Genetic data are now routinely used to study the history of population size, subdivision, and gene flow. A variety of formal statistical methods is available for testing hypotheses and fitting models to data. Yet it is often unclear which hypotheses are worth testing, which models worth fitting. There is a need for less formal methods that can be used in exploratory analysis of genetic data. One approach to this problem uses *nucleotide site patterns*, which provide a simple summary of the pattern in genetic data. This article shows how to use them in exploratory data analysis.
Over the last fifty years, geneticists have made great strides in understanding how our species' evolutionary history gave rise to current patterns of human genetic diversity classically summarized by Lewontin in his 1972 paper, 'The Apportionment of Human Diversity'. One evolutionary process that requires special attention in both population genetics and statistical genetics is admixture: gene flow between two or more previously separated source populations to form a new admixed population. The admixture process introduces unique patterns of genetic variation within and between populations, w…
I review the evolutionary history of human populations in Europe with an emphasis on what has been learned in recent years through the study of ancient DNA. Human populations in Europe ~430-39kya (archaic Europeans) included Neandertals and their ancestors, who were genetically differentiated from other archaic Eurasians (such as the Denisovans of Siberia), as well as modern humans. Modern humans arrived to Europe by ~45kya, and are first genetically attested by ~39kya when they were still mixing with Neandertals. The first Europeans who were recognizably genetically related to modern ones app…
Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where do they live? How do they move and interbreed across the landscape? How were they moving a thousand years ago, and where were the ancestors of a particular individual alive today? Answers to these questions can have profound consequences for our understanding of history, ecology, and the evolutionary process. In this review, we discuss how geographic aspects of the distribution, movement, and reproduction of organisms are reflected in their pedigree across space …
Human populations have a complex history of introgression and of changing population size. Human genetic variation has been affected by both these processes, so that inference of past population size depends upon the pattern of gene flow and introgression among past populations. One remarkable aspect of human population history as inferred from genetics is a consistent "wave" of larger effective population size, prior to the bottlenecks and expansions of the last 100,000 years. Here I carry out a series of simulations to investigate how introgression and gene flow from genetically divergent an…
The recent genealogical history of human populations is a complex mosaic formed by individual migration, large-scale population movements, and other demographic events. Population genomics datasets can provide a window into this recent history, as rare traces of recent shared genetic ancestry are detectable due to long segments of shared genomic material. We make use of genomic data for 2,257 Europeans (the POPRES dataset) to conduct one of the first surveys of recent genealogical ancestry over the past three thousand years at a continental scale. We detected 1.9 million shared genomic segment…
The Caribbean basin is home to some of the most complex interactions in recent history among previously diverged human populations. Here, by making use of genome-wide SNP array data, we characterize ancestral components of Caribbean populations on a sub-continental level and unveil fine-scale patterns of population structure distinguishing insular from mainland Caribbean populations as well as from other Hispanic/Latino groups. We provide genetic evidence for an inland South American origin of the Native American component in island populations and for extensive pre-Columbian gene flow across …
Mitochondrial hypervariable region I genetic data from ancient populations at two sites from Asia, Linzi in Shandong (northern China) and Egyin Gol in Mongolia, were reanalyzed to detect population affinities. Data from a total of 51 modern populations were used to generate distance measures (Fst's) to the two ancient populations. The tests first analyzed relationships at the regional level, and then compiled the top regional matches for an overall comparison to the two probe populations. The reanalysis showed that the Egyin Gol and Linzi populations have clear distinctions in genetic affinity…
Studying how diverse human populations are related is of historical and anthropological interest, in addition to providing a realistic null model for testing for signatures of natural selection or disease associations. Furthermore, understanding the demographic histories of other species is playing an increasingly important role in conservation genetics. A number of statistical methods have been developed to infer population demographic histories using whole-genome sequence data, with recent advances focusing on allowing for more flexible modeling choices, scaling to larger data sets, and incr…
Experimental evolution has yielded surprising insights into human history and evolution by shedding light on the roles of chance and contingency in history and evolution, and on the deep evolutionary roots of cooperation, conflict and kin discrimination. We argue that an interesting research direction would be to develop computational and experimental systems for studying evolutionary processes that involve multiple layers of inheritance (such as genes, epigenetic inheritance, language, and culture) and feedbacks (such as gene-culture coevolution and mate choice) as well as open-ended niche co…
The study of the origins of crops is of interest from both a fundamental evolutionary understanding viewpoint, and from an applied agricultural technology perspective. The date palm (Phoenix dactylifera L.) is the iconic fruit crop of hot and arid regions of North Africa and the Middle East, producing sugar-rich fruits, known as dates. There are many different cultivars each with distinctive fruit traits, and there are many wild Phoenix species too, which in total form a complex of related species. The understanding of plant domestication involves multiple disciplines, including phylogeography…
Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the correlation of gene histories in established demographic models for genetic evolution and show how to extend the analysis to more realistic (but more complicated) models of demographic structure. We identify two contributions to the correlation of gene histories in divergent populations: linkage disequilibrium, and differences in the demographic history of individu…
Human populations have undergone dramatic changes in population size in the past 100,000 years, including a severe bottleneck of non-African populations and recent explosive population growth. There is currently great interest in how these demographic events may have affected the burden of deleterious mutations in individuals and the allele frequency spectrum of disease mutations in populations. Here we use population genetic models to show that--contrary to previous conjectures--recent human demography has likely had very little impact on the average burden of deleterious mutations carried by…
Identifying drivers of complex traits from the noisy signals of genetic variation obtained from high throughput genome sequencing technologies is a central challenge faced by human geneticists today. We hypothesize that the variants involved in complex diseases are likely to exhibit non-neutral evolutionary signatures. Uncovering the evolutionary history of all variants is therefore of intrinsic interest for complex disease research. However, doing so necessitates the simultaneous elucidation of the targets of natural selection and population-specific demographic history. Here we characterize …
Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of deleterious variation, as well as the number, frequencies, and effect sizes of mutations that contribute risk to complex traits. Here I use simulations under population genetic models where a proportion of the heritability of the trait is accounted for by mutations in a subset of the exome. I show that recent population growth increases the proportion of nonsynony…
Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we provide tight bounds on the amount of exact coalescence time data needed to recover the population size history of a single, panmictic population at a certain level of accuracy. In practice, coalescence times are estimated from sequence data and so our lower bounds should be taken as rather conservative.
There is an urgent and well-recognized need to extend genetic studies to diverse populations, but several obstacles continue to be prohibitive, including (but not limited to) the difficulty of recruiting individuals from diverse populations in large numbers and the lack of representation in available genomic references. These obstacles notwithstanding, studying multiple diverse populations would provide informative, population-specific insights. Using Native Hawaiians as an example of an understudied population with a unique evolutionary history, I will argue that by developing key genomic res…
A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. However, many species are repeatedly introduced to the same location and eventually one population may overcome the Allee effect by chance. With the help of stochastic models, we investigate how much genetic diversity such successful populations harbour on average and how this depends on offspring-number variation, an important source of stochastic variability in population size. We find that…
The usefulness of a `total-evidence' approach to human population genetics was assessed through a clustering analysis of combined genome-wide SNP datasets. The combination contained only 3146 SNPs. Detailed examination of the results nonetheless enables the extraction of relevant clues about the history of human populations, some pertaining to events as ancient as the first migration out of Africa. The results are mostly coherent with what is known from history, linguistics, and previous genetic analyses. These promising results suggest that cross-studies data confrontation have the potential …
A topological approach to the study of genetic recombination, based on persistent homology, was introduced by Chan, Carlsson, and Rabadán in 2013. This associates a sequence of signatures called barcodes to genomic data sampled from an evolutionary history. In this paper, we develop theoretical foundations for this approach. First, we present a novel formulation of the underlying inference problem. Specifically, we introduce and study the novelty profile, a simple, stable statistic of an evolutionary history which not only counts recombination events but also quantifies how recombination creat…
In sexual populations, selection operates neither on the whole genome, which is repeatedly taken apart and reassembled by recombination, nor on individual alleles that are tightly linked to the chromosomal neighborhood. The resulting interference between linked alleles reduces the efficiency of selection and distorts patterns of genetic diversity. Inference of evolutionary history from diversity shaped by linked selection requires an understanding of these patterns. Here, we present a simple but powerful scaling analysis identifying the unit of selection as the genomic "linkage block" with a c…
Inference with population genetic data usually treats the population pedigree as a nuisance parameter, the unobserved product of a past history of random mating. However, the history of genetic relationships in a given population is a fixed, unobserved object, and so an alternative approach is to treat this network of relationships as a complex object we wish to learn about, by observing how genomes have been noisily passed down through it. This paper explores this point of view, showing how to translate questions about population genetic data into calculations with a Poisson process of mutati…
The rapid development of sequencing technologies represents new opportunities for population genetics research. It is expected that genomic data will increase our ability to reconstruct the history of populations. While this increase in genetic information will likely help biologists and anthropologists to reconstruct the demographic history of populations, it also represents new challenges. Recent work has shown that structured populations generate signals of population size change. As a consequence it is often difficult to determine whether demographic events such as expansions or contractio…
Southern and eastern African populations that speak non-Bantu languages with click consonants are known to harbour some of the most ancient genetic lineages in humans, but their relationships are poorly understood. Here, we report data from 23 populations analyzed at over half a million single nucleotide polymorphisms, using a genome-wide array designed for studying human history. The southern African Khoisan fall into two genetic groups, loosely corresponding to the northwestern and southeastern Kalahari, which we show separated within the last 30,000 years. We find that all individuals deriv…
The Genographic Project is an international effort using genetic data to chart human migratory history. The project is non-profit and non-medical, and through its Legacy Fund supports locally led efforts to preserve indigenous and traditional cultures. In its second phase, the project is focusing on markers from across the entire genome to obtain a more complete understanding of human genetic variation. Although many commercial arrays exist for genome-wide SNP genotyping, they were designed for medical genetic studies and contain medically related markers that are not appropriate for global po…
GWAS in humans are revealing the genetic architecture of biomedical and anthropomorphic traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to understand how genetic architecture is shaped by basic population genetics processes-notably, by mutation, natural selection and genetic drift. Because many quantitative traits are subject to stabilizing selection and genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabili…
1) Micro-evolutionary predictions are complicated by ecological feedbacks like density dependence, while ecological predictions can be complicated by evolutionary change. A widely used approach in micro-evolution, quantitative genetics, struggles to incorporate ecological processes into predictive models, while structured population modelling, a tool widely used in ecology, rarely incorporates evolution explicitly. 2) In this paper we develop a flexible, general framework that links quantitative genetics and structured population models. We use the quantitative genetic approach to write down t…
The Roma people, living throughout Europe, are a diverse population linked by the Romani language and culture. Previous linguistic and genetic studies have suggested that the Roma migrated into Europe from South Asia about 1000-1500 years ago. Genetic inferences about Roma history have mostly focused on the Y chromosome and mitochondrial DNA. To explore what additional information can be learned from genome-wide data, we analyzed data from six Roma groups that we genotyped at hundreds of thousands of single nucleotide polymorphisms (SNPs). We estimate that the Roma harbor about 80% West Eurasi…
Recent improvements in high-throughput genotyping and sequencing technologies have afforded the collection of massive, genome-wide datasets of DNA information from hundreds of thousands of individuals. These datasets, in turn, provide unprecedented opportunities to reconstruct the history of human populations and detect genotype-phenotype association. Recently developed computational methods can identify long-range chromosomal segments that are identical across samples, and have been transmitted from common ancestors that lived tens to hundreds of generations in the past. These segments reveal…
The paternally inherited Y chromosome has been widely used in population genetic studies to understand relationships among human populations. Our interpretation of Y chromosomal evidence about population history and genetics has rested on the assumption that all the Y chromosomal markers in the male-specific region (MSY) are selectively neutral. However, the very low diversity of Y chromosome has drawn a long debate about whether natural selection has affected this chromosome or not. In recent several years, the progress in Y chromosome sequencing has helped to address this dispute. Purifying …
Globally, we are witnessing the rise of complex, non-communicable diseases (NCDs) related to changes in our daily environments. Obesity, asthma, cardiovascular disease, and type 2 diabetes are part of a long list of "lifestyle" diseases that were rare throughout human history but are now common. A key idea from anthropology and evolutionary biology--the evolutionary mismatch hypothesis--seeks to explain this phenomenon. It posits that humans evolved in environments that radically differ from the ones experienced by most people today, and thus traits that were advantageous in past environments …
The theory of life history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens in both epidemic and endemic situations. This framework, however, relies on the assumption that pathogen populations are very large and that one can neglect the effects of demographic stochasticity. Here we expand the theory of life history evolution to account for the effects of finite population size on the evolution of pathogen virulence. We show that demographic stochasticity introduces additional evolutionary forces that can qualitatively affect the dynamics and the evol…
Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract this information (at least partially) but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIYABC) for inference based on Approximate Bayesian Computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number o…
Drosophila melanogaster, a small dipteran of African origin, represents one of the best-studied model organisms. Early work in this system has uniquely shed light on the basic principles of genetics and resulted in a versatile collection of genetic tools that allow to uncover mechanistic links between genotype and phenotype. Moreover, given its world-wide distribution in diverse habitats and its moderate genome-size, Drosophila has proven very powerful for population genetics inference and was one of the first eukaryotes whose genome was fully sequenced. In this book-chapter, we provide a brie…
Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic variants within and between populations. For candidate models we numerically compute the expected spectrum using a diffusion approximation to the one-locus two-allele Wright-Fisher process, involving up to three simultaneous populations. Our approach is a composite likelihood scheme, since linkage between neutral loci alters the variance but not the expecta…
There is great scientific and popular interest in understanding the genetic history of populations in the Americas. We wish to understand when different regions of the continent were inhabited, where settlers came from, and how current inhabitants relate genetically to earlier populations. Recent studies unraveled parts of the genetic history of the continent using genotyping arrays and uniparental markers. The 1000 Genomes Project provides a unique opportunity for improving our understanding of population genetic history by providing over a hundred sequenced low coverage genomes and exomes fr…
Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed \textit{a priori} known, the evolution of the genetic composition of a population does not affect demography nor population structure, and there is no selection nor interaction between and within genetic strains. In this paper, we present a stochastic birth-death model with competitive interactions and asexual reproduction. We develop an inferential procedure fo…
Gene duplication is a major mechanism through which new genetic material is generated. Although numerous methods have been developed to differentiate the ortholog and paralogs, very few differentiate the "Parent-Daughter" relationship among paralogous pairs. As coined by the Mira et al, we refer the "Parent" copy as the paralogous copy that stays at the original genomic position of the "original copy" before the duplication event, while the "Daughter" copy occupies a new genomic locus. Here we present a novel method which combines the phylogenetic reconstruction of duplications at different ev…
Population genetics theory has laid the foundations for genomics analyses including the recent burst in genome scans for selection and statistical inference of past demographic events in many prokaryote, animal and plant species. Identifying SNPs under natural selection and underpinning species adaptation relies on disentangling the respective contribution of random processes (mutation, drift, migration) from that of selection on nucleotide variability. Most theory and statistical tests have been developed using the Kingman coalescent theory based on the Wright-Fisher population model. However…
Han Chinese experienced substantial population migrations and admixture in history, yet little is known about the evolutionary process of Chinese dialects. Here, we used phylogenetic approaches and admixture inference to explicitly decompose the underlying structure of the diversity of Chinese dialects, based on the total phoneme inventories of 140 dialect samples from seven traditional dialect groups: Mandarin, Wu, Xiang, Gan, Hakka, Min and Yue. We found a north-south gradient of phonemic differences in Chinese dialects induced from historical population migrations. We also quantified extens…
Adaptation to local environments often occurs through natural selection acting on a large number of loci, each having a weak phenotypic effect. One way to detect these loci is to identify genetic polymorphisms that exhibit high correlation with environmental variables used as proxies for ecological pressures. Here, we propose new algorithms based on population genetics, ecological modeling, and statistical learning techniques to screen genomes for signatures of local adaptation. Implemented in the computer program "latent factor mixed model" (LFMM), these algorithms employ an approach in which…
Spatially resolved genetic data is increasingly used to reconstruct the migrational history of species. To assist such inference, we study, by means of simulations and analytical methods, the dynamics of neutral gene frequencies in a population undergoing a continual range expansion in one dimension. During such a colonization period, lineages can fix at the wave front by means of a ``surfing'' mechanism [Edmonds C.A., Lillie A.S. & Cavalli-Sforza L.L. (2004) Proc Natl Acad Sci USA 101: 975-979]. We quantify this phenomenon in terms of (i) the spatial distribution of lineages that reach fixati…
Very low levels of genetic diversity have been reported in vertebrates with large genomes, notably salamanders and lungfish [1-3]. Interpreting differences in heterozygosity, which reflects genetic diversity in a population, is complicated because levels of heterozygosity vary widely between conspecific populations, and correlate with many different physiological and demographic variables such as body size and effective population size. Here we return to the question of genetic variability in salamanders and report on the relationship between evolutionary rates and genome sizes in five differe…
The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak or infrequent evolutionary force. However, many species, particularly pathogens, are under continuous pressure to adapt in response to changing environments. A statistical framework for inference from diversity data of such populations is currently lacking. Toward this goal, we explore the properties of genealogies in a model of continual adaptation in asexual pop…
We study the univariate moment problem of piecewise-constant density functions on the interval $[0,1]$ and its consequences for an inference problem in population genetics. We show that, up to closure, any collection of $n$ moments is achieved by a step function with at most $n-1$ breakpoints and that this bound is tight. We use this to show that any point in the $n$th coalescence manifold in population genetics can be attained by a piecewise constant population history with at most $n-2$ changes. Both the moment cones and the coalescence manifold are projected spectrahedra and we describe the…
The history of southern Africa involved interactions between indigenous hunter-gatherers and a range of populations that moved into the region. Here we use genome-wide genetic data to show that there are at least two admixture events in the history of Khoisan populations (southern African hunter-gatherers and pastoralists who speak non-Bantu languages with click consonants). One involved populations related to Niger-Congo-speaking African populations, and the other introduced ancestry most closely related to west Eurasian (European or Middle Eastern) populations. We date this latter admixture …
The shift from outcrossing to self-fertilization is among the most common transitions in plants. Until recently, however, a genome-wide view of this transition has been obscured by a dearth of appropriate data and the lack of appropriate population genomic methods to interpret such data. Here, we present novel analyses detailing the origin of the selfing species, Capsella rubella, which recently split from its outcrossing sister, Capsella grandiflora. Due to the recency of the split, most variation within C. rubella is found within C. grandiflora. We can therefore identify genomic regions wher…
Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to adaptation when co-opted - e.g. following a mutation increasing expression from a low, attenuated baseline. This view is described, for example, by the metaphor of the spread of a population across a neutral network in genotype space. As an alternative view, consider the fact that most phenotypic traits are affected by multiple sequences, including cryptic ones. Eve…
Long-range migrations and the resulting admixtures between populations have been important forces shaping human genetic diversity. Most existing methods for detecting and reconstructing historical admixture events are based on allele frequency divergences or patterns of ancestry segments in chromosomes of admixed individuals. An emerging new approach harnesses the exponential decay of admixture-induced linkage disequilibrium (LD) as a function of genetic distance. Here, we comprehensively develop LD-based inference into a versatile tool for investigating admixture. We present a new weighted LD…
Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics. Kingman's coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. A major goal of demographic reconstruction is understanding the association between the effective population size and potential explanatory factors. Building upon Bayesi…
The coalescent revolutionised theoretical population genetics, simplifying, or making possible for the first time, many analyses, proofs, and derivations, and offering crucial insights about the way in which the structure of data in samples from populations depends on the demographic history of the population. However statistical inference under the coalescent model is extremely challenging, effectively because no explicit expressions are available for key sampling probabilities. This led initially to approximation of these probabilities by ingenious application of modern computationally-inten…
By demonstrating the role that historical population replacements and waves of admixture have played around the world, the genetics work of Reich and colleagues has provided a paradigm for understanding human history [Reich et al. 2009; Reich et al. 2012; Patterson et al. 2012]. Although we show in Ioannidis et al. [2021] that the peopling of Polynesia was a range expansion, and not, as suggested by Huang et al. [2022], yet another example of waves of admixture and large-scale gene flow between populations, we believe that our result in this recently settled oceanic expanse is the exception th…
