Coalescent Process Research Articles

The TMRCA of general genealogies in populations of variable size.

We study the time to the most recent common ancestor of a sample of finite size in a wide class of genealogical models for populations with variable size. This is made possible by recently developed results on inhomogeneous phase-type random variables, allowing us to obtain the density and the moments of the TMRCA of time-dependent coalescent processes in terms of matrix formulas. We also provide matrix simplifications permitting a more straightforward calculation. With these results, the TMRCA provides an explicative variable to distinguish different evolutionary scenarios.

Identifiability of speciation times under the multispecies coalescent

The advent of rapid and inexpensive sequencing technologies has necessitated the development of computationally efficient methods for analyzing sequence data for many genes simultaneously in a phylogenetic framework. The coalescent process is the most commonly used model for linking the underlying genealogies of individual genes with the global species-level phylogeny, but inference under the coalescent model is computationally daunting in the typical inference frameworks (e.g., the likelihood and Bayesian frameworks) due to the dimensionality of the space of both gene trees and species trees. Here we consider estimation of the branch lengths in fixed species trees with three or four taxa, and show that these branch lengths are identifiable. We also show that for three and four taxa simple estimators for the branch lengths can be derived based on observed site pattern frequencies. Properties of these estimators, such as their asymptotic variances and large-sample distributions, are examined, and performance of the estimators is assessed using simulation. Finally, we use these estimators to develop a hypothesis test that can be used to delimit species under the coalescent model for three or four putative taxa.

The coalescent in finite populations with arbitrary, fixed structure

The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary – but fixed – spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings C=Ctt=0∞ from a finite set G to itself. The set G represents the “sites” (in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, Ct:G→G, maps each site g∈G to the site containing g’s ancestor, t time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio r, we find that measures of genetic dissimilarity, among any set of sites, are scaled by 4r(1−r) relative to the even sex ratio case.

Coalescent processes emerging from large deviations

The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman’s coalescent process, which produces a binary tree, emerges universally from many microscopic models in which the variance in the number of offspring is finite. It is understood that power-law offsprings distributions with infinite variance can result in a very different type of coalescent structure with merging of more than two lineages. Here, we investigate the regime where the variance of the offspring distribution is finite but comparable to the population size. This is achieved by studying a model in which the log offspring sizes have stretched exponential tails. Such offspring distributions are motivated by biology, where they emerge from a toy model of growth in a heterogeneous environment, but also from mathematics and statistical physics, where limit theorems and phase transitions for sums over random exponentials have received considerable attention due to their appearance in the partition function of Derrida’s random energy model (REM). We find that the limit coalescent is a β-coalescent—a previously studied model emerging from evolutionary dynamics models with heavy-tailed offspring distributions. We also discuss the connection to previous results on the REM.

Neutral diversity in experimental metapopulations

New automated and high-throughput methods allow the manipulation and selection of numerous bacterial populations. In this manuscript we are interested in the neutral diversity patterns that emerge from such a setup in which many bacterial populations are grown in parallel serial transfers, in some cases with population-wide extinction and splitting events. We model bacterial growth by a birth–death process and use the theory of coalescent point processes. We show that there is a dilution factor that optimises the expected amount of neutral diversity for a given number of cycles, and study the power law behaviour of the mutation frequency spectrum for different experimental regimes. We also explore how neutral variation diverges between two recently split populations by establishing a new formula for the expected number of shared and private mutations. Finally, we show the interest of such a setup to select a phenotype of interest that requires multiple mutations.

Bursts of coalescence within population pedigrees whenever big families occur.

We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright-Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination. Our population model is of the type for which multiple-merger coalescent processes have been described. We prove that the conditional distribution of the pairwise coalescence time given the random pedigree converges to a limit law as the population size tends to infinity. This limit law may or may not be the usual exponential distribution of the Kingman coalescent, depending on the frequency of big families. But because it includes the number and times of big families, it differs from the usual multiple-merger coalescent models. The usual multiple-merger coalescent models are seen as describing the ancestral process marginal to, or averaging over, the pedigree. In the limiting ancestral process conditional on the pedigree, the intervals between big families can be modeled using the Kingman coalescent but each big family causes a discrete jump in the probability of coalescence. Analogous results should hold for larger samples and other population models. We illustrate these results with simulations and additional analysis, highlighting their implications for inference and understanding of multilocus data.

Coalescence and sampling distributions for Feller diffusions

Consider the diffusion process defined by the forward equation ut(t,x)=12{xu(t,x)}xx−α{xu(t,x)}x for t,x≥0 and −∞<α<∞, with an initial condition u(0,x)=δ(x−x0). This equation was introduced and solved by Feller to model the growth of a population of independently reproducing individuals. We explore important coalescent processes related to Feller’s solution. For any α and x0>0 we calculate the distribution of the random variable An(s;t), defined as the finite number of ancestors at a time s in the past of a sample of size n taken from the infinite population of a Feller diffusion at a time t since since its initiation. In a subcritical diffusion we find the distribution of population and sample coalescent trees from time t back, conditional on non-extinction as t→∞. In a supercritical diffusion we construct a coalescent tree which has a single founder and derive the distribution of coalescent times.

Coalescent point process of branching trees in a varying environment

Coalescent point process of branching trees in a varying environment

Genomic inference of a severe human bottleneck during the Early to Middle Pleistocene transition.

Population size history is essential for studying human evolution. However, ancient population size history during the Pleistocene is notoriously difficult to unravel. In this study, we developed a fast infinitesimal time coalescent process (FitCoal) to circumvent this difficulty and calculated the composite likelihood for present-day human genomic sequences of 3154 individuals. Results showed that human ancestors went through a severe population bottleneck with about 1280 breeding individuals between around 930,000 and 813,000 years ago. The bottleneck lasted for about 117,000 years and brought human ancestors close to extinction. This bottleneck is congruent with a substantial chronological gap in the available African and Eurasian fossil record. Our results provide new insights into our ancestry and suggest a coincident speciation event.

The structured coalescent in the context of gene copy number variation

The Structured Coalescent was introduced to describe the coalescent process in spatially subdivided populations with migration. Here, we re-interpret migration routes of individuals in the original model as “migration routes” of single genes in tandemly arranged gene arrays. A gene copy may change its position within the array via unequal recombination. Hence, in a coalescent framework, two copies sampled from two chromosomes may coalesce only if they are at exactly homologous positions. Otherwise, one or multiple recombination events have to occur before they can coalesce, thereby increasing mean coalescence time and expected genetic diversity among the copies in a gene array.We explicitly calculate the transition probabilities on these routes backward in time. We simulate the structured coalescent with migration and coalescence rates informed by the unequal recombination process of gene copies. With this novel interpretation of population structure models we determine coalescence times and expected genetic diversity in samples of orthologous and paralogous copies from a gene family. As a case study, we discuss the site frequency spectrum of a small gene family in the two scenarios of high and of no gene copy number variation among individuals. These examples underline the significance of our model, since standard test-statistics may lead to misinterpretations when analyzing sequence data of multi-copy genes due to their different expected genetic diversity.

Comparison between p-distance and single-locus species delimitation models for delineating reproductively tested strains of pennate diatoms (Bacillariophyceae) using cox1, rbcL and ITS.

Several automated molecular methods have emerged for distinguishing eukaryote species based on DNA sequence data. However, there are knowledge gaps around which of these single-locus methods is more accurate for the identification of microalgal species, such as the highly diverse and ecologically relevant diatoms. We applied genetic divergence, Automatic Barcode Gap Discovery for primary species delimitation (ABGD), Assemble Species by Automatic Partitioning (ASAP), Statistical Parsimony Network Analysis (SPNA), Generalized Mixed Yule Coalescent (GMYC) and Poisson Tree Processes (PTP) using partial cox1, rbcL, 5.8S + ITS2, ITS1 + 5.8S + ITS2 markers to delineate species and compare to published polyphasic identification data (morphological features, phylogeny and sexual reproductive isolation) to test the resolution of these methods. ASAP, ABGD, SPNA and PTP models resolved species of Eunotia, Seminavis, Nitzschia, Sellaphora and Pseudo-nitzschia corresponding to previous polyphasic identification, including reproductive isolation studies. In most cases, these models identified diatom species in similar ways, regardless of sequence fragment length. GMYC model presented smallest number of results that agreed with previous published identification. Following the recommendations for proper use of each model presented in the present study, these models can be useful tools to identify cryptic or closely related species of diatoms, even when the datasets have relatively few sequences.

Occurrence of five distinct clades of mermithid nematodes (Nematoda: Mermithidae) infecting black fly larvae (Diptera: Simuliidae) in tropical streams in Malaysia.

Mermithids are the most common parasites of black flies and are associated with host feminization and sterilization in infected hosts. However, information on the species / lineage of black fly mermithids in Southeast Asia, including Malaysia requires further elucidation. In this study, mermithids were obtained from black fly larvae collected from 138 freshwater stream sites across East and West Malaysia. A molecular approach based on nuclear-encoded 18S ribosomal RNA (18S rRNA) gene was used to identify the species identity / lineage of 77 nematodes successfully extracted and sequenced from the specimens collected. Maximum likelihood and neighbor-joining phylogenetic analyses demonstrated five distinct mermithid lineages. Four species delimitation analyses: automated simultaneous analysis phylogenetics (ASAP), maximum likelihood Poisson tree processes with Bayesian inferences (bPTP_ML), generalized mixed yule coalescent (GMYC) and single rate Poisson tree processes (PTP) were applied to delimit the species boundaries of mermithid lineages in this data set along with genetic distance analysis. Data analysis supports five distinct lineages or operational taxonomic units for mermithids in the present study, with two requiring further investigation as they may represent intraspecific variation or closely related taxa. One mermithid lineage was similar to that previously observed in Simulium nigrogilvum from Thailand. Co-infection with two mermithids of different lineages was observed in one larva of Simulium trangense. This study represents an important first step towards exploring other aspects of host - parasite interactions in black fly mermithids.

PhyloCoalSimulations: A Simulator for Network Multispecies Coalescent Models, Including a New Extension for the Inheritance of Gene Flow.

We consider the evolution of phylogenetic gene trees along phylogenetic species networks, according to the network multispecies coalescent process, and introduce a new network coalescent model with correlated inheritance of gene flow. This model generalizes two traditional versions of the network coalescent: with independent or common inheritance. At each reticulation, multiple lineages of a given locus are inherited from parental populations chosen at random, either independently across lineages or with positive correlation according to a Dirichlet process. This process may account for locus-specific probabilities of inheritance, for example. We implemented the simulation of gene trees under these network coalescent models in the Julia package PhyloCoalSimulations, which depends on PhyloNetworks and its powerful network manipulation tools. Input species phylogenies can be read in extended Newick format, either in numbers of generations or in coalescent units. Simulated gene trees can be written in Newick format, and in a way that preserves information about their embedding within the species network. This embedding can be used for downstream purposes, such as to simulate species-specific processes like rate variation across species, or for other scenarios as illustrated in this note. This package should be useful for simulation studies and simulation-based inference methods. The software is available open source with documentation and a tutorial at https://github.com/cecileane/PhyloCoalSimulations.jl.

Testing Multispecies Coalescent Simulators Using Summary Statistics.

As genomic-scale datasets motivate research on species tree inference, simulators of the multispecies coalescent (MSC) process have become essential for the testing and evaluation of new inference methods. However, the simulators themselves must be tested to ensure that they give valid samples. This work develops methods for checking whether a collection of gene trees is in accord with the MSC model on a given species tree. When applied to well-known simulators, we find that several give flawed samples. The tests presented are capable of validating both topological and metric properties of gene tree samples, and are implemented in a freely available R package MSCsimtester so that developers and users may easily apply them.

Spatial evolution of human cultures inferred through Bayesian phylogenetic analysis.

Spatial distribution of human culture reflects both descent from the common ancestor and horizontal transmission among neighbouring populations. To analyse empirically documented geographical variations in cultural repertoire, we will describe a framework for Bayesian statistics in a spatially explicit model. To consider both horizontal transmission and mutation of the cultural trait in question, our method employs a network model in which populations are represented by nodes. Using algorithms borrowed from Bayesian phylogenetic analysis, we will perform a Markov chain Monte Carlo (MCMC) method to compute the posterior distributions of parameters, such as the rate of horizontal transmission and the mutation rates among trait variants, as well as the identity of trait variants in unobserved populations. Besides the inference of model parameters, our method enables the reconstruction of the genealogical tree of the focal trait, provided that the mutation rate is sufficiently small. We will also describe a heuristic algorithm to reduce the dimension of the parameter space explored in the MCMC method, where we simulate the coalescent process in the network of populations. Numerical examples show that our algorithms compute the posterior distribution of model parameters within a practical computation time, although the posterior distribution tends to be broad if we use uninformative priors.

Species tree estimation under joint modeling of coalescence and duplication: Sample complexity of quartet methods

We consider species tree estimation under a standard stochastic model of gene tree evolution that incorporates incomplete lineage sorting (as modeled by a coalescent process) and gene duplication and loss (as modeled by a branching process). Through a probabilistic analysis of the model, we derive sample complexity bounds for widely used quartet-based inference methods that highlight the effect of the duplication and loss rates in both subcritical and supercritical regimes.

Diversity of Siphonaria Sowerby I, 1823 (Gastropoda, Siphonariidae) in the Seychelles Bank and beyond

AbstractMolecular phylogenetic studies have shown that the characters of the reduced shell of the false limpets of the genus Siphonaria Sowerby I, 1823 are highly variable and often insufficient for species delimitation. The taxonomy and distribution of Siphonaria in the Indian Ocean are poorly known. We sampled Siphonaria in the Seychelles Bank to check the occurrence of recorded species using DNA sequences and to study the paths through which Siphonaria species have colonised the Seychelles Bank by reconstructing their phylogenetic relationships. Analyses of a dataset comprising 16 S rRNA gene sequences of 33 specimens from the Seychelles Bank and 300 additional Siphonaria sequences from other regions from GenBank with various methods for species delimitation resulted in 19–102 primary species hypotheses. Assemble Species by Automatic Partitioning provided a conservative estimate of the species number (42) in which several indisputable species were lumped. The results of Automatic Barcode Gap Discovery depended strongly on the assumed prior maximum intraspecific divergence, whereas the tree‐based methods Generalised Mixed Yule Coalescent and Poisson Tree Processes resulted in high overestimates. The specimens from the Seychelles Bank represent three clades, belonging to the Siphonaria ‘atra’ group, the Siphonaria ‘normalis’ group and a possibly undescribed species recorded previously only from Hainan. At least two of the three species recorded from the Seychelles Bank came from the east, i.e., from the Coral Triangle in the Indo‐Australian Archipelago, the region with the highest marine biodiversity worldwide. A major transport mechanism across the Indian Ocean was probably the South Equatorial Current.

Mathematics of coalescent gene trees

Using the coalescent process continuously until all the lineages have become one, we get different possible gene trees. In this paper I had computed the probabilities of such different gene trees that occur depending on the way lineages can form. In particular I had shown the probability of any 3 sample gene tree is 1/3 and for four samples resembling caterpillar gene trees the probability is 1/18 and probability for any balanced gene tree with 4 samples is 1/9. I have also proved a theorem providing the number of ranked gene trees. This estimate will help us to determine the probability of any gene tree.

Site pattern probabilities under the multispecies coalescent and a relaxed molecular clock: Theory and applications

The first step in statistical inference of the evolutionary histories of species is developing a probability model that describes the mutation process as accurately and realistically as possible. A major complication of this inference is that different loci on the genome can have histories that diverge from the common species history and each other. The multispecies coalescent process is commonly used to model one source of this divergence, incomplete lineage sorting, or ILS. In Chifman and Kubatko (2015), the authors computed the site pattern probabilities for four taxa under a full probability model based on the Jukes-Cantor substitution model when the molecular clock holds. This paper generalizes that work to a relaxed clock model, allowing for mutation rates to differ among species. This will enable better phylogentic inference in cases where the molecular clock does not hold.

Phylogeny, species delimitation, and ecological and morphological diversity of Characithecium (Monogenoidea: Dactylogyridae).

Abstract Characithecium (Monogenoidea, Dactylogyridae) is a genus containing nine species that live on the gills of a characid clade containing genera Astyanax, Andromakhe, Psalidodon and Oligosarcus (Characiformes, Characidae) in South and Central America. Earlier studies suggest a tight coevolutionary history between these parasites and their hosts mainly due to the phylogenetic proximity between these genera of fish. Hence, this study explores phylogenetic relationships, species limits and extrinsic factors (geography and ecology) explaining parasite prevalence. To understand the evolutionary history of the genus, we constructed a time-calibrated phylogenetic hypothesis, which includes eight of the nine known species of Characithecium sampled from a broad spectrum of host species. The phylogeny supports the monophyly of Characithecium, with its most recent common ancestor dating from the Miocene. Using generalized mixed-yule coalescent and Bayesian Poisson tree process methods, species delimitation analyses suggested fewer species than the proposed delimitation based on morphology alone, recovering four and six entities, respectively. The results indicate that species of Characithecium have wider geographical and host distribution and higher prevalence on Oligosarcus species compared to Astyanax and Psalidodon. Correlation between parasite prevalence and biotic and abiotic traits, based on generalized linear models, indicates that the frequency of occurrence of different species of Characithecium is associated with distinct factors, such as host genus, high altitudes, rivers and streams, and different ecoregions. Our results suggest that species of Characithecium are highly opportunistic, exploring resources in different manner as our data reveal the ability of these parasites to explore a diverse environment of variable biotic (e.g. hosts) and abiotic features.