Coalescent Genealogy Research Articles

A coalescent sampler successfully detects biologically meaningful population structure overlooked by F-statistics.

Assessing the geographic structure of populations has relied heavily on Sewell Wright's F‐statistics and their numerous analogues for many decades. However, it is well appreciated that, due to their nonlinear relationship with gene flow, F‐statistics frequently fail to reject the null model of panmixia in species with relatively high levels of gene flow and large population sizes. Coalescent genealogy samplers instead allow a model‐selection approach to the characterization of population structure, thereby providing the opportunity for stronger inference. Here, we validate the use of coalescent samplers in a high gene flow context using simulations of a stepping‐stone model. In an example case study, we then re‐analyze genetic datasets from 41 marine species sampled from throughout the Hawaiian archipelago using coalescent model selection. Due to the archipelago's linear nature, it is expected that most species will conform to some sort of stepping‐stone model (leading to an expected pattern of isolation by distance), but F‐statistics have only supported this inference in ~10% of these datasets. Our simulation analysis shows that a coalescent sampler can make a correct inference of stepping‐stone gene flow in nearly 100% of cases where gene flow is ≤100 migrants per generation (equivalent to F ST = 0.002), while F‐statistics had mixed results. Our re‐analysis of empirical datasets found that nearly 70% of datasets with an unambiguous result fit a stepping‐stone model with varying population sizes and rates of gene flow, although 37% of datasets yielded ambiguous results. Together, our results demonstrate that coalescent samplers hold great promise for detecting weak but meaningful population structure, and defining appropriate management units.

Topological linkage disequilibrium calculated from coalescent genealogies

We revisit the classical, and introduce a novel, concept of two-locus linkage disequilibrium (LD). In contrast to defining haplotypes as allele combinations at two marker loci, we concentrate on the clustering of a sample of chromosomes induced by their coalescent genealogy. The root of a binary coalescent tree defines two clusters of chromosomes, each one of them containing the left and right descendants of the root. At two different loci this assignment may be different as a result of recombination. We show that the proportion of shared chromosomes among clusters at two different loci, measured by the squared correlation, constitutes a natural measure of LD. We call this topological LD (tLD) since it is induced by the topology of the coalescent tree. We find that it is, on average, larger than classical LD for any given distance between loci. Furthermore, tLD has a smaller coefficient of variation, which should provide an advantage, compared to the use of classical LD, for any kind of mapping purposes. We conclude with a practical application to the LCT region in human populations.

Population Genetics of Verticillium dahliae in Iran Based on Microsatellite and Single Nucleotide Polymorphism Markers.

Verticillium dahliae is a plant pathogenic fungus that reproduces asexually and its population structure is highly clonal. In the present study, 78 V. dahliae isolates from Iran were genotyped for mating type, single nucleotide polymorphisms (SNPs), and microsatellites to assign them to clonal lineages and to determine population genetic structure in Iran. The mating type of all isolates was MAT1-2. Based on neighbor-joining analysis and minimum spanning networks constructed from SNPs and microsatellite genotypes, respectively, all but four isolates were assigned to lineage 2B824; four isolates were assigned to lineage 4B. The inferred coalescent genealogy of isolates in lineage 2B824 showed a clear divergence into two clades that corresponded to geographic origin and host. Haplotypes of cotton and pistachio isolates sampled from central Iran were in one clade, and those of isolates from Prunus spp. sampled from northwestern Iran were in the other. The strong divergence in haplotypes between the two clades suggests that there were at least two separate introductions of lineage 2B824 to different parts of Iran. Given the history of cotton and pistachio cultivation and Verticillium wilt in Iran, these results are consistent with the hypothesis that cotton was historically a likely source inoculum causing Verticillium wilt in pistachio.

Wright–Fisher diffusion bridges

The trajectory of the frequency of an allele which begins at x at time 0 and is known to have frequency z at time T can be modelled by the bridge process of the Wright–Fisher diffusion. Bridges when x=z=0 are particularly interesting because they model the trajectory of the frequency of an allele which appears at a time, then is lost by random drift or mutation after a time T. The coalescent genealogy back in time of a population in a neutral Wright–Fisher diffusion process is well understood. In this paper we obtain a new interpretation of the coalescent genealogy of the population in a bridge from a time t∈(0,T). In a bridge with allele frequencies of 0 at times 0 and T the coalescence structure is that the population coalesces in two directions from t to 0 and t to T such that there is just one lineage of the allele under consideration at times 0 and T. The genealogy in Wright–Fisher diffusion bridges with selection is more complex than in the neutral model, but still with the property of the population branching and coalescing in two directions from time t∈(0,T). The density of the frequency of an allele at time t is expressed in a way that shows coalescence in the two directions. A new algorithm for exact simulation of a neutral Wright–Fisher bridge is derived. This follows from knowing the density of the frequency in a bridge and exact simulation from the Wright–Fisher diffusion. The genealogy of the neutral Wright–Fisher bridge is also modelled by branching Pólya urns, extending a representation in a Wright–Fisher diffusion. This is a new very interesting representation that relates Wright–Fisher bridges to classical urn models in a Bayesian setting.

Detecting the existence of gene flow between Spanish and North African goats through a coalescent approach.

Human-driven migrations are one of the main processes shaping the genetic diversity and population structure of domestic species. However, their magnitude and direction have been rarely analysed in a statistical framework. We aimed to estimate the impact of migration on the population structure of Spanish and African goats. To achieve this goal, we analysed a dataset of 1,472 individuals typed with 23 microsatellites. Population structure of African and Spanish goats was moderate (mean FST = 0.07), with the exception of the Canarian and South African breeds that displayed a significant differentiation when compared to goats from North Africa and Nigeria. Measurement of gene flow with Migrate-n and IMa coalescent genealogy samplers supported the existence of a bidirectional gene flow between African and Spanish goats. Moreover, IMa estimates of the effective number of migrants were remarkably lower than those calculated with Migrate-n and classical approaches. Such discrepancies suggest that recent divergence, rather than extensive gene flow, is the main cause of the weak population structure observed in caprine breeds.

Exact coalescent simulation of new haplotype data from existing reference haplotypes

We introduce a coalescent-based method (RECOAL) for the simulation of new haplotype data from a reference population of haplotypes. A coalescent genealogy for the reference haplotype data is sampled from the appropriate posterior probability distribution, then a coalescent genealogy is simulated which extends the sampled genealogy to include new haplotype data. The new haplotype data will, therefore, contain both some of the existing polymorphic sites and new polymorphisms added based on the structure of the simulated coalescent genealogy. This allows exact coalescent simulation of new haplotype data, compared with other methods which are more approximate in nature. We demonstrate the performance of our method using a variety of data simulated under a coalescent model, before applying it to data from the 1000 Genomes project.

Duality, ancestral and diffusion processes in models with selection

The ancestral selection graph in population genetics was introduced by Krone and Neuhauser [Krone, S.M., Neuhauser, C., 1997. Ancestral process with selection. Theor. Popul. Biol. 51, 210–237] as an analogue of the coalescent genealogy of a sample of genes from a neutrally evolving population. The number of particles in this graph, followed backwards in time, is a birth and death process with quadratic death and linear birth rates. In this paper an explicit form of the probability distribution of the number of particles is obtained by using the density of the allele frequency in the corresponding diffusion model obtained by Kimura [Kimura, M., 1955. Stochastic process and distribution of gene frequencies under natural selection. Cold Spring Harbor Symposia on Quantitative Biology 20, 33–53]. It is shown that the process of fixation of the allele in the diffusion model corresponds to convergence of the ancestral process to its stationary measure. The time to fixation of the allele conditional on fixation is studied in terms of the ancestral process.

LAMARC 2.0: maximum likelihood and Bayesian estimation of population parameters

We present a Markov chain Monte Carlo coalescent genealogy sampler, LAMARC 2.0, which estimates population genetic parameters from genetic data. LAMARC can co-estimate subpopulation Theta = 4N(e)mu, immigration rates, subpopulation exponential growth rates and overall recombination rate, or a user-specified subset of these parameters. It can perform either maximum-likelihood or Bayesian analysis, and accomodates nucleotide sequence, SNP, microsatellite or elecrophoretic data, with resolved or unresolved haplotypes. It is available as portable source code and executables for all three major platforms. LAMARC 2.0 is freely available at http://evolution.gs.washington.edu/lamarc

Minimal clade size and external branch length under the neutral coalescent

Given a sample of genes taken from a large population, we consider the neutral coalescent genealogy and study the theoretical and empirical distributions of the size of the smallest clade containing a fixed gene. We show that the theoretical distribution is strongly related to a Yule distribution of parameter 2, and that the empirical count statistics are asymptotically Gaussian as the number of genes grows to infinity. Then we consider external branches of the coalescent tree, and describe their lengths. Using the infinitely many sites model of mutation, we also describe the conditional distribution of the external branch lengths, given the number of pairwise differences between a reference DNA sequence and the sequence of one closest relative in the sample.

Minimal clade size and external branch length under the neutral coalescent

Given a sample of genes taken from a large population, we consider the neutral coalescent genealogy and study the theoretical and empirical distributions of the size of the smallest clade containing a fixed gene. We show that the theoretical distribution is strongly related to a Yule distribution of parameter 2, and that the empirical count statistics are asymptotically Gaussian as the number of genes grows to infinity. Then we consider external branches of the coalescent tree, and describe their lengths. Using the infinitely many sites model of mutation, we also describe the conditional distribution of the external branch lengths, given the number of pairwise differences between a reference DNA sequence and the sequence of one closest relative in the sample.

Estimation of effective population size of HIV-1 within a host: a pseudomaximum-likelihood approach.

Using pseudomaximum-likelihood approaches to phylogenetic inference and coalescent theory, we develop a computationally tractable method of estimating effective population size from serially sampled viral data. We show that the variance of the maximum-likelihood estimator of effective population size depends on the serial sampling design only because internal node times on a coalescent genealogy can be better estimated with some designs than with others. Given the internal node times and the number of sequences sampled, the variance of the maximum-likelihood estimator is independent of the serial sampling design. We then estimate the effective size of the HIV-1 population within nine hosts. If we assume that the mutation rate is 2.5 x 10(-5) substitutions/generation and is the same in all patients, estimated generation lengths vary from 0.73 to 2.43 days/generation and the mean (1.47) is similar to the generation lengths estimated by other researchers. If we assume that generation length is 1.47 days and is the same in all patients, mutation rate estimates vary from 1.52 x 10(-5) to 5.02 x 10(-5). Our results indicate that effective viral population size and evolutionary rate per year are negatively correlated among HIV-1 patients.