The joint allele frequency spectrum of multiple populations: a coalescent theory approach

The allele frequency spectrum is a series of statistics that describe genetic polymorphism, and is commonly used for inferring population genetic parameters and detecting natural selection. Population genetic theory on the allele frequency spectrum for a single population has been well studied using both coalescent theory and diffusion equations. Recently, the theory was extended to the joint allele frequency spectrum (JAFS) for three populations using diffusion equations and was shown to be very useful in inferring human demographic history. In this paper, I show that the JAFS can be analytically derived with coalescent theory for a basic model of two isolated populations and then extended to multiple populations and various complex scenarios, such as those involving population growth and bottleneck, migration, and positive selection. Simulation study is used to demonstrate the accuracy and applicability of the theoretical model. The coalescent theory-based approach for the JAFS can characterize the demographic history with comprehensive statistical models as the diffusion approach does, and in addition gains several novel advantages: the computational complexity of calculating the JAFS with coalescent theory is reduced, and thus it is feasible to analytically obtain the JAFS for multiple populations; the hitchhiking effect can be efficiently modeled in coalescent theory, enabling the development of methodologies for detecting selection via multi-population polymorphism data. As an alternative to the diffusion approximation approach, the coalescent theory for the JAFS also provides a foundation for population genetic inference with the advent of large-scale genomic polymorphism data.     

Non-equilibrium theory of the allele frequency spectrum

A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection and varying population size, the boundary condition is lim(x downward arrow0)xf(x,t)=thetarho(t), where f(.,t) is the frequency spectrum of derived alleles at independent loci at time t and rho(t) is the relative population size at time t. When population size and selection intensity are independent of time, the forward equation is equivalent to the backwards diffusion usually used to derive the frequency spectrum, but this approach allows computation of the time dependence of the spectrum both before an equilibrium is attained and when population size and selection intensity vary with time. From the diffusion equation, a set of ordinary differential equations for the moments of f(.,t) is derived and the expected spectrum of a finite sample is expressed in terms of those moments. The use of the forward equation is illustrated by considering neutral and selected alleles in a highly simplified model of human history. For example, it is shown that approximately 30% of the expected total heterozygosity of neutral loci is attributable to mutations that arose since the onset of population growth in roughly the last 150,000 years.     

The frequency spectrum of a mutation,and its age,in a general diffusion model

General formulae are derived for the probability density and expected age of a mutation of frequency x in a population, and similarly for a mutation with b copies in a sample of n genes. A general formula is derived for the frequency spectrum of a mutation in a sample. Variable population size models are included. Results are derived in two frameworks: diffusion process models for the frequency of the mutation; and birth and death process models. The coalescent structure within the mutant gene group and the non-mutant group is considered.     

Molecular evolutionary clock and the neutral theory

Summary From the standpoint of the neutral theory of molecular evolution, it is expected that a universally valid and exact molecular evolutionary clock would exist if, for a given molecule, the mutation rate for neutral allelesper year were exactly equal among all organisms at all times. Any deviation from the equality of neutral mutation rate per year makes the molecular clock less exact. Such deviation may be due to two causes: one is the change of the mutation rate per year (such as due to change of generation span), and the other is the alteration of the selective constraint of each molecule (due to change of internal molecular environment). A statistical method was developed to investigate the equality of evolutionary rates among lineages. This was used to analyze protein data to demonstrate that these two causes are actually at work in molecular evolution. It was emphasized that departures from exact clockwise progression of molecular evolution by no means invalidates the neutral theory. It was pointed out that experimental studies should be done to settle the issue of whether the mutation rate for nucleotide change is more constant per year or per generation among organisms whose generation spans are very different.     

Pool‐hmm: a Python program for estimating the allele frequency spectrum and detecting selective sweeps from next generation sequencing of pooled samples

Due to its cost effectiveness, next generation sequencing of pools of individuals (Pool‐Seq) is becoming a popular strategy for genome‐wide estimation of allele frequencies in population samples. As the allele frequency spectrum provides information about past episodes of selection, Pool‐seq is also a promising design for genomic scans for selection. However, no software tool has yet been developed for selection scans based on Pool‐Seq data. We introduce Pool‐hmm, a Python program for the estimation of allele frequencies and the detection of selective sweeps in a Pool‐Seq sample. Pool‐hmm includes several options that allow a flexible analysis of Pool‐Seq data, and can be run in parallel on several processors. Source code and documentation for Pool‐hmm is freely available at https://qgsp.jouy.inra.fr/ .     

Composite stepwise mutation model under the neutral mutation hypothesis

Summary As an extension of the conventional (Ohta-Kimura) stepwise mutation model, a new model is proposed. In this model, it is assumed that each charge state (electromorph) is represented byK alleles and that a mutation changes an allele either by one step in the charge space or to one of the other members of the identical electromorph. It is shown that the net genetic variability within a population is similar to that predicted by the infinite-allele model (Kimura-Crow model) rather than to that predicted by the stepwise mutation model, and theK-dependence of genetic variability is rather weak whenK 2 and the effective population size is not much greater than the reciprocal of mutation rate. The results are compared with the recent observations at the xanthine dehydrogenase locus inDrosophila pseudoobscura. Contribution No. 1218 from the National Institute of Genetics, Mishima, 411, Japan.     

Time-dependent solutions of the spatially implicit neutral model of biodiversity

Previous research into the neutral theory of biodiversity has focused mainly on equilibrium solutions rather than time-dependent solutions. Understanding the time-dependent solutions is essential for applying neutral theory to ecosystems in which time-dependent processes, such as succession and invasion, are driving the dynamics. Time-dependent solutions also facilitate tests against data that are stronger than those based on static equilibrium patterns. Here I investigate the time-dependent solutions of the classic spatially implicit neutral model, in which a small local community is coupled to a much larger metacommunity through immigration. I present explicit general formulas for the eigenvalues, left eigenvectors and right eigenvectors of the models’s transition matrix. The time-dependent solutions can then be expressed in terms of these eigenvalues and eigenvectors. Some of these results are translated directly from existing results for the classic Moran model of population genetics (the Moran model is equivalent to the spatially implicit neutral model after a reparameterization); others of the results are new. I demonstrate that the asymptotic time-dependent solution corresponding to just these first two eigenvectors can be a good approximation to the full time-dependent solution. I also demonstrate the feasibility of a partial eigendecomposition of the transition matrix, which facilitates direct application of the results to a biologically relevant example in which a newly invading species is initially present in the metacommunity but absent from the local community.     

The aggregate site frequency spectrum for comparative population genomic inference

Understanding how assemblages of species responded to past climate change is a central goal of comparative phylogeography and comparative population genomics, an endeavour that has increasing potential to integrate with community ecology. New sequencing technology now provides the potential to perform complex demographic inference at unprecedented resolution across assemblages of nonmodel species. To this end, we introduce the aggregate site frequency spectrum (aSFS), an expansion of the site frequency spectrum to use single nucleotide polymorphism (SNP) data sets collected from multiple, co‐distributed species for assemblage‐level demographic inference. We describe how the aSFS is constructed over an arbitrary number of independent population samples and then demonstrate how the aSFS can differentiate various multispecies demographic histories under a wide range of sampling configurations while allowing effective population sizes and expansion magnitudes to vary independently. We subsequently couple the aSFS with a hierarchical approximate Bayesian computation (hABC) framework to estimate degree of temporal synchronicity in expansion times across taxa, including an empirical demonstration with a data set consisting of five populations of the threespine stickleback (Gasterosteus aculeatus). Corroborating what is generally understood about the recent postglacial origins of these populations, the joint aSFS/hABC analysis strongly suggests that the stickleback data are most consistent with synchronous expansion after the Last Glacial Maximum (posterior probability = 0.99). The aSFS will have general application for multilevel statistical frameworks to test models involving assemblages and/or communities, and as large‐scale SNP data from nonmodel species become routine, the aSFS expands the potential for powerful next‐generation comparative population genomic inference.     

The effect of recombination on the neutral evolution of genetic robustness

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 only through neutral mutations can evolve mutational robustness [E. van Nimwegen, J.P. Crutchfield, M. Huynen, Neutral evolution of mutational robustness, Proc. Natl. Acad. Sci. USA 96(17), 9716-9720 (1999)], by concentrating the population on regions of high neutrality. Introducing recombination we demonstrate, through numerically calculating the stationary distribution of an infinite population on ensembles of random neutral networks that mutational robustness is significantly enhanced and further that the magnitude of this enhancement is sensitive to details of the neutral network topology. Through the simulation of finite populations of genotypes evolving on random neutral networks and a scaled down microRNA neutral network, we show that even in finite populations recombination will still act to focus the population on regions of locally high neutrality.     

How to optimize the precision of allele and haplotype frequency estimates using pooled‐sequencing data

Sequencing pools of individuals rather than individuals separately reduces the costs of estimating allele frequencies at many loci in many populations. Theoretical and empirical studies show that sequencing pools comprising a limited number of individuals (typically fewer than 50) provides reliable allele frequency estimates, provided that the DNA pooling and DNA sequencing steps are carefully controlled. Unequal contributions of different individuals to the DNA pool and the mean and variance in sequencing depth both can affect the standard error of allele frequency estimates. To our knowledge, no study separately investigated the effect of these two factors on allele frequency estimates; so that there is currently no method to a priori estimate the relative importance of unequal individual DNA contributions independently of sequencing depth. We develop a new analytical model for allele frequency estimation that explicitly distinguishes these two effects. Our model shows that the DNA pooling variance in a pooled sequencing experiment depends solely on two factors: the number of individuals within the pool and the coefficient of variation of individual DNA contributions to the pool. We present a new method to experimentally estimate this coefficient of variation when planning a pooled sequencing design where samples are either pooled before or after DNA extraction. Using this analytical and experimental framework, we provide guidelines to optimize the design of pooled sequencing experiments. Finally, we sequence replicated pools of inbred lines of the plant Medicago truncatula and show that the predictions from our model generally hold true when estimating the frequency of known multilocus haplotypes using pooled sequencing.     

Research of population with impulsive perturbations based on dynamics of a neutral delay equation and ecological quality system

This paper studies the global behaviors of a nonlinear autonomous neutral delay differential population model with impulsive perturbation. This model may be suitable for describing the dynamics of population with long larval and short adult phases. It is shown that the system may have global stability of the extinction and positive equilibria, or grow without being bounded under some conditions.     

The effect of recurrent mutation on the frequency spectrum of a segregating site and the age of an allele

The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to be polymorphic. This distribution is widely used in population genetic inferences, including statistical tests of neutrality in which a skew in the observed frequency spectrum across independent sites is taken as a signature of departure from neutral evolution. Theoretical aspects of the frequency spectrum have been well studied and several interesting results are available, but they are usually under the assumption that a site has undergone at most one mutation event in the history of the sample. Here, we extend previous theoretical results by allowing for at most two mutation events per site, under a general finite allele model in which the mutation rate is independent of current allelic state but the transition matrix is otherwise completely arbitrary. Our results apply to both nested and nonnested mutations. Only the former has been addressed previously, whereas here we show it is the latter that is more likely to be observed except for very small sample sizes. Further, for any mutation transition matrix, we obtain the joint sample frequency spectrum of the two mutant alleles at a triallelic site, and derive a closed-form formula for the expected age of the younger of the two mutations given their frequencies in the population. Several large-scale resequencing projects for various species are presently under way and the resulting data will include some triallelic polymorphisms. The theoretical results described in this paper should prove useful in population genomic analyses of such data.     

Improving the image quality in STED nanoscopy using frequency spectrum modulation

Since stimulated emission depletion (STED) nanoscopy was invented in 1994, this technique has been widely used in the fields of biomedicine and materials science. According to the imaging principle of STED technology, increasing the power of the depletion laser within a certain threshold can improve the resolution. However, it will cause not only severe photo-damage to the samples and photo-bleaching to the fluorophores but also serious background noise, leading to the degeneration of the quality of STED images. Here we propose a new processing method based on frequency spectrum modulation to improve the quality of STED images, abbreviated as FM-STED. We have demonstrated the performance of FM-STED in improving the signal-to-noise ratio and the resolution using fluorescent beads and biological cells as samples.     

不同杀虫剂选育对家蝇抗药性水平及kdr基因频率的影响

采用杀虫剂（溴氰菊酯和甲基嘧啶磷）筛选及不接触药物自然衰退的方法,研究了家蝇Musca domestica氯氟氰菊酯高抗品系(Cyh-R)对杀虫剂的抗性变化,探讨蝇类抗药性治理的方法。用点滴法测定氯氟氰菊酯对不同家蝇品系的毒力,比较抗药性的变化,结合特异性等位基因PCR扩增（PASA）技术检测了不同家蝇品系的kdr基因频率,探讨kdr基因频率与抗性水平之间的关系。结果表明:甲基嘧啶磷筛选后,氯氟氰菊酯对第2~8代Cyh-R品系的LD₅₀呈递减趋势,从F₀的2.8434 μg/蝇降为F₈的0.4404 μg/蝇,但第8~18代Cyh-R品系的LD₅₀呈逐代递增趋势;溴氰菊酯筛选后,氯氟氰菊酯对Cyh-R品系第2~16代的LD₅₀呈上升趋势,从F₀的2.8434 μg/蝇升至F₁₆的24.3249 μg/蝇;表明了施用有机磷杀虫剂可降低其对氯氟氰菊酯的抗药性,而施用拟除虫菊酯药剂则有助于其对氯氟氰菊酯抗药性的增长;不使用任何杀虫剂也能降低其对氯氟氰菊酯的抗药性,但下降速率低于甲基嘧啶磷。PASA技术检测表明Cyh-R品系的kdr抗性基因频率为88.8%,不经过任何药剂筛选其kdr抗性基因频率下降程度最大,达到69.7%;甲基嘧啶磷筛选后其结果降为78.8%,而经溴氰菊酯筛选后kdr抗性基因频率则明显升高,达到98.9%。通过对kdr抗性基因频率和抗性水平进行相关和回归分析表明kdr抗性基因频率与家蝇对氯氟氰菊酯的LD₅₀呈对数关系,即LD₅₀值高的品系其kdr抗性基因频率相应的也较高。建议在家蝇防治中考虑轮换用药。     

The influence of the frequency of periodic disturbances on the maintenance of phytoplankton diversity

The influence of periodic disturbances of various frequency on the maintenance of the phytoplankton diversity was studied by semicontinuous competition experiments. Disturbances consisted of dilution events, which meant both addition of fresh nutrients and elimination of organisms. The intervals between dilution events varied from 1 to 14 days. Diversity was found to increase with increasing intervals between disturbances. coexisting species belonged to different strategy types: (a) species with rapid growth under enriched conditions, (b) species with good competitive abilities under impoverished conditions, (c) species with the ability to build up storage pools of the limiting nutrient. An increase of the number of coexisting species over the number that would have coexisted in steady state was only found when the interval exceeded one generation time.     

Stochastic modelling of shifts in allele frequencies reveals a strongly polygynous mating system in the re‐introduced Asiatic wild ass

Small populations are prone to loss of genetic variation and hence to a reduction in their evolutionary potential. Therefore, studying the mating system of small populations and its potential effects on genetic drift and genetic diversity is of high importance for their viability assessments. The traditional method for studying genetic mating systems is paternity analysis. Yet, as small populations are often rare and elusive, the genetic data required for paternity analysis are frequently unavailable. The endangered Asiatic wild ass (Equus hemionus), like all equids, displays a behaviourally polygynous mating system; however, the level of polygyny has never been measured genetically in wild equids. Combining noninvasive genetic data with stochastic modelling of shifts in allele frequencies, we developed an alternative approach to paternity analysis for studying the genetic mating system of the re‐introduced Asiatic wild ass in the Negev Desert, Israel. We compared the shifts in allele frequencies (as a measure of genetic drift) that have occurred in the wild ass population since re‐introduction onset to simulated scenarios under different proportions of mating males. We revealed a strongly polygynous mating system in which less than 25% of all males participate in the mating process each generation. This strongly polygynous mating system and its potential effect on the re‐introduced population's genetic diversity could have significant consequences for the long‐term persistence of the population in the Negev. The stochastic modelling approach and the use of allele‐frequency shifts can be further applied to systems that are affected by genetic drift and for which genetic data are limited.     

Why sampling scheme matters: the effect of sampling scheme on landscape genetic results

There has been a recent trend in genetic studies of wild populations where researchers have changed their sampling schemes from sampling pre-defined populations to sampling individuals uniformly across landscapes. This reflects the fact that many species under study are continuously distributed rather than clumped into obvious “populations”. Once individual samples are collected, many landscape genetic studies use clustering algorithms and multilocus genetic data to group samples into subpopulations. After clusters are derived, landscape features that may be acting as barriers are examined and described. In theory, if populations were evenly sampled, this course of action should reliably identify population structure. However, genetic gradients and irregularly collected samples may impact the composition and location of clusters. We built genetic models where individual genotypes were either randomly distributed across a landscape or contained gradients created by neighbor mating for multiple generations. We investigated the influence of six different sampling protocols on population clustering using program STRUCTURE, the most commonly used model-based clustering method for multilocus genotype data. For models where individuals (and their alleles) were randomly distributed across a landscape, STRUCTURE correctly predicted that only one population was being sampled. However, when gradients created by neighbor mating existed, STRUCTURE detected multiple, but different numbers of clusters, depending on sampling protocols. We recommend testing for fine scale autocorrelation patterns prior to sample clustering, as the scale of the autocorrelation appears to influence the results. Further, we recommend that researchers pay attention to the impacts that sampling may have on subsequent population and landscape genetic results. The U.S. Government's right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Genetic heterogeneity among the Hindus and their relationships with the other “Caucasoid” populations: New data on Punjab-Haryana and Rajasthan Indian States

The genetic structure of Rajasthan Hindus and Punjab-Haryana Hindus and Sikhs has been studied for ABO, RH, APOC2, C6, C7, F13A, F13B, HP, ORM1, ACP1, ADA, AK1, ESD, GLO1, PGD, PGM1 subtyping, and PGP. This is the first genetic survey on Hindus of Rajasthan. Furthermore, many of these markers have never been studied on Hindus before (APOC2, C6, 07, F13A, F13B, ORMl, PGP). These data, together with those previously available for Hindus, have been utilized to analyze the within-Hindus genetic heterogeneity by R_ST statistic and correspondence analysis. The genetic relationships of Hindus to other Causcasoid populations were also investigated. In the first analysis, two eastern states (Orissa and Andhra Pradesh) were found to be quite separate from each other and clearly distinct from the northwestern and western states. Out of the markers which could not be utilized in this analysis, PGM1 subtyping turned out to discriminate between the Dravidian—speaking and the Indo-Aryan-speaking Hindus. The second analysis shows a clear-cut separation of Hindus from Europeans, with Near Eastern and Middle Eastern populations genetically in an intermediate position. © 1995 Wiley-Liss, Inc.     

A new method for studying population genetics of cyst nematodes based on Pool‐Seq and genomewide allele frequency analysis

Cyst nematodes are important agricultural pests responsible for billions of dollars of losses each year. Plant resistance is the most effective management tool, but it requires a close monitoring of population genetics. Current technologies for pathotyping and genotyping cyst nematodes are time‐consuming, expensive and imprecise. In this study, we capitalized on the reproduction mode of cyst nematodes to develop a simple population genetic analysis pipeline based on genotyping‐by‐sequencing and Pool‐Seq. This method yielded thousands of SNPs and allowed us to study the relationships between populations of different origins or pathotypes. Validation of the method on well‐characterized populations also demonstrated that it was a powerful and accurate tool for population genetics. The genomewide allele frequencies of 23 populations of golden nematode, from nine countries and representing the five known pathotypes, were compared. A clear separation of the pathotypes and fine genetic relationships between and among global populations were obtained using this method. In addition to being powerful, this tool has proven to be very time‐ and cost‐efficient and could be applied to other cyst nematode species.