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 underlying a population's phenotypic distribution.
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…
The relationship between the M-species stochastic Lotka-Volterra competition (SLVC) model and the M-allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection and the Moran model with frequency-dependent selection (equivalently, a game-theoretic formulation of the Moran model). We demonstrate how these mappings …
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…
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…
If deleterious mutations near a fitness maximum in a spatially distributed population are sufficiently frequent or detrimental, the population can undergo a fitness collapse, similarly to the Muller's ratchet effect in well-mixed populations. Recent studies of one-dimensional habitats (e.g., the frontier of a two-dimensional range expansion) have shown that the onset of the fitness collapse is described by a directed percolation phase transition with its associated critical exponents. We consider population fitness collapse in three-dimensional range expansions with both inflating and fixed-si…
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.
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 …
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.
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…
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…
The growth and evolution of microbial populations is often subjected to advection by fluid flows in spatially extended environments, with immediate consequences for questions of spatial population genetics in marine ecology, planktonic diversity and origin of life scenarios. Here, we review recent progress made in understanding this rich problem in the simplified setting of two competing genetic microbial strains subjected to fluid flows. As a pedagogical example we focus on antagonsim, i.e., two killer microorganism strains, each secreting toxins that impede the growth of their competitors (c…
In the context of population genetics, active information can be extended to measure the change of information of a given event (e.g., fixation of an allele) from a neutral model in which only genetic drift is taken into account to a non-neutral model that includes other sources of frequency variation (e.g., selection and mutation). In this paper we illustrate active information in population genetics through the Wright-Fisher model.
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…
Theory predicts rapid genetic drift during invasions, yet many expanding populations maintain high genetic diversity. We find that genetic drift is dramatically suppressed when dispersal rates increase with the population density because many more migrants from the diverse, high-density regions arrive at the expansion edge. When density-dependence is weak or negative, the effective population size of the front scales only logarithmically with the carrying capacity. The dependence, however, switches to a sublinear power law and then to a linear increase as the density-dependence becomes strongl…
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 …
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…
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 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…
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, …
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）
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）
