What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups of randomly mating individuals, which is well defined in theory for any type of (sexual) organism. We discuss generative models using drift, admixture and spatial structure, and the ancestral recombination graph. These are contrasted with statistical models for inference, principle component analysis and other `non-parametric' methods. The relationships between these approaches are explored with both simulated and real-data examples. The state-of-the-art practical software tools are discussed and contrasted. We conclude that populations are a useful theoretical construct that can be well defined in theory and often approximately exist in practice.
To learn about the past from a sample of genomic sequences, one needs to understand how evolutionary processes shape genetic diversity. Most population genetic inference is based on frameworks assuming adaptive evolution is rare. But if positive selection operates on many loci simultaneously, as has recently been suggested for many species including animals such as flies, a different approach is necessary. In this review, I discuss recent progress in characterizing and understanding evolution in rapidly adapting populations where random associations of mutations with genetic backgrounds of dif…
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…
Heterozygote disadvantage is potentially a potent driver of population genetic divergence. Also referred to as underdominance, this phenomena describes a situation where a genetic heterozygote has a lower overall fitness than either homozygote. Attention so far has mostly been given to underdominance within a single population and the maintenance of genetic differences between two populations exchanging migrants. Here we explore the dynamics of an underdominant system in a network of multiple discrete, yet interconnected, populations. Stability of genetic differences in response to increases i…
A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic modeling approach to investigate levels of genetic diversity in populations that successfully overcame a strong demographic Allee effect, a scenario in which populations smaller than a certain critical size are expected to decline. Our results indicate that compared to successful populations without Allee effect, successful Allee-effect populations tend to …
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…
These lecture notes introduce key concepts of mathematical population genetics within the most elementary setting and describe a few recent applications to microbial evolution experiments. Pointers to the literature for further reading are provided, and some of the derivations are left as exercises for the reader.
Computer simulations of the Penna ageing model suggest that already a small fraction of births with enhanced number of new mutations can negatively influence the whole population.
The origin and diversification of Sino-Tibetan populations have been a long-standing hot debate. However, the limited genetic information of Tibetan populations keeps this topic far from clear. In the present study, we genotyped 15 forensic autosomal STRs from 803 unrelated Tibetan individuals from Gansu Province (635 from Gannan and 168 from Tianzhu). We combined these data with published dataset to infer a detailed population affinities and admixture of Sino-Tibetan populations. Our results revealed that the genetic structure of Sino-Tibetan populations was strongly correlated with linguisti…
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.
We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a birth-death process to analytically calculate the probability that the parent of a given genotype will go extinct. We compare the results with numerical simulations and show how this turnover of genetic clones can be used to infer the rates underlying the population dynamics. Our work is motivated by growing populations of tumour cells, the epidemic spread …
fwdpp is a C++ library of routines intended to facilitate the development of forward-time simulations under arbitrary mutation and fitness models. The library design provides a combination of speed, low memory overhead, and modeling flexibility not currently available from other forward simulation tools. The library is particularly useful when the simulation of large populations is required, as programs implemented using the library are much more efficient that other available forward simulation programs.
We consider the hypothesis that Evolution promotes population-wide genome patterns that, under randomization, ensures the External Validity of adaptations across population members. An adaptation is Externally Valid (EV) if its effect holds under a wide range of population genetic variations. A prediction following the hypothesis is that pairwise base substitutions in segregating regions must be 'random' as in Erdos-Renyi-Gilbert random graphs, but with edge probabilities derived from Experimental-Design concepts. We demonstrate these probabilities, and consequent mutation rates, in the full-g…
Partial clonality is widespread across the tree of life, but most population genetics models are designed for exclusively clonal or sexual organisms. This gap hampers our understanding of the influence of clonality on evolutionary trajectories and the interpretation of population genetics data. We performed forward simulations of diploid populations at increasing rates of clonality (c), analysed their relationships with genotypic (clonal richness, R, and distribution of clonal sizes, Pareto β) and genetic (FIS and linkage disequilibrium) indices, and tested predictions of c from population gen…
We will give a simple, unified, possible explanation of several debated genetic issues on today's humans, Neandertals and Denisovans. In particular it is shown by means of a simple mathematical model why there is little genetic variation in todays's human population or in Western Neandertal population, why all mtDNA and y-chromosomes in today's humans seem to have African origin with no trace of Neandertal nor Denosovan mtDNA or y-chromosomes, why a big part of the European gene pool is young (from Neolitic time), and why today's East Asians have mode Neandertal genes than today's Europeans.
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…
Positive selection distorts the structure of genealogies and hence alters patterns of genetic variation within a population. Most analyses of these distortions focus on the signatures of hitchhiking due to hard or soft selective sweeps at a single genetic locus. However, in linked regions of rapidly adapting genomes, multiple beneficial mutations at different loci can segregate simultaneously within the population, an effect known as clonal interference. This leads to a subtle interplay between hitchhiking and interference effects, which leads to a unique signature of rapid adaptation on genet…
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…
We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we have computed the distributions of the total branch lengths of its sample genealogies. Within the coalescent approximation we have obtained a general expression, Eq. (27), for the moments of these distributions for an arbitrary smooth dependence of the population size on time. We investigate how the frequency of population-size variations alters the distributions. This allows us to discuss their influence on the distribution of the number of …
Background: Caenorhabditis elegans is a major model system in biology, yet very little is known about its biology outside the laboratory. Especially, its unusual mode of reproduction with self-fertile hermaphrodites and facultative males raises the question of its frequency of outcrossing in natural populations. Results: We describe the first analysis of C. elegans individuals sampled directly from natural populations. C. elegans is found predominantly in the dauer stage and with a very low frequency of males compared with hermaphrodites. While C. elegans was previously shown to display a low …
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook derivation of diffusion equations as scaling limits requires evolutionary parameters (selection coefficients, mutation rates) to scale like the inverse population size -- a severe restriction that does not always reflect biological reality. Here we note that the Wright-Fisher model can be approximated by diffusion equations under more general conditions, incl…
Spatial models where growth is limited to the edge of the expansions have been instrumental to understand the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular tumours. A complete characterization of the coalescence process generated by spatial growth is still lacking, limiting our ability to apply classic population genetics inference to spatially growing populations. Here, we start filling this gap by investigating the statistical properties of the cell lineages generated by the two dimensional Eden model, leveraging…
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 …
Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed knowledge about the specific loci underlying polygenic traits has begun to emerge from genome-wide association studies (GWAS). Here we combine this knowledge from GWAS with robust population genetic modeling to identify traits that may have been influenced by local adaptation. We exploit the fact that GWAS provide an estimate of the additive effect size of many loc…
The rights and wrongs of rescaling in population genetics simulations
The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique（法国国家科学研究中心，数字科学跨学科实验室）；Institute of Ecology and Evolution, School of Biological Sciences, University of Edinburgh（爱丁堡大学生物科学学院生态与进化研究所）
In genetic drift of small population, it is well known that even when the ratio of alleles is 0.5, specific genes are fixed in or disappear from the population. It seems the reason why inbreeding is avoided. On the other hand, this phenomenon suggests an interesting possibility. The mutant gene does not increase the number of genes at once in a large population. A gene is partially fixed by increasing the number within a small population because of inbreeding, and the gene increases in a large group by Darwin's natural selection. It would be more reasonable to think in this way. We studied thi…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But extinction can result from failure to adapt not only to catastrophes, but also to a backlog of environmental challenges. We model long-term evolution to long series of small challenges, where fitter populations reach higher population sizes. The population's long-term fitness dynamic is well approximated by a simple stochastic Markov chain model. Long-term pers…
The evolution of drug resistance in HIV occurs by the fixation of specific, well-known, drug-resistance mutations, but the underlying population genetic processes are not well understood. By analyzing within-patient longitudinal sequence data, we make four observations that shed a light on the underlying processes and allow us infer the short-term effective population size of the viral population in a patient. Our first observation is that the evolution of drug resistance usually occurs by the fixation of one drug-resistance mutation at a time, as opposed to several changes simultaneously. Sec…
The accumulation of beneficial mutations on many competing genetic backgrounds in rapidly adapting populations has a striking impact on evolutionary dynamics. This effect, known as clonal interference, causes erratic fluctuations in the frequencies of observed mutations, randomizes the fixation times of successful mutations, and leaves distinct signatures on patterns of genetic variation. Here, we show how this form of `genetic draft' affects the forward-time dynamics of site frequencies in rapidly adapting asexual populations. We calculate the probability that mutations at individual sites sh…
Genetic drift is stochastic fluctuations of alleles frequencies in a population due to sampling effects. We consider a model of drift in an equilibrium population, with high mutation rates: few functional mutations per generation. Such mutation rates are common in multicellular organisms including humans, however they are not explicitly considered in most population genetics models. Under these assumptions the drift shows properties distinct from the classical drift models, which ignore realistic mutation rates: i) All (non-lethal) variants of a site have a characteristic average frequencies, …
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 …
Tread lightly interpreting group differences in genetic risk
Bioinformatics and Computational Biology Program, University of Minnesota（明尼苏达大学生物信息学与计算生物学项目）；Department of Genetics, Cell Biology, and Development, University of Minnesota（明尼苏达大学生物学、细胞生物学与发展系）；Department of Biomedical Informatics, University of Colorado Anschutz（科罗拉多大学安舒茨医学校区生物医学信息学系）；Colorado Center for Personalized Medicine, University of Colorado Anschutz（科罗拉多大学安舒茨医学校区个性化医疗中心）；Institute of Health Informatics, University of Minnesota（明尼苏达大学健康信息学研究所）
How self-incompatibility systems are maintained in plant populations is still a debated issue. Theoretical models predict that self-incompatibility systems break down according to the intensity of inbreeding depression and number of S-alleles. Other studies have explored the function of asexual reproduction in the maintenance of self-incompatibility. However, the population genetics of partially asexual, self-incompatible populations are poorly understood and previous studies have failed to consider all possible effects of asexual reproduction or could only speculate on those effects. In this …
We have presented the basic knowledge on the structure of molecules coding the genetic information, mechanisms of transfer of this information from DNA to proteins and phenomena connected with replication of DNA. In particular, we have described the differences of mutational pressure connected with replication of the leading and lagging DNA strands. We have shown how the asymmetric replication of DNA affects the structure of genomes, positions of genes, their function and amino acid composition. Results of Monte Carlo simulations of evolution of protein coding sequences have shown a specific r…
All non-human great apes are endangered in the wild, and it is therefore important to gain an understanding of their demography and genetic diversity. To date, however, genetic studies within these species have largely been confined to mitochondrial DNA and a small number of other loci. Here, we present a genome-wide survey of genetic variation in gorillas using a reduced representation sequencing approach, focusing on the two lowland subspecies. We identify 3,274,491 polymorphic sites in 14 individuals: 12 western lowland gorillas (Gorilla gorilla gorilla) and 2 eastern lowland gorillas (Gori…
Estimating wolf population size in France using non-invasive genetic sampling and spatial capture recapture models
CEFE, Univ Montpellier, CNRS, EPHE, IRD（法国国家科学研究中心生态、演化与功能实验室）；Office Français de la Biodiversité (OFB)（法国生物多样性办公室）；Norwegian University of Life Sciences（挪威生命科学大学）；ANTAGENE, Animal Genomics Laboratory（安塔基因动物基因组实验室）
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…
It is the first time, when genetic diversity and the common kilka population structure were investigated throughout the areal. Data about the species condition at the Upper Volga basins were updated accordingly to modern condition. Physiological and ecological adaptations to northern water basins were evaluated. Significance of interaction between some loci and the most important abiotic environmental factors at the selection was demonstrated. The results suggest that the common kilka Clupeonella cultriventris (Nordmann, 1840) is presented by uniform set of population throughout the areal. The…
Facing an alarming continuing decline of wild sea cucumber resources, management strategies were developed over the past three decades to sustainably promote development, maintenance, or regeneration of wild sea cucumber fisheries. In New Caledonia (South Pacific), dedicated management efforts via restocking and sea ranching programs were implemented to cope with the overharvesting of the sandfish Holothuria scabra and the recent loss of known populations. In order to investigate genetic implications of a major H. scabra restocking program, we assessed the genetic diversity and structure of wi…
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…
Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to stochastic fluctuations of allele frequencies above and beyond genetic drift - an effect known as genetic draft. Since recombination disrupts associations between alleles, draft is strong when recombination is rare. Here, we study a facultatively outcrossing population in a regime where the frequency of out-crossing and recombination, r, is small compared t…
This paper shows that differentiating the lifetimes of two phenotypes independently from their fertility can lead to a qualitative change in the equilibrium of a population: since survival and reproduction are distinct functional aspects of an organism, this observation contributes to extend the population-genetical characterisation of biological function. To support this statement a mathematical relation is derived to link the lifetime ratio T_1/T_2, which parametrizes the different survival ability of two phenotypes, with population variables that quantify the amount of neutral variation und…
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…
Deleterious genetic variants can be evaluated as quantitative traits using information theory-based sequence analysis of recognition sites. To assess the effect of such variants, fitness and genetic load of SNPs which alter binding site affinity are derived from changes in individual information and allele frequencies. Human SNPs that alter mRNA splicing are partitioned according to their genetic load. SNPs with high genetic loads (>0.5) are common in the genome and, in many instances, predicted effects are supported by gene expression studies.
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 observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context of antibiotic treatments or exponential growth in constant environments, non-genetic variability has shown to have significant effects on population dynamics. Here, we review research that elucidates the relationship between cell-to-cell variability and population dynamics. After summarizing the relevant experimental observations, we discuss models of bet-he…
Patterns of isolation-by-distance arise when population differentiation increases with increasing geographic distances. Patterns of isolation-by-distance are usually caused by local spatial dispersal, which explains why differences of allele frequencies between populations accumulate with distance. However, spatial variations of demographic parameters such as migration rate or population density can generate non-stationary patterns of isolation-by-distance where the rate at which genetic differentiation accumulates varies across space. To characterize non-stationary patterns of isolation-by-di…
Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype-phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure…
Maintenance of sexual reproduction and genetic recombination imposes physiological costs when compared to parthenogenic reproduction, most prominently: for maintaining the corresponding (molecular) machinery, for finding a mating partner, and through the decreased fraction of females in a population, which decreases the reproductive capacity. Based on principles from information theory, we have previously developed a new population genetic model, and applying it in simulations, we have recently hypothesized that all species maintain the maximum genomic complexity that is required by their nich…
We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or sexual. Biological events (e.g.~births, deaths, mating, dispersal) depend in arbitrary fashion on the current population state. Our formalism is based on the idea of genetic sites. Each genetic site resides at a particular locus and houses a single allele. Each individual contains a number of sites equal to its ploidy (one for haploids, two for diploids, etc.). S…
In order to analyze data from cancer genome sequencing projects, we need to be able to distinguish causative, or "driver," mutations from "passenger" mutations that have no selective effect. Toward this end, we prove results concerning the frequency of neutural mutations in exponentially growing multitype branching processes that have been widely used in cancer modeling. Our results yield a simple new population genetics result for the site frequency spectrum of a sample from an exponentially growing population.
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is reviewed. We then study a situation such that the competing species are neutral at the equilibrium population size but population size fluctuations nevertheless favor fixation of one species over the other. In this case, a separation of timescales emerges naturally and allows adiabatic elimination of a fast population size variable to deduce the fluctuations-induc…
A deterministic model of an age-structured population with genetics analogous to the discrete time Penna model of genetic evolution is constructed on the basis of the Lotka-Volterra scheme. It is shown that if, as in the Penna model, genetic information is represented by the fraction of defective genes in the population, the population numbers for each specific individual's age are represented by exactly the same functions of age in both models. This gives us a new possibility to consider multi-species evolution without using detailed microscopic Penna model. We discuss a particular case of th…
In the present article, we investigate the effects of dormancy on an abstract population genetic level. We first provide a short review of seed bank models in population genetics, and the role of dormancy for the interplay of evolutionary forces in general, before we discuss two recent paradigmatic models, referring to spontaneous resp. simultaneous switching of individuals between the active and the dormant state. We show that both mechanisms give rise to non-trivial mathematical objects, namely the (continuous) seed bank diffusion and the seed bank diffusion with jumps, as well as their dual…
It is widely accepted that population genetics theory is the cornerstone of evolutionary analyses. Empirical tests of the theory, however, are challenging because of the complex relationships between space, dispersal, and evolution. Critically, we lack quantitative validation of the spatial models of population genetics. Here we combine analytics, on and off-lattice simulations, and experiments with bacteria to perform quantitative tests of the theory. We study two bacterial species, the gut microbe Escherichia coli and the opportunistic pathogen Pseudomonas aeruginosa, and show that spatio-ge…
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…
