Coalescent process with fluctuating population size and its effective size

We consider a Wright-Fisher model whose population size is a finite Markov chain. We introduce a sequence of two-dimensional discrete time Markov chains whose components describe the coalescent process and the fluctuation of population size. For the limiting process of the sequence of Markov chains, the relationship of the expectation of coalescence time to the harmonic and the arithmetic means of population sizes is shown, and the Laplace transform of the distribution of coalescence time is calculated. We define the coalescence effective population size (cEPS) by the expectation of coalescence time. We show that cEPS is strictly larger (resp. smaller) than the harmonic (resp. arithmetic) mean. As the population size fluctuates more quickly (resp. slowly), cEPS is closer to the harmonic (resp. arithmetic) mean. For the case of a two-valued Markov chain, we show the explicit expression of cEPS and its dependency on the sample size.     

The Variance of Coalescent Time Estimates from DNA Sequences

A method for estimating the variance of a simple estimate of the time of the most recent common ancestor of a sample of sequences is described. [Reviewing Editor: Dr. Rasmus Nielson]     

一个具选择、突变、迁移的群体的遗传差分模型

假设一个群体是由“单位点—双基因”的个体所组成的,在该群体内存在选择、突变、迁移、生死等效应的作用。本文给出了在上述假设下并满足:(1)世代重叠,选择、突变、迁移、生死等效应的作用均在世代遗传之间完成;(2)群体适当大,个体间交配随机,符合孟德尔式遗传;(3)没有任何意外的灾祸等约定的群体遗传的数学模型。通过模型分析,我们能够进一步用数学语言来解释一些生命现象。模型分析指出:虽然某些群体不满足Hardy-Weinberg定律所叙述的条件,但可能具有和Hardy-Weinberg定律的结论相似的结果。该文中还就几个主要参数的变化讨论了群体遗传和进化的某些性质,如平衡等。最后,我们给出了该模型的一个数值例子。     

The coalescent in two colonies with symmetric migration

Kingman's coalescent process is extended to two colonies with symmetric migration. The mean waiting time until a sample of genes taken from two colonies coalesces to a common ancestor is obtained. The final step in the waiting time before the process is absorbed at 1 is observed to have an intriguing behaviour. The distribution of this final waiting time converges to the known distribution of the corresponding waiting time in the case of a single population as the migration rate tends to zero. The mean, however, does not converge. The waiting time until a sample has two common ancestors is modeled as a function of the migration rate. Finally bounds for the expected waiting time for the two colonies to have j > 1 ancestors are derived.     

A Computational Approach for Modeling the Allele Frequency Spectrum of Populations with Arbitrarily Varying Size

The allele frequency spectrum (AFS), or site frequency spectrum, is commonly used to summarize the genomic polymorphism pattern of a sample, which is informative for inferring population history and detecting natural selection. In 2013, Chen and Chen developed a method for analytically deriving the AFS for populations with temporally varying size through the coalescence time-scaling function. However, their approach is only applicable to population history scenarios in which the analytical form of the time-scaling function is tractable. In this paper, we propose a computational approach to extend the method to populations with arbitrary complex varying size by numerically approximating the time-scaling function. We demonstrate the performance of the approach by constructing the AFS for two population history scenarios: the logistic growth model and the Gompertz growth model, for which the AFS are unavailable with existing approaches. Software for implementing the algorithm can be downloaded at http://chenlab.big.ac.cn/software/.     

Likelihood-based inference for genetic correlation coefficients

We review Wright's original definitions of the genetic correlation coefficients F(ST), F(IT), and F(IS), pointing out ambiguities and the difficulties that these have generated. We also briefly survey some subsequent approaches to defining and estimating the coefficients. We then propose a general framework in which the coefficients are defined, their properties established, and likelihood-based inference implemented. Likelihood methods of inference are proposed both for bi-allelic and multi-allelic loci, within a hierarchical model which allows sharing of information both across subpopulations and across loci, but without assuming constancy in either case. This framework can be used, for example, to detect environment-related diversifying selection.     

A continuous migration model with stable demography

A probability model of a population undergoing migration, mutation, and mating in a geographic continuum R is constructed, and an integrodifferential equation is derived for the probability of genetic identity. The equation is solved in one case, and asymptotic analysis done in others. Individuals at x, y R in the model mate with probability V(x, y) dt in any time interval (t, t + dt). In two dimensions, if V(x,y) = V(x–y) where V(x) V(x/)/ ² approaches a delta function, the equilibrium probability of identity vanishes as 0. The asymptotic rate at which this occurs is discussed for mutation rates u u _o > 0 and for Cu , > 0, and u 0.Partially supported by NSF grant MCS79-03472Research was partially supported by Task Agreement No. DE-AT06-76EV71005 under Contract No. DE-AM06-76RL02225 between the U.S. Dept. Energy and the University of Washington     

Coalescent patterns in diploid exchangeable population models

A class of two-sex population models is considered with N females and equal number N of males constituting each generation. Reproduction is assumed to undergo three stages: 1) random mating, 2) exchangeable reproduction, 3) random sex assignment. Treating individuals as pairs of genes at a certain locus we introduce the diploid ancestral process (the past genealogical tree) for n such genes sampled in the current generation. Neither mutation nor selection are assumed. A convergence criterium for the diploid ancestral process is proved as N goes to infinity while n remains unchanged. Conditions are specified when the limiting process (coalescent) is the Kingman coalescent and situations are discussed when the coalescent allows for multiple mergers of ancestral lines.Work supported by the Bank of Sweden Tercentenary Foundation.Mathematics Subject Classification (2000):Primary 92F25, 60J70; Secondary 92D15, 60F17     

Methods for assessing gene content diversity of KIR with examples from a global set of populations

A number of statistical methods are widely used to describe allelic variation at specific genetic loci and its implication on the evolutionary history of these loci. Although the methods were developed primarily to study allelic variation at loci that are virtually always present in the genome, they are often applied to data of gene content variation (i.e., presence/absence of multiple homologous genes) at the killer cell immunoglobulin-like receptor (KIR) gene cluster. In this paper, we discuss methodological issues involved in the analysis of gene content variation data in the KIR region and also its covariation with polymorphism at the human leukocyte antigen class I loci, which encode ligands for KIR. A comparison of several statistical methods and measures (gene frequency, haplotype frequency, and linkage disequilibrium estimation) using the Centre d’Etude du Polymorphisme Humain data will be provided using KIR haplotypes that have been determined by segregation analysis, noting the strengths and weaknesses of the methods when only the presence/absence data is considered. Finally, application of these methods to a set of globally distributed populations is described (see Single et al., Nat Genet 39:1114–1119, 2007) in order to illustrate the challenges faced when inferring the joint effects of natural selection and demographic history on these immune-related genes.     

Markov Model of Haploid Random Mating with Given Distribution of Population Size

An exact Markov chain model is formulated and computed for random mating in a haploid gamete pool. There are two versions of the gamete, and there is a finite number of diploid monoecious organisms. The founder population is given, and the subsequent generations allow a prescribed statistical distribution over different population sizes. The non-homogeneous Markov chain works on the haploid gamete level provided the probability of self-fertilization is 1/n, where n is the number of diploid individuals. Standard deviations of gamete frequencies and fixation probabilities are calculated. Effective population sizes for different population size distributions are estimated, including periodic bottlenecks.     

Lichenicolous fungi show population subdivision by host species but do not share population history with their hosts

Lichenicolous fungi are a species-rich biological group growing on lichen thalli. Here, we analyze the genetic structure of the lichenicolous basidiomycete Tremella lobariacearum and three host species (Lobaria pulmonaria, Lobaria macaronesica, and Lobaria immixta) in Macaronesia. We used ordination and analysis of molecular variance to investigate the structuring of genetic variation, and a simulation test to investigate whether rDNA haplotypes of T. lobariacearum were significantly associated with host species. To investigate the evolutionary and demographic history of the lichenicolous fungus and its hosts, we used coalescent samplers to generate trees, and Bayesian skyline plots. We found that the hosts were most important in structuring populations of the lichenicolous species. Despite their wide geographic distribution, the same haplotypes of T. lobariacearum consistently associated with a given host species. Our results suggest that the Lobaria hosts create a selective environment for the lichenicolous fungus. Both the pathogen and the host populations exhibited substantial genetic structure. However, evolutionary and demographic histories differed between the parasite and its hosts, as evidenced by different divergence times and tree topologies.     

Selection, mutation and sexual reproduction in an infinite haploid population with a genome of finite length

We present a model which describes mutation, selection and sexual reproduction in an infinite haploid population with a finite genome. Each generation is described using an approximation which assures a certain persistent form of the distribution of the number of deleterious elements. The steady state exists and is determined. In addition, we conclude that the introduction of sexual reproduction increases the mean fitness in the equilibrium.     

Populations with Explicit Borders in Space and Time: Concept,Terminology, and Estimation of Characteristic Parameters

Biologists studying short-lived organisms have become aware of the need to recognize an explicit temporal extend of a population over a considerable time. In this article we outline the concept and the realm of populations with explicit spatial and temporary boundaries. We call such populations “temporally bounded populations”. In the concept, time is of the same importance as space in terms of a dimension to which a population is restricted. Two parameters not available for populations that are only spatially defined characterise temporally bounded populations: total population size, which is the total number of individuals present within the temporal borders, and total residence time, which is the sum of the residence times of all individuals. We briefly review methods to estimate these parameters. We illustrate the concept for the large blue butterfly (Maculinea nausithous) and outline insights into ecological and conservation-relevant processes that cannot be gained without the use of the concept.     

两点法测量组织光学特性中有效时间的选择

在改进两点法的基础上,对不同约化散射系数与吸收系数之比（μｓ’／μａ）的生物组织进行了模拟测量。结果表明有效时间决定于生物组织的光学特性和探测位置,μｓ’／μａ值一定时,有效时间随光源和探测点间的距离增大而增大;光源和探测点的距离一定是,有效时间随μｓ’／μａ值的减小而增大,反之亦然。