Coalescent Theory Research Articles

Effect of Incomplete Lineage Sorting On Tree-Reconciliation-Based Inference of Gene Duplication.

In the tree reconciliation approach to infer the duplication history of a gene family, the gene (family) tree is compared to the corresponding species tree. Incomplete lineage sorting (ILS) gives rise to stochastic variation in the topology of a gene tree and hence likely introduces false duplication events when a tree reconciliation method is used. We quantify the effect of ILS on gene duplication inference in a species tree in terms of the expected number of false duplication events inferred from reconciling a random gene tree, which occurs with a probability predicted in coalescent theory, and the species tree. We computationally examine the relationship between the effect of ILS on duplication inference in a species tree and its topological parameters. Our findings suggest that ILS may cause non-negligible bias on duplication inference, particularly on an asymmetric species tree. Hence, when gene duplication is inferred via tree reconciliation or any other approach that takes gene tree topology into account, the ILS-induced bias should be examined cautiously.

Bayesian inference of local trees along chromosomes by the sequential Markov coalescent.

We propose a genealogy-sampling algorithm, Sequential Markov Ancestral Recombination Tree (SMARTree), that provides an approach to estimation from SNP haplotype data of the patterns of coancestry across a genome segment among a set of homologous chromosomes. To enable analysis across longer segments of genome, the sequence of coalescent trees is modeled via the modified sequential Markov coalescent (Marjoram and Wall, Genetics 7:16, 2006). To assess performance in estimating these local trees, our SMARTree implementation is tested on simulated data. Our base data set is of the SNPs in 10 DNA sequences over 50 kb. We examine the effects of longer sequences and of more sequences, and of a recombination and/or mutational hotspot. The model underlying SMARTree is an approximation to the full recombinant-coalescent distribution. However, in a small trial on simulated data, recovery of local trees was similar to that of LAMARC (Kuhner et al. Genetics 156:1393-1401, 2000a), a sampler which uses the full model.

An analytical framework in the general coalescent tree setting for analyzing polymorphisms created by two mutations.

This paper presents an analytical framework for analyzing polymorphisms created by two mutation events in samples of DNA sequences modeled in the general coalescent tree setting. I developed the framework by deriving analytical formulas for the numbers of the topologies of the genealogies with two mutation events. This approach gives an advantage to analyze polymorphisms in large samples of DNA sequences at a non-recombining locus under vicarious evolutionary scenarios. Particularly the framework allows to estimate the probability of polymorphism data created by two mutation events as well as the ages of the events. Based on these results I extended the definition of the site frequency spectrum by classifying pairs of polymorphic sites into groups and presented analytical expressions for computing the expected sizes of these groups. Within the framework I also designed a Bayesian approach for inferring the haplotype of the most recent common ancestor at two polymorphic sites. Lastly, the framework was applied to polymorphism data from human APOE gene region under various demographic scenarios for ancestral human population and explored the signature of linkage disequilibrium for inferring the ancestral haplotype at two polymorphic sites. Interestingly enough, the results show that the most frequent haplotype at two completely linked polymorphic sites is not always the most likely candidate for the haplotype of the most recent common ancestor.

Phylodynamic inference for structured epidemiological models.

Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.

When is Sampling Complete? The Effects of Geographical Range and Marker Choice on Perceived Diversity in Nitzschia palea (Bacillariophyta)

DNA barcoding, being developed for biomonitoring, requires a database of reference sequences and knowledge of how much sequences can deviate before they are assigned to separate species. The molecular hunt for hidden species also raises the question of species definitions. We examined whether there are objective criteria for sequence-based species delimitation in diatoms, using Nitzschia palea, an important monophyletic indicator species already known to contain cryptic diversity. Strains from a wide geographical range were sequenced for 28S rRNA, COI and rbcL. Homogeneity indices and the Chao index failed to objectively select a precise number of species existing in N. palea as well as an evolutionary method based on coalescence theory. COI always gave higher diversity estimations than 28S rRNA or rbcL. Mating data did not provide a precise calibration of molecular species thresholds. Rarefaction curves indicated that further MOTUs would be detected with more isolates than we sampled (81 clones, 42 localities). Although some genotypes had intercontinental distributions, there was a positive relationship between genetic and geographical distance, suggesting even higher richness than we assessed, given that many regions were not sampled. Overall, no objective criteria were found for species separation; instead barcoding will need a consensual approach to molecular species limits.

Molecular systematics of the world's most polytypic bird: the <italic>Pachycephala pectoralis</italic>/<italic>melanura</italic> (Aves: Pachycephalidae) species complex

With more than 70 described subspecies distributed from Java to Fiji, the Golden Whistler species complex (Aves: Pachycephala pectoralis/melanura) is the world's most geographically variable bird species. We sequenced ten genes totalling 5743 bp from 202 individuals and 32 nominal subspecies, mostly from the Australasian and Polynesian lineages. We used concatenated maximum likelihood and Bayesian inference, as well as coalescent species tree analysis, to reconstruct a phylogeny. The resulting phylogeny is the most densely sampled and robust estimate of this group's evolutionary history to date and many novel relationships are revealed. The ingroup comprised three well-supported clades. An Australasian clade inclusive of Vanuatu was sister to a clade including the Bismarck Archipelago, the Solomon Islands, and the Polynesian taxa minus Vanuatu, and sister to these two clades was Pachycephala citreogaster collaris of the Louisiade Archipelago. Some species-level taxa endemic to the Pacific were found to be embedded in the ingroup (e.g. Pachycephala feminina, Pachycephala flavifrons, and Pachycephala jacquinoti), whereas others were found to be outside of the species complex (e.g. Pachycephala implicata). Generally, most nodes in the tree had strong support with the exception of several Polynesian lineages whose relationships remain equivocal. Relationships within each clade are discussed in detail, and current taxonomic treatments are critiqued in light of our results. © 2013 The Linnean Society of London

Distinguishing neutral from deleterious mutations in growing populations

Distinguishing neutral from deleterious mutations in growing populations

General Triallelic Frequency Spectrum Under Demographic Models with Variable Population Size

It is becoming routine to obtain data sets on DNA sequence variation across several thousands of chromosomes, providing unprecedented opportunity to infer the underlying biological and demographic forces. Such data make it vital to study summary statistics that offer enough compression to be tractable, while preserving a great deal of information. One well-studied summary is the site frequency spectrum-the empirical distribution, across segregating sites, of the sample frequency of the derived allele. However, most previous theoretical work has assumed that each site has experienced at most one mutation event in its genealogical history, which becomes less tenable for very large sample sizes. In this work we obtain, in closed form, the predicted frequency spectrum of a site that has experienced at most two mutation events, under very general assumptions about the distribution of branch lengths in the underlying coalescent tree. Among other applications, we obtain the frequency spectrum of a triallelic site in a model of historically varying population size. We demonstrate the utility of our formulas in two settings: First, we show that triallelic sites are more sensitive to the parameters of a population that has experienced historical growth, suggesting that they will have use if they can be incorporated into demographic inference. Second, we investigate a recently proposed alternative mechanism of mutation in which the two derived alleles of a triallelic site are created simultaneously within a single individual, and we develop a test to determine whether it is responsible for the excess of triallelic sites in the human genome.

Most parsimonious reconciliation in the presence of gene duplication, loss, and deep coalescence using labeled coalescent trees

Accurate gene tree-species tree reconciliation is fundamental to inferring the evolutionary history of a gene family. However, although it has long been appreciated that population-related effects such as incomplete lineage sorting (ILS) can dramatically affect the gene tree, many of the most popular reconciliation methods consider discordance only due to gene duplication and loss (and sometimes horizontal gene transfer). Methods that do model ILS are either highly parameterized or consider a restricted set of histories, thus limiting their applicability and accuracy. To address these challenges, we present a novel algorithm DLCpar for inferring a most parsimonious (MP) history of a gene family in the presence of duplications, losses, and ILS. Our algorithm relies on a new reconciliation structure, the labeled coalescent tree (LCT), that simultaneously describes coalescent and duplication-loss history. We show that the LCT representation enables an exhaustive and efficient search over the space of reconciliations, and, for most gene families, the least common ancestor (LCA) mapping is an optimal solution for the species mapping between the gene tree and species tree in an MP LCT. Applying our algorithm to a variety of clades, including flies, fungi, and primates, as well as to simulated phylogenies, we achieve high accuracy, comparable to sophisticated probabilistic reconciliation methods, at reduced run time and with far fewer parameters. These properties enable inferences of the complex evolution of gene families across a broad range of species and large data sets.

LET US NOT BE UNFAIR TO ASEXUALS: THEIR EPHEMERALITY MAY BE EXPLAINED BY NEUTRAL MODELS WITHOUT INVOKING ANY EVOLUTIONARY CONSTRAINTS OF ASEXUALITY

Phylogenetic studies typically demonstrate lower evolutionary ages of clones, relative to their sexual ancestors. This has often been attributed to heightened extinction risk of asexual organisms. We previously criticized such interpretations and demonstrated that the life span of clones is ultimately limited by neutral drift depending on the rate at which new clones are spawned into an asexual community of a finite size. Therefore, it is important to investigate whether the natural rates of such influxes are sufficiently high to account for the relative ephemerality of clones without assuming their increased extinction rate. I applied the neutral clonal turnover model to phylogenies of polyploid asexual ferns and simulated the coalescent trees over a wide range of demographic structures and sampling schemes. On parameterizing the model with biologically relevant estimates of population sizes and plant polyploidization rates, simulated clonal assemblages appeared younger than their sexual counterparts even in the absence of selection against clones. Therefore, differences observed between the ages of sexual and clonal lineages may be explained by the neutral clonal turnover. Researchers should consider the possibility that natural clones may get lost by neutral drift before their fate could eventually be affected by any long-term constraints of asexuality.

Uncovering cryptic diversity and refugial persistence among small mammal lineages across the Eastern Afromontane biodiversity hotspot

The Eastern Afromontane region of Africa is characterized by striking levels of endemism and species richness accompanied by significant conservation threat, a pattern typical across biodiversity hotspots. Using multi-locus molecular data under a coalescent species tree framework we identify major cryptic biogeographic patterns within and between two endemic montane small mammal species complexes, Hylomyscus mice and Sylvisorex shrews, co-distributed across the Albertine Rift and Kenya Highlands of the Eastern Afromontane Biodiversity Hotspot (EABH). Hypotheses put forward to account for the high diversity of the region include retention of older palaeo-endemic lineages across major regions in climatically stable refugia, as well as the accumulation of lineages associated with more recent differentiation between allopatric populations separated by unsuitable habitat during periods of Pleistocene aridification. Sympatric pairs of sister lineages were found to have significantly older divergence times than allopatric pairs. Genetic analyses and historical distribution modeling suggest that regional meta-populations have persisted since the Pliocene to mid-Pleistocene across a climatic gradient from the Albertine Rift in the west to the Kenya Highlands in the east for both focal taxa. Differing patterns of regional sub-division and demographic expansion were detected and are consistent with differing life histories as well as shared responses to regional variation in stability of suitable habitat. There is also strong support in both mice and shrew species for Late Miocene divergence with subsequent range expansion into sympatry in previously unidentified cryptic species pairs. These results highlight the broad temporal scale at which climatic and geological changes may have facilitated rare dispersal events between montane habitats as well as the long-term persistence of populations in both the Albertine Rift and the Kenyan Highlands that together contributed to the high species diversity and endemism in the EABH.

Molecular systematics of the world's most polytypic bird: thePachycephala pectoralis/melanura(Aves: Pachycephalidae) species complex

With more than 70 described subspecies distributed from Java to Fiji, the Golden Whistler species complex (Aves: Pachycephala pectoralis/melanura) is the world's most geographically variable bird species. We sequenced ten genes totalling 5743 bp from 202 individuals and 32 nominal subspecies, mostly from the Australasian and Polynesian lineages. We used concatenated maximum likelihood and Bayesian inference, as well as coalescent species tree analysis, to reconstruct a phylogeny. The resulting phylogeny is the most densely sampled and robust estimate of this group's evolutionary history to date and many novel relationships are revealed. The ingroup comprised three well-supported clades. An Australasian clade inclusive of Vanuatu was sister to a clade including the Bismarck Archipelago, the Solomon Islands, and the Polynesian taxa minus Vanuatu, and sister to these two clades was Pachycephala citreogaster collaris of the Louisiade Archipelago. Some species-level taxa endemic to the Pacific were found to be embedded in the ingroup (e.g. Pachycephala feminina, Pachycephala flavifrons, and Pachycephala jacquinoti), whereas others were found to be outside of the species complex (e.g. Pachycephala implicata). Generally, most nodes in the tree had strong support with the exception of several Polynesian lineages whose relationships remain equivocal. Relationships within each clade are discussed in detail, and current taxonomic treatments are critiqued in light of our results. © 2013 The Linnean Society of London

The Effective Population Sizes of the Anthropoid Ancestors of the Human-Chimpanzee Lineage Provide Insights on the Historical Biogeography of the Great Apes

The recent development of methods that apply coalescent theory to phylogenetic problems has enabled the study of the population-level phenomena that drove the diversification of anthropoid primates. Effective population size, Ne, is one of the main parameters that constitute the theoretical underpinning of these new analytical approaches. For this reason, the ancestral N(e) of selected primate lineages has been thoroughly investigated. However, for some of these lineages, the estimates of ancestral N(e) reported in several studies present significant variation. This is the case for the common ancestor of humans and chimpanzees. Moreover, several ancestral anthropoid lineages have been ignored in the studies conducted so far. Because N(e) is fundamental to understand historic species demography, it is a crucial component of a complete description of the historical scenario of primate evolution. It also provides information that is helpful for differentiating between competing biogeographical hypotheses. In this study, the effective population sizes of the anthropoid ancestors of the human-chimp lineage are inferred using data sets of coding and noncoding sequences. A general pattern of a serial decline of population sizes is found between the ancestral lineage of Anthropoidea and that of Homo and Pan. When the theoretical distribution of gene trees was derived from the parametric estimates obtained, it closely corresponded to the empirical frequency of inferred gene trees along the genome. The most abrupt decrease of N(e) was found between the ancestors of all great apes and those of the African great apes alone. This suggests the occurrence of a genetic bottleneck during the evolution of Homininae, which corroborates the origin of African apes from a Eurasian ancestor.

TESTING MITOCHONDRIAL CAPTURE AND DEEP COALESCENCE IN AMAZONIAN CICHLID FISHES (CICHLIDAE:CICHLA)

Hybridization and introgression have important consequences in evolution, such as increasing the genetic diversity and adaptive potential of a species. One of their most conspicuous footprints is discordance among gene trees or between genes and phenotypes. However, most studies that report introgression fail to disprove the null hypothesis that genetic incongruence may result from stochastic sorting of ancestral allelic polymorphisms. In the case of ancient introgression, these two processes may be especially difficult to distinguish topologically, but they make different predictions about the patterns of coalescence among loci. Here we apply three methods, molecular dating, multispecies coalescent models, and gene tree simulation under coalescence, to compare these two hypotheses that explain the polyphyletic mtDNA of the butterfly peacock bass, Cichla orinocensis. In comparison with a species tree based on 20 unlinked nuclear loci, we determined that mtDNA divergences were too recent to be explained by ancestral polymorphism. Similarly, coalescent species tree branches were significantly shorter when putative introgressed mtDNA was incorporated, and simulations showed the mtDNA topology to be unlikely under lineage sorting only. We conclude that introgression approximately 1.5 million years ago resulted in capture by C. orinocensis of an mtDNA lineage ancestral to the modern subspecies C. oc. monoculus.

Factors Influencing Ascertainment Bias of Microsatellite Allele Sizes: Impact on Estimates of Mutation Rates

Microsatellite loci play an important role as markers for identification, disease gene mapping, and evolutionary studies. Mutation rate, which is of fundamental importance, can be obtained from interspecies comparisons, which, however, are subject to ascertainment bias. This bias arises, for example, when a locus is selected on the basis of its large allele size in one species (cognate species 1), in which it is first discovered. This bias is reflected in average allele length in any noncognate species 2 being smaller than that in species 1. This phenomenon was observed in various pairs of species, including comparisons of allele sizes in human and chimpanzee. Various mechanisms were proposed to explain observed differences in mean allele lengths between two species. Here, we examine the framework of a single-step asymmetric and unrestricted stepwise mutation model with genetic drift. Analysis is based on coalescent theory. Analytical results are confirmed by simulations using the simuPOP software. The mechanism of ascertainment bias in this model is a tighter correlation of allele sizes within a cognate species 1 than of allele sizes in two different species 1 and 2. We present computations of the expected average allele size difference, given the mutation rate, population sizes of species 1 and 2, time of separation of species 1 and 2, and the age of the allele. We show that when the past demographic histories of the cognate and noncognate taxa are different, the rate and directionality of mutations affect the allele sizes in the two taxa differently from the simple effect of ascertainment bias. This effect may exaggerate or reverse the effect of difference in mutation rates. We reanalyze literature data, which indicate that despite the bias, the microsatellite mutation rate estimate in the ancestral population is consistently greater than that in either human or chimpanzee and the mutation rate estimate in human exceeds or equals that in chimpanzee with the rate of allele length expansion in human being greater than that in chimpanzee. We also demonstrate that population bottlenecks and expansions in the recent human history have little impact on our conclusions.

Multilocus genetic diversity and historical biogeography of the endemic wall lizard from Ibiza and Formentera,Podarcis pityusensis(Squamata: Lacertidae)

Two monophyletic sister species of wall lizards inhabit the two main groups of Balearic Islands: Podarcis lilfordi from islets and small islands around Mallorca and Menorca and Podarcis pityusensis from Ibiza, Formentera and associated islets. Genetic diversity within the endangered P. lilfordi has been well characterized, but P. pityusensis has not been studied in depth. Here, 2430 bp of mtDNA and 15 microsatellite loci were analysed from P. pityusensis populations from across its natural range. Two main genetic groupings were identified, although geographical structuring differed slightly between the mtDNA and the nuclear loci. In general, individuals from islets/islands adjacent to the main island of Ibiza were genetically distinct from those from Formentera and the associated Freus islands for both mtDNA and the nuclear loci. However, most individuals from the island of Ibiza were grouped with neighbouring islets/islands for nuclear loci, but with Formentera and Freus islands for the mitochondrial locus. A time-calibrated Bayesian tree was constructed for the principal mitochondrial lineages within the Balearics, using the multispecies coalescent model, and provided statistical support for divergence of the two main P. pityusensis lineages 0.111-0.295 Ma. This suggests a mid-late Pleistocene intraspecific divergence, compared with an early Pleistocene divergence in P. lilfordi, and postdates some major increases in sea level between 0.4 and 0.6 Ma, which may have flooded Formentera. The program IMa2 provided a posterior divergence time of 0.089-0.221 Ma, which was similar to the multispecies coalescent tree estimate. More significantly, it indicated low but asymmetric effective gene copy migration rates, with higher migration from Formentera to Ibiza populations. Our findings suggest that much of the present-day diversity may have originated from a late Pleistocene colonization of one island group from the other, followed by allopatric divergence of these populations. Subsequent gene flow between these insular groups seems likely to be explained by recent human introductions. Two evolutionary significant units can be defined for P. pityusensis but these units would need to exclude the populations that have been the subjects of recent admixture.

Identity by descent: variation in meiosis, across genomes, and in populations.

Gene identity by descent (IBD) is a fundamental concept that underlies genetically mediated similarities among relatives. Gene IBD is traced through ancestral meioses and is defined relative to founders of a pedigree, or to some time point or mutational origin in the coalescent of a set of extant genes in a population. The random process underlying changes in the patterns of IBD across the genome is recombination, so the natural context for defining IBD is the ancestral recombination graph (ARG), which specifies the complete ancestry of a collection of chromosomes. The ARG determines both the sequence of coalescent ancestries across the chromosome and the extant segments of DNA descending unbroken by recombination from their most recent common ancestor (MRCA). DNA segments IBD from a recent common ancestor have high probability of being of the same allelic type. Non-IBD DNA is modeled as of independent allelic type, but the population frame of reference for defining allelic independence can vary. Whether of IBD, allelic similarity, or phenotypic covariance, comparisons may be made to other genomic regions of the same gametes, or to the same genomic regions in other sets of gametes or diploid individuals. In this review, I present IBD as the framework connecting evolutionary and coalescent theory with the analysis of genetic data observed on individuals. I focus on the high variance of the processes that determine IBD, its changes across the genome, and its impact on observable data.

Coalescent Tree Imbalance and a Simple Test for Selective Sweeps Based on Microsatellite Variation

Selective sweeps are at the core of adaptive evolution. We study how the shape of coalescent trees is affected by recent selective sweeps. To do so we define a coarse-grained measure of tree topology. This measure has appealing analytical properties, its distribution is derived from a uniform, and it is easy to estimate from experimental data. We show how it can be cast into a test for recent selective sweeps using microsatellite markers and present an application to an experimental data set from Plasmodium falciparum.

Viscous coalescence of droplets: A lattice Boltzmann study

The coalescence of two resting liquid droplets in a saturated vapor phase is investigated by Lattice Boltzmann simulations in two and three dimensions. We find that, in the viscous regime, the bridge radius obeys a t1/2-scaling law in time with the characteristic time scale given by the viscous time. Our results differ significantly from the predictions of existing analytical theories of viscous coalescence as well as from experimental observations. While the underlying reason for these deviations is presently unknown, a simple scaling argument is given that describes our results well.

Study on Adhesion-Resistant Materials for Improving the Restoration of Exercise-Induced Muscle Tendon Fracture

The muscle tendon is connective tissue, the fracture can occur when its stress is not reasonable. With the establishment of tendon external and endogenous coalescence theory, the suppression of external coalescence and promotion of endogenous coalescence became the crucial problem of resolve adhesion of tendon. The application of adhesion prevention materials in the part of tendon surrounding was the hotspot of recent research. At present, the research about adhesion prevention materials has made remarkable achievements. However, the materials studied in exercise-induced tendon rupture were cut both ways, therefore, as a material for adhesion prevention and functional reconstruction to treatment of tendon rupture. There are still many unsolved problems in the application of adhesion prevention materials.