Coalescent Theory Research Articles

The Impact of the Tree Prior on Molecular Dating of Data Sets Containing a Mixture of Inter- and Intraspecies Sampling

In Bayesian phylogenetic analyses of genetic data, prior probability distributions need to be specified for the model parameters, including the tree. When Bayesian methods are used for molecular dating, available tree priors include those designed for species-level data, such as the pure-birth and birth-death priors, and coalescent-based priors designed for population-level data. However, molecular dating methods are frequently applied to data sets that include multiple individuals across multiple species. Such data sets violate the assumptions of both the speciation and coalescent-based tree priors, making it unclear which should be chosen and whether this choice can affect the estimation of node times. To investigate this problem, we used a simulation approach to produce data sets with different proportions of within- and between-species sampling under the multispecies coalescent model. These data sets were then analyzed under pure-birth, birth-death, constant-size coalescent, and skyline coalescent tree priors. We also explored the ability of Bayesian model testing to select the best-performing priors. We confirmed the applicability of our results to empirical data sets from cetaceans, phocids, and coregonid whitefish. Estimates of node times were generally robust to the choice of tree prior, but some combinations of tree priors and sampling schemes led to large differences in the age estimates. In particular, the pure-birth tree prior frequently led to inaccurate estimates for data sets containing a mixture of inter- and intraspecific sampling, whereas the birth-death and skyline coalescent priors produced stable results across all scenarios. Model testing provided an adequate means of rejecting inappropriate tree priors. Our results suggest that tree priors do not strongly affect Bayesian molecular dating results in most cases, even when severely misspecified. However, the choice of tree prior can be significant for the accuracy of dating results in the case of data sets with mixed inter- and intraspecies sampling. [Bayesian phylogenetic methods; model testing; molecular dating; node time; tree prior.].

Colonization and diversification of aquatic insects on three Macaronesian archipelagos using 59 nuclear loci derived from a draft genome

The study of processes driving diversification requires a fully sampled and well resolved phylogeny, although a lack of phylogenetic markers remains a limitation for many non-model groups. Multilocus approaches to the study of recent diversification provide a powerful means to study the evolutionary process, but their application remains restricted because multiple unlinked loci with suitable variation for phylogenetic or coalescent analysis are not available for most non-model taxa. Here we identify novel, putative single-copy nuclear DNA (nDNA) phylogenetic markers to study the colonization and diversification of an aquatic insect species complex, Cloeon dipterum L. 1761 (Ephemeroptera: Baetidae), in Macaronesia. Whole-genome sequencing data from one member of the species complex were used to identify 59 nDNA loci (32,213 base pairs), followed by Sanger sequencing of 29 individuals sampled from 13 islands of three Macaronesian archipelagos. Multispecies coalescent analyses established six putative species. Three island species formed a monophyletic clade, with one species occurring on the Azores, Europe and North America. Ancestral state reconstruction indicated at least two colonization events from the mainland (to the Canaries, respectively Azores) and one within the archipelago (between Madeira and the Canaries). Random subsets of the 59 loci showed a positive linear relationship between number of loci and node support. In contrast, node support in the multispecies coalescent tree was negatively correlated with mean number of phylogenetically informative sites per locus, suggesting a complex relationship between tree resolution and marker variability. Our approach highlights the value of combining genomics, coalescent-based phylogeography, species delimitation, and phylogenetic reconstruction to resolve recent diversification events in an archipelago species complex.

Fumio Tajima and the Origin of Modern Population Genetics.

![Figure][1] A fundamental concept in population genetics is the representation of the evolutionary history of a sample, of a single locus, as a tree. The theory describing such trees is called “coalescence theory,” and the primary mathematical model used is called “the coalescent,”

SCOTTI: Efficient Reconstruction of Transmission within Outbreaks with the Structured Coalescent.

Exploiting pathogen genomes to reconstruct transmission represents a powerful tool in the fight against infectious disease. However, their interpretation rests on a number of simplifying assumptions that regularly ignore important complexities of real data, in particular within-host evolution and non-sampled patients. Here we propose a new approach to transmission inference called SCOTTI (Structured COalescent Transmission Tree Inference). This method is based on a statistical framework that models each host as a distinct population, and transmissions between hosts as migration events. Our computationally efficient implementation of this model enables the inference of host-to-host transmission while accommodating within-host evolution and non-sampled hosts. SCOTTI is distributed as an open source package for the phylogenetic software BEAST2. We show that SCOTTI can generally infer transmission events even in the presence of considerable within-host variation, can account for the uncertainty associated with the possible presence of non-sampled hosts, and can efficiently use data from multiple samples of the same host, although there is some reduction in accuracy when samples are collected very close to the infection time. We illustrate the features of our approach by investigating transmission from genetic and epidemiological data in a Foot and Mouth Disease Virus (FMDV) veterinary outbreak in England and a Klebsiella pneumoniae outbreak in a Nepali neonatal unit. Transmission histories inferred with SCOTTI will be important in devising effective measures to prevent and halt transmission.

Species delimitation in the reef coral genera Echinophyllia and Oxypora (Scleractinia, Lobophylliidae) with a description of two new species

Scleractinian corals are affected by environment-induced phenotypic plasticity and intraspecific morphological variation caused by genotype. In an effort to identify new strategies for resolving this taxonomic issue, we applied a molecular approach for species evaluation to two closely related genera, Echinophyllia and Oxypora, for which few molecular data are available. A robust multi-locus phylogeny using DNA sequence data across four loci of both mitochondrial (COI, ATP6-NAD4) and nuclear (histone H3, ITS region) origin from 109 coral colonies was coupled with three independent putative species delimitation methods based on barcoding threshold (ABGD) and coalescence theory (PTP, GMYC). Observed overall congruence across multiple genetic analyses distinguished two traditional species (E. echinoporoides and O. convoluta), a species complex composed of E. aspera, E. orpheensis, E. tarae, and O. glabra, whereas O. lacera and E. echinata were indistinguishable with the sequenced loci. The combination of molecular species delimitation approaches and skeletal character observations allowed the description of two new reef coral species, E. bulbosa sp. n. from the Red Sea and E. gallii sp. n. from the Maldives and Mayotte. This work demonstrated the efficiency of multi-locus phylogenetic analyses and recently developed molecular species delimitation approaches as valuable tools to disentangle taxonomic issues caused by morphological ambiguities and to re-assess the diversity of scleractinian corals.

Genome-wide SNP data suggest complex ancestry of sympatric North Pacific killer whale ecotypes.

Three ecotypes of killer whale occur in partial sympatry in the North Pacific. Individuals assortatively mate within the same ecotype, resulting in correlated ecological and genetic differentiation. A key question is whether this pattern of evolutionary divergence is an example of incipient sympatric speciation from a single panmictic ancestral population, or whether sympatry could have resulted from multiple colonisations of the North Pacific and secondary contact between ecotypes. Here, we infer multilocus coalescent trees from >1000 nuclear single-nucleotide polymorphisms (SNPs) and find evidence of incomplete lineage sorting so that the genealogies of SNPs do not all conform to a single topology. To disentangle whether uncertainty in the phylogenetic inference of the relationships among ecotypes could also result from ancestral admixture events we reconstructed the relationship among the ecotypes as an admixture graph and estimated f4-statistics using TreeMix. The results were consistent with episodes of admixture between two of the North Pacific ecotypes and the two outgroups (populations from the Southern Ocean and the North Atlantic). Gene flow may have occurred via unsampled 'ghost' populations rather than directly between the populations sampled here. Our results indicate that because of ancestral admixture events and incomplete lineage sorting, a single bifurcating tree does not fully describe the relationship among these populations. The data are therefore most consistent with the genomic variation among North Pacific killer whale ecotypes resulting from multiple colonisation events, and secondary contact may have facilitated evolutionary divergence. Thus, the present-day populations of North Pacific killer whale ecotypes have a complex ancestry, confounding the tree-based inference of ancestral geography.

Short tandem repeat number estimation from paired-end reads for multiple individuals by considering coalescent tree.

BackgroundTwo types of approaches are mainly considered for the repeat number estimation in short tandem repeat (STR) regions from high-throughput sequencing data: approaches directly counting repeat patterns included in sequence reads spanning the region and approaches based on detecting the difference between the insert size inferred from aligned paired-end reads and the actual insert size. Although the accuracy of repeat numbers estimated with the former approaches is high, the size of target STR regions is limited to the length of sequence reads. On the other hand, the latter approaches can handle STR regions longer than the length of sequence reads. However, repeat numbers estimated with the latter approaches is less accurate than those with the former approaches.ResultsWe proposed a new statistical model named coalescentSTR that estimates repeat numbers from paired-end read distances for multiple individuals simultaneously by connecting the read generative model for each individual with their genealogy. In the model, the genealogy is represented by handling coalescent trees as hidden variables, and the summation of the hidden variables is taken on coalescent trees sampled based on phased genotypes located around a target STR region with Markov chain Monte Carlo. In the sampled coalescent trees, repeat number information from insert size data is propagated, and more accurate estimation of repeat numbers is expected for STR regions longer than the length of sequence reads.For finding the repeat numbers maximizing the likelihood of the model on the estimation of repeat numbers, we proposed a state-of-the-art belief propagation algorithm on sampled coalescent trees.ConclusionsWe verified the effectiveness of the proposed approach from the comparison with existing methods by using simulation datasets and real whole genome and whole exome data for HapMap individuals analyzed in the 1000 Genomes Project.

In the light of evolution X: Comparative phylogeography

Phylogeography is the study of the spatial arrangement of genealogical lineages, especially within and among conspecific populations and closely related species (10). Ever since its inception in the late 1970s (11, 12) and mid-1980s (13), the field has sought to extend phylogenetic reasoning to the intraspecific level, and thereby build empirical and conceptual bridges between the formerly separate disciplines of microevolutionary population genetics and macroevolutionary phylogenetics. In the early years, phylogeographers relied on data from restriction-site surveys of mitochondrial (mt) DNA to draw inferences about population structure and historical demography, but stunning improvements in molecular techniques (14, 15) and extensions of coalescent theory and other analytical methods (16) later broadened the field’s scope dramatically (17). Phylogeographic perspectives have transformed aspects of population biology, biogeography, systematics, ecology, genetics, and biodiversity conservation. One aim of this colloquium was to bring together leading scientists to address the current state of phylogeography as the discipline enters its fourth decade. The broader goal was to update a wide audience on recent developments in phylogeographic research and their relevance to past accomplishments and future research directions.

Interpretation of findings of founder population genetics studies applying lineage extinction theory

Population genetic investigation of founder events produce intriguing results and this work discusses how branching processes help the cross-examination of such results. For example one reads that 40% of the current Ashkenazi population carry the mtDNA of four founding mothers, (Behar et al., 2006) half of the Ashkenazi Levites descend from one founder (Behar et al., 2003), and 22% of the Malagasy population are descendants of a Polynesian ancestor, (Cox et al., 2012). Probability distributions obtained using a Galton–Watson lineage extinction model yield statistical relations between current population and founder population data. These relations lead to most likely estimates and 90% confidence intervals of the founder population size. The investigation compares the Galton–Watson methodology with the Wright–Fisher model adopted by coalescent theory and a back-to-back analysis of the Malagasy founder event produces matching results. The results reconcile the previous knowledge about the roots of Ashkenazi Jewry with published population genetic findings. They also confirm that random drift is sufficient to explain the genetic findings of the examined examples.

Stochastic evolutionary dynamics in minimum-effort coordination games

The minimum-effort coordination game draws recently more attention for the fact that human behavior in this social dilemma is often inconsistent with the predictions of classical game theory. Here, we combine evolutionary game theory and coalescence theory to investigate this game in finite populations. Both analytic results and individual-based simulations show that effort costs play a key role in the evolution of contribution levels, which is in good agreement with those observed experimentally. Besides well-mixed populations, set structured populations have also been taken into consideration. Therein we find that large number of sets and moderate migration rate greatly promote effort levels, especially for high effort costs.

Migration Route Out of Africa Unresolved by 225 Egyptian and Ethiopian Whole Genome Sequences.

Population structure is a fundamental part of population genetics. In coalescent theory, the impact of population structure or a restriction of gene flow is well-studied (Hudson, 1990; Nordborg, 2003). Admixture is inter-mating between previously isolated populations, although the biological characteristics of genetically diverged parental populations can be debated. The pairwise sequentially Markovian coalescent model (Li and Durbin, 2011) and the multiple sequentially Markovian coalescent model (Schiffels and Durbin, 2014), both recently developed methods designed for whole genome sequence analysis, do not model admixture in a formal sense. However, simulations have shown that these models are sensitive to admixture (Li and Durbin, 2011), because admixture increases heterozygosity and consequently appears as an increase in the effective population size. The issue of ancient vs. recent admixture, and the actual time depths, is of concern due to the potentially obscuring effects of a range of evolutionary processes. Both of these models divide time into intervals, theoretically permitting detection of events at different time depths. Consequently, these genetic models have the potential to complement anthropological and archeological studies of the distant past.

Reproductive skew in Japanese sardine inferred from DNA sequences

AbstractAn excess of low-frequency mutations is a ubiquitous characteristic of many marine species, and may be explained by three hypotheses. First, the demographic expansion hypothesis postulates that many species experienced a post-glacial expansion following a Pleistocene population bottleneck. The second invokes some form of natural selection, such as directional selection and selective sweeps. The third explanation, the reproductive skew hypothesis, postulates that high variation in individual reproductive success in many marine species influences genetic diversity. In this study, we focused on demography and reproductive success and the use of coalescent theory to analyse mitochondrial DNA sequences from the Japanese sardine. Our results show that population parameters estimated from both the site-frequency spectrum and the mismatch distribution of pairwise nucleotide differences refute the demographic expansion hypothesis. Further, the observed mismatch distribution, compared with the expectations of the reproductive skew hypothesis, supports the presence of multiple mergers in the genealogy. Many short external branches but few long terminal branches are found in the sardine genealogy. Model misspecification can lead to misleading contemporary and historical estimates of the genetically effective population sizes in marine species. The prevalence of reproductive skew in marine species influences not only the analysis of genetic data but also has ecological implications for understanding variation in reproductive and recruitment patterns in exploited species.

Coalescent models for developmental biology and the spatio-temporal dynamics of growing tissues.

Development is a process that needs to be tightly coordinated in both space and time. Cell tracking and lineage tracing have become important experimental techniques in developmental biology and allow us to map the fate of cells and their progeny. A generic feature of developing and homeostatic tissues that these analyses have revealed is that relatively few cells give rise to the bulk of the cells in a tissue; the lineages of most cells come to an end quickly. Computational and theoretical biologists/physicists have, in response, developed a range of modelling approaches, most notably agent-based modelling. These models seem to capture features observed in experiments, but can also become computationally expensive. Here, we develop complementary genealogical models of tissue development that trace the ancestry of cells in a tissue back to their most recent common ancestors. We show that with both bounded and unbounded growth simple, but universal scaling relationships allow us to connect coalescent theory with the fractal growth models extensively used in developmental biology. Using our genealogical perspective, it is possible to study bulk statistical properties of the processes that give rise to tissues of cells, without the need for large-scale simulations.

The influence of grain boundary angle on the hot cracking of single crystal superalloy DD6

Grain boundary is found to be the most vulnerable place to produce hot cracking during casting and welding processes. Understanding the underlying mechanism of it is helpful to prevent the crack for the repair of aerospace and automotive parts. By producing bi-crystal with pure tilt grain boundary, the effect of boundary misorientation on hot cracking susceptibility was studied for Ni-based superalloy DD6. It is found that the crack takes place when the grain boundary angle is larger than 16° under the present processing conditions. The experimental results are discussed by the theory of coalescence at the last stage of solidification. Furthermore, the calculated temperature interval corresponding to the vulnerable regime in the intradendritic region is much smaller than the coalescence undercooling for the residual liquid film at the boundary, indicating that if the grain boundary exists, the key factor to the hot cracking is the liquid film but not those in the intradendritic region.

Probabilistic models for the (sub)tree(s) of life

The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths), culminating in the $\beta$-family of Aldous' branching models. We next introduce real trees (trees as metric spaces) and show how to study them through their contour, provided they are properly measured and ordered. We then focus on the reduced tree, or coalescent tree, which is the tree spanned by individuals/species alive at the same fixed time. We show how reduced trees, like any compact ultrametric space, can be represented in a simple way via the so-called comb metric. Beautiful examples of random combs include the Kingman coalescent and coalescent point processes. We end up displaying some recent biological applications of coalescent point processes to the inference of species diversification, to conservation biology and to epidemiology.

Effect of the dendritic morphology on hot tearing of carbon steels

Hot tears form during solidification in the brittle region of the dendritic front. Most hot tearing criteria are based on solid and fluid mechanics, being the phenomenon strictly depending on the solid resistance to applied strains and on the liquid capability of filling the void spaces. Modelling both mechanisms implies the precise description of the dendritic morphology. To this scope, the theory of coalescence of the dendritic arms at grain boundaries of Rappaz et al. has been applied, in this work, to the columnar growth of carbon steels by means of a simple mathematical model. Depending on the alloy composition, solid bridging starts at solid fractions down to about 0.8 and up to above 0.995 (very low carbon). The morphology of the brittle region changes drastically with increasing carbon and adding other solutes. In particular, ferritic dendrites, typical of low carbon steels, tend to offer short and wide interdendritic spaces to the surrounding liquid making possible their complete filling, and few solid bridges; peritectic steels show the rise of austenite growing and bridging rapidly in the interdendritic spaces, preventing void formation; austenitic dendrites form long and narrow interdendritic spaces difficult to reach for the liquid and with a lot of solid bridges. Sulphur addition mainly acts in delaying the coalescence end, more markedly in ferritic dendrites.

Old but not ancient: coalescent species tree of New Caledonian geckos reveals recent post‐inundation diversification

AbstractAimNew Caledonia is a remnant of the land mass Tasmantis that harbours high levels of endemism. Two primary hypotheses have been proposed for the origin of such endemic lineages; the first suggests a vicariant origin arising from the sundering of eastern Gondwana in the Cretaceous. The second posits more recent dispersal and colonization. We use concatenated and coalescent time‐calibrated phylogenies to test whether New Caledonian diplodactylid geckos diversified steadily following an ancient vicariance event or experienced an early burst of diversification followed by a decline in net diversification after long‐distance dispersal.LocationNew Caledonia, Gondwana.MethodsPhylogenetic relationships were elucidated from a multilocus DNA data set. Divergence times were inferred using relaxed clock Bayesian methods on the concatenated data set and in a multispecies coalescent framework using *beast. In order to elucidate patterns of diversification for the New Caledonian clade we tested models of diversification using laser and ddd.ResultsThe divergence of the New Caledonian clade from its Australian sister clade occurred well after Gondwanan fragmentation, and the age of the crown clade is younger than the proposed drowning period of the island. Diversification analyses strongly suggest that the group experienced an early burst of diversification, which has slowed towards the present.Main conclusionsWe demonstrate that the species‐rich diplodactylid geckos endemic to New Caledonia are of recent origin and that the diversification of the clade is consistent with the expectations of a recent radiation. Diversification in this clade does not conform to a constant‐rate model, but rather experienced an initial burst followed by a decline in net diversification. This pattern is consistent with a decline in diversification as ecological niche space was filled. Our results add to the growing body of evidence that recent adaptive radiations have contributed to the remarkable endemism of New Caledonia.

Admixture, Population Structure, and F-Statistics.

Many questions about human genetic history can be addressed by examining the patterns of shared genetic variation between sets of populations. A useful methodological framework for this purpose isF-statistics that measure shared genetic drift between sets of two, three, and four populations and can be used to test simple and complex hypotheses about admixture between populations. This article provides context from phylogenetic and population genetic theory. I review how F-statistics can be interpreted as branch lengths or paths and derive new interpretations, using coalescent theory. I further show that the admixture tests can be interpreted as testing general properties of phylogenies, allowing extension of some ideas applications to arbitrary phylogenetic trees. The new results are used to investigate the behavior of the statistics under different models of population structure and show how population substructure complicates inference. The results lead to simplified estimators in many cases, and I recommend to replace F3 with the average number of pairwise differences for estimating population divergence.

A unified criterion for the growth and coalescence of microvoids

A yield criterion is developed which unifies void growth and void coalescence theories. Standard void growth theory assumes that plastic flow is diffuse, if not prevalent everywhere within the matrix of the elementary cell considered. On the other hand, void coalescence theory assumes states of post-localized plasticity whereby plastic flow is restricted to intervoid ligaments. The new theory accommodates both scenarios through some appropriate choice of microscopic velocity fields. An important implication for actual evolution problems is a seamless transition from void growth to void coalescence. This is in contrast with previous hybrid approaches whereby abrupt transitions are associated with the presence of unavoidable corners in the effective yield surface. More generally, the new criterion is applicable to describe yielding in porous metal plasticity for both low and high void volume fractions.

The Genomic Signature of Population Reconnection Following Isolation: From Theory to HIV.

Ease of worldwide travel provides increased opportunities for organisms not only to colonize new environments but also to encounter related but diverged populations. Such events of reconnection and secondary contact of previously isolated populations are widely observed at different time scales. For example, during the quaternary glaciation, sea water level fluctuations caused temporal isolation of populations, often to be followed by secondary contact. At shorter time scales, population isolation and reconnection of viruses are commonly observed, and such events are often associated with epidemics and pandemics. Here, using coalescent theory and simulations, we describe the temporal impact of population reconnection after isolation on nucleotide differences and the site frequency spectrum, as well as common summary statistics of DNA variation. We identify robust genomic signatures of population reconnection after isolation. We utilize our development to infer the recent evolutionary history of human immunodeficiency virus 1 (HIV-1) in Asia and South America, successfully retrieving the successive HIV subtype colonization events in these regions. Our analysis reveals that divergent HIV-1 subtype populations are currently admixing in these regions, suggesting that HIV-1 may be undergoing a process of homogenization, contrary to popular belief.