

Detection of positive selection signatures in populations around the world is helping to uncover recent human evolutionary history as well as the genetic basis of diseases. Most human evolutionary genomic studies have been performed in European, African, and Asian populations. However, populations with Native American ancestry have been largely underrepresented. Here, we used a genome-wide local ancestry enrichment approach complemented with neutral simulations to identify postadmixture adaptations underwent by admixed Chileans through gene flow from Europeans into local Native Americans. The top significant hits (P = 2.4×10-7) are variants in a region on chromosome 12 comprising multiple regulatory elements. This region includes rs12821256, which regulates the expression of KITLG, a well-known gene involved in lighter hair and skin pigmentation in Europeans as well as in thermogenesis. Another variant from that region is associated with the long noncoding RNA RP11-13A1.1, which has been specifically involved in the innate immune response against infectious pathogens. Our results suggest that these genes were relevant for adaptation in Chileans following the Columbian exchange.

Neutral syndrome

Neutral models of evolution assume the absence of natural selection. Formerly confined to ecology and evolutionary biology, neutral models are spreading. In recent years they've been applied to explaining the diversity of baby names, scientific citations, cryptocurrencies, pot decorations, literary lexica, tumour variants and much more besides. Here, we survey important neutral models and highlight their similarities. We investigate the most widely used tests of neutrality, show that they are weak and suggest more powerful methods. We conclude by discussing the role of neutral models in the explanation of diversity. We suggest that the ability of neutral models to fit low-information distributions should not be taken as evidence for the absence of selection. Nevertheless, many studies, in increasingly diverse fields, make just such claims. We call this tendency 'neutral syndrome'.

Inference of Selection from Genetic Time Series Using Various Parametric Approximations to the Wright-Fisher Model

Detecting genomic regions under selection is an important objective of population genetics. Typical analyses for this goal are based on exploiting genetic diversity patterns in present time data but rapid advances in DNA sequencing have increased the availability of time series genomic data. A common approach to analyze such data is to model the temporal evolution of an allele frequency as a Markov chain. Based on this principle, several methods have been proposed to infer selection intensity. One of their differences lies in how they model the transition probabilities of the Markov chain. Using the Wright-Fisher model is a natural choice but its computational cost is prohibitive for large population sizes so approximations to this model based on parametric distributions have been proposed. Here, we compared the performance of some of these approximations with respect to their power to detect selection and their estimation of the selection coefficient. We developped a new generic Hidden Markov Model likelihood calculator and applied it on genetic time series simulated under various evolutionary scenarios. The Beta with spikes approximation, which combines discrete fixation probabilities with a continuous Beta distribution, was found to perform consistently better than the others. This distribution provides an almost perfect fit to the Wright-Fisher model in terms of selection inference, for a computational cost that does not increase with population size. We further evaluated this model for population sizes not accessible to the Wright-Fisher model and illustrated its performance on a dataset of two divergently selected chicken populations.

Detecting Signatures of Positive Selection along Defined Branches of a Population Tree Using LSD

Identifying the genomic basis underlying local adaptation is paramount to evolutionary biology, and bears many applications in the fields of conservation biology, crop, and animal breeding, as well as personalized medicine. Although many approaches have been developed to detect signatures of positive selection within single populations and population pairs, the increasing wealth of high-throughput sequencing data requires improved methods capable of handling multiple, and ideally large number of, populations in a single analysis. In this study, we introduce LSD (levels of exclusively shared differences), a fast and flexible framework to perform genome-wide selection scans, along the internal and external branches of a given population tree. We use forward simulations to demonstrate that LSD can identify branches targeted by positive selection with remarkable sensitivity and specificity. We illustrate a range of potential applications by analyzing data from the 1000 Genomes Project and uncover a list of adaptive candidates accompanying the expansion of anatomically modern humans out of Africa and their spread to Europe.

Mutational load causes stochastic evolutionary outcomes in acute RNA viral infection

Mutational load is known to be of importance for the evolution of RNA viruses, the combination of a high mutation rate and large population size leading to an accumulation of deleterious mutations. However, while the effects of mutational load on global viral populations have been considered, its quantitative effects at the within-host scale of infection are less well understood. We here show that even on the rapid timescale of acute disease, mutational load has an effect on within-host viral adaptation, reducing the effective selection acting upon beneficial variants by ∼10 per cent. Furthermore, mutational load induces considerable stochasticity in the pattern of evolution, causing a more than five-fold uncertainty in the effective fitness of a transmitted beneficial variant. Our work aims to bridge the gap between classic models from population genetic theory and the biology of viral infection. In an advance on some previous models of mutational load, we replace the assumption of a constant variant fitness cost with an experimentally-derived distribution of fitness effects. Expanding previous frameworks for evolutionary simulation, we introduce the Wright-Fisher model with continuous mutation, which describes a continuum of possible modes of replication within a cell. Our results advance our understanding of adaptation in the context of strong selection and a high mutation rate. Despite viral populations having large absolute sizes, critical events in viral adaptation, including antigenic drift and the onset of drug resistance, arise through stochastic evolutionary processes.

A novel framework for inferring parameters of transmission from viral sequence data

Transmission between hosts is a critical part of the viral lifecycle. Recent studies of viral transmission have used genome sequence data to evaluate the number of particles transmitted between hosts, and the role of selection as it operates during the transmission process. However, the interpretation of sequence data describing transmission events is a challenging task. We here present a novel and comprehensive framework for using short-read sequence data to understand viral transmission events, designed for influenza virus, but adaptable to other viral species. Our approach solves multiple shortcomings of previous methods for this purpose; for example, we consider transmission as an event involving whole viruses, rather than sets of independent alleles. We demonstrate how selection during transmission and noisy sequence data may each affect naive inferences of the population bottleneck, accounting for these in our framework so as to achieve a correct inference. We identify circumstances in which selection for increased viral transmission may or may not be identified from data. Applying our method to experimental data in which transmission occurs in the presence of strong selection, we show that our framework grants a more quantitative insight into transmission events than previous approaches, inferring the bottleneck in a manner that accounts for selection, both for within-host virulence, and for inherent viral transmissibility. Our work provides new opportunities for studying transmission processes in influenza, and by extension, in other infectious diseases.

Rapid sex-specific evolution of age at maturity is shaped by genetic architecture in Atlantic salmon

Understanding the mechanisms by which populations adapt to their environments is a fundamental aim in biology. However, it remains challenging to identify the genetic basis of traits, provide evidence of genetic changes and quantify phenotypic responses. Age at maturity in Atlantic salmon represents an ideal trait to study contemporary adaptive evolution as it has been associated with a single locus in the vgll3 region, and has also strongly changed in recent decades. Here, we provide an empirical example of contemporary adaptive evolution of a large effect locus driving contrasting sex-specific evolutionary responses at the phenotypic level. We identified an 18% decrease in the vgll3 allele associated with late maturity (L) in a large and diverse salmon population over 36 years, induced by sex-specific selection during the sea migration. Those genetic changes resulted in a significant evolutionary response in males only, due to sex-specific dominance patterns and vgll3 allelic effects. The vgll3 allelic and dominance effects differed greatly in a second population and were likely to generate different selection and evolutionary patterns. Our study highlights the importance of knowledge of genetic architecture to better understand fitness trait evolution and phenotypic diversity. It also emphasizes the potential role of adaptive evolution in the trend toward earlier maturation observed in numerous Atlantic salmon populations worldwide.

Inferring Fitness Effects from Time-Resolved Sequence Data with a Delay-Deterministic Model

A broad range of approaches have considered the challenge of inferring selection from time-resolved genome sequence data. Models describing deterministic changes in allele or haplotype frequency have been highlighted as providing accurate and computationally...

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model.

Inferring sex-specific demographic history from SNP data

The relative female and male contributions to demography are of great importance to better understand the history and dynamics of populations. While earlier studies relied on uniparental markers to investigate sex-specific questions, the increasing amount of sequence data now enables us to take advantage of tens to hundreds of thousands of independent loci from autosomes and the X chromosome. Here, we develop a novel method to estimate effective sex ratios or ESR (defined as the female proportion of the effective population) from allele count data for each branch of a rooted tree topology that summarizes the history of the populations of interest. Our method relies on Kimura’s time-dependent diffusion approximation for genetic drift, and is based on a hierarchical Bayesian model to integrate over the allele frequencies along the branches. We show via simulations that parameters are inferred robustly, even under scenarios that violate some of the model assumptions. Analyzing bovine SNP data, we infer a strongly female-biased ESR in both dairy and beef cattle, as expected from the underlying breeding scheme. Conversely, we observe a strongly male-biased ESR in early domestication times, consistent with an easier taming and management of cows, and/or introgression from wild auroch males, that would both cause a relative increase in male effective population size. In humans, analyzing a subsample of non-African populations, we find a male-biased ESR in Oceanians that may reflect complex marriage patterns in Aboriginal Australians. Because our approach relies on allele count data, it may be applied on a wide range of species.

The history of populations and their social organization is often intricate due to breeding structures, migration patterns or population bottlenecks. Estimation of the female proportion of the effective population (sex ratio) is therefore important to better understand this underlying social structure and dynamics. This question has been mainly investigated so far by comparing genetic variation of mitochondrial DNA and the Y chromosome, two uniparentally inherited markers that reflect the demographic history of females and males, respectively. To overcome the intrinsic limitations of these genetic markers, and to take advantage of the increasing amount of sequence data, we propose a new approach that uses large numbers of independent polymorphisms from autosomes and the X chromosome to estimate sex ratios, throughout the history of populations. This method allows us to confirm a strongly female-biased sex ratio in modern dairy and beef cattle breeds. Yet, we find a strongly male-biased sex ratio during domestication times, consistent with an easier taming and management of cows, and/or introgression from wild auroch males. Analyzing human data from a sample of non-African populations, we find a male bias in Oceanians, possibly indicating complex marriage patterns among Aboriginal Australian groups.

Evaluating genetic drift in time-series evolutionary analysis

The Wright-Fisher model is the most popular population model for describing the behaviour of evolutionary systems with a finite population size. Approximations have commonly been used but the model itself has rarely been tested against time-resolved genomic data. Here, we evaluate the extent to which it can be inferred as the correct model under a likelihood framework. Given genome-wide data from an evolutionary experiment, we validate the Wright-Fisher drift model as the better option for describing evolutionary trajectories in a finite population. This was found by evaluating its performance against a Gaussian model of allele frequency propagation. However, we note a range of circumstances under which standard Wright-Fisher drift cannot be correctly identified.

Effects of the Ordering of Natural Selection and Population Regulation Mechanisms on Wright-Fisher Models

We explore the effect of different mechanisms of natural selection on the evolution of populations for one- and two-locus systems. We compare the effect of viability and fecundity selection in the context of the Wright-Fisher model with selection under the assumption of multiplicative fitness. We show that these two modes of natural selection correspond to different orderings of the processes of population regulation and natural selection in the Wright-Fisher model. We find that under the Wright-Fisher model these two different orderings can affect the distribution of trajectories of haplotype frequencies evolving with genetic recombination. However, the difference in the distribution of trajectories is only appreciable when the population is in significant linkage disequilibrium. We find that as linkage disequilibrium decays the trajectories for the two different models rapidly become indistinguishable. We discuss the significance of these findings in terms of biological examples of viability and fecundity selection, and speculate that the effect may be significant when factors such as gene migration maintain a degree of linkage disequilibrium.