Coalescents and genealogical structure under neutrality

Bayesian Inference of Pathogen Phylogeography using the Structured Coalescent Model

Over the past decade, pathogen genome sequencing has become well established as a powerful approach to study infectious disease epidemiology. In particular, when multiple genomes are available from several geographical locations, comparing them is informative about the relative size of the local pathogen populations as well as past migration rates and events between locations. The structured coalescent model has a long history of being used as the underlying process for such phylogeographic analysis. However, the computational cost of using this model does not scale well to the large number of genomes frequently analysed in pathogen genomic epidemiology studies. Several approximations of the structured coalescent model have been proposed, but their effects are difficult to predict. Here we show how the exact structured coalescent model can be used to analyse a precomputed dated phylogeny, in order to perform Bayesian inference on the past migration history, the effective population sizes in each location, and the directed migration rates from any location to another. We describe an efficient reversible jump Markov Chain Monte Carlo scheme which is implemented in a new R package StructCoalescent. We use simulations to demonstrate the scalability and correctness of our method and to compare it with existing software. We also applied our new method to several state-of-the-art datasets on the population structure of real pathogens to showcase the relevance of our method to current data scales and research questions.

A comprehensive review of livestock development: insights into domestication, phylogenetics, diversity, and genomic advances

Livestock plays an essential role in sustaining human livelihoods, offering a diverse range of species integral to food security, economic stability, and cultural traditions. The domestication of livestock, which began over 10,000 years ago, has driven significant genetic changes in species such as cattle, buffaloes, sheep, goats, and pigs. Recent advancements in genomic technologies, including next-generation sequencing (NGS), genome-wide association studies (GWAS), and genomic selection, have dramatically enhanced our understanding of these genetic developments. This review brings together key research on the domestication process, phylogenetics, genetic diversity, and selection signatures within major livestock species. It emphasizes the importance of admixture studies and evolutionary forces like natural selection, genetic drift, and gene flow in shaping livestock populations. Additionally, the integration of machine learning with genomic data offers new perspectives on the functional roles of genes in adaptation and evolution. By exploring these genomic advancements, this review provides insights into genetic variation and evolutionary processes that could inform future approaches to improving livestock management and adaptation to environmental challenges, including climate change.

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 [Formula: see text] 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.

The meaning of wild: Genetic and adaptive consequences from large-scale releases of domestic mallards

The translocation of individuals around the world is leading to rising incidences of anthropogenic hybridization, particularly between domestic and wild congeners. We apply a landscape genomics approach for thousands of mallard (Anas platyrhynchos) samples across continental and island populations to determine the result of over a century of supplementation practices. We establish that a single domestic game-farm mallard breed is the source for contemporary release programs in Eurasia and North America, as well as for established feral populations in New Zealand and Hawaii. In particular, we identify central Europe and eastern North America as epicenters of ongoing anthropogenic hybridization, and conclude that the release of game-farm mallards continues to affect the genetic integrity of wild mallards. Conversely, self-sustaining feral populations in New Zealand and Hawaii not only show strong differentiation from their original stock, but also signatures of local adaptation occurring in less than a half-century since game-farm mallard releases have ceased. We conclude that 'wild' is not singular, and that even feral populations are capable of responding to natural processes. Although considered paradoxical to biological conservation, understanding the capacity for wildness among feral and feral admixed populations in human landscapes is critical as such interactions increase in the Anthropocene.

Model design for nonparametric phylodynamic inference and applications to pathogen surveillance

Inference of effective population size from genomic data can provide unique information about demographic history and, when applied to pathogen genetic data, can also provide insights into epidemiological dynamics. The combination of nonparametric models for population dynamics with molecular clock models which relate genetic data to time has enabled phylodynamic inference based on large sets of time-stamped genetic sequence data. The methodology for nonparametric inference of effective population size is well-developed in the Bayesian setting, but here we develop a frequentist approach based on nonparametric latent process models of population size dynamics. We appeal to statistical principles based on out-of-sample prediction accuracy in order to optimize parameters that control shape and smoothness of the population size over time. Our methodology is implemented in a new R package entitled mlesky. We demonstrate the flexibility and speed of this approach in a series of simulation experiments and apply the methodology to a dataset of HIV-1 in the USA. We also estimate the impact of non-pharmaceutical interventions for COVID-19 in England using thousands of SARS-CoV-2 sequences. By incorporating a measure of the strength of these interventions over time within the phylodynamic model, we estimate the impact of the first national lockdown in the UK on the epidemic reproduction number.

Distinguishing imported cases from locally acquired cases within a geographically limited genomic sample of an infectious disease

MOTIVATION

The ability to distinguish imported cases from locally acquired cases has important consequences for the selection of public health control strategies. Genomic data can be useful for this, for example, using a phylogeographic analysis in which genomic data from multiple locations are compared to determine likely migration events between locations. However, these methods typically require good samples of genomes from all locations, which is rarely available.

RESULTS

Here, we propose an alternative approach that only uses genomic data from a location of interest. By comparing each new case with previous cases from the same location, we are able to detect imported cases, as they have a different genealogical distribution than that of locally acquired cases. We show that, when variations in the size of the local population are accounted for, our method has good sensitivity and excellent specificity for the detection of imports. We applied our method to data simulated under the structured coalescent model and demonstrate relatively good performance even when the local population has the same size as the external population. Finally, we applied our method to several recent genomic datasets from both bacterial and viral pathogens, and show that it can, in a matter of seconds or minutes, deliver important insights on the number of imports to a geographically limited sample of a pathogen population.

AVAILABILITY AND IMPLEMENTATION

The R package DetectImports is freely available from https://github.com/xavierdidelot/DetectImports.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Sweepstakes reproductive success via pervasive and recurrent selective sweeps

Highly fecund natural populations characterized by high early mortality abound, yet our knowledge about their recruitment dynamics is somewhat rudimentary. This knowledge gap has implications for our understanding of genetic variation, population connectivity, local adaptation, and the resilience of highly fecund populations. The concept of sweepstakes reproductive success, which posits a considerable variance and skew in individual reproductive output, is key to understanding the distribution of individual reproductive success. However, it still needs to be determined whether highly fecund organisms reproduce through sweepstakes and, if they do, the relative roles of neutral and selective sweepstakes. Here, we use coalescent-based statistical analysis of population genomic data to show that selective sweepstakes likely explain recruitment dynamics in the highly fecund Atlantic cod. We show that the Kingman coalescent (modelling no sweepstakes) and the Xi-Beta coalescent (modelling random sweepstakes), including complex demography and background selection, do not provide an adequate fit for the data. The Durrett-Schweinsberg coalescent, in which selective sweepstakes result from recurrent and pervasive selective sweeps of new mutations, offers greater explanatory power. Our results show that models of sweepstakes reproduction and multiple-merger coalescents are relevant and necessary for understanding genetic diversity in highly fecund natural populations. These findings have fundamental implications for understanding the recruitment variation of fish stocks and general evolutionary genomics of high-fecundity organisms.

Emerging biological archives can reveal ecological and climatic change in Antarctica

Anthropogenic climate change is causing observable changes in Antarctica and the Southern Ocean including increased air and ocean temperatures, glacial melt leading to sea-level rise and a reduction in salinity, and changes to freshwater water availability on land. These changes impact local Antarctic ecosystems and the Earth's climate system. The Antarctic has experienced significant past environmental change, including cycles of glaciation over the Quaternary Period (the past ~2.6 million years). Understanding Antarctica's paleoecosystems, and the corresponding paleoenvironments and climates that have shaped them, provides insight into present day ecosystem change, and importantly, helps constrain model projections of future change. Biological archives such as extant moss beds and peat profiles, biological proxies in lake and marine sediments, vertebrate animal colonies, and extant terrestrial and benthic marine invertebrates, complement other Antarctic paleoclimate archives by recording the nature and rate of past ecological change, the paleoenvironmental drivers of that change, and constrain current ecosystem and climate models. These archives provide invaluable information about terrestrial ice-free areas, a key location for Antarctic biodiversity, and the continental margin which is important for understanding ice sheet dynamics. Recent significant advances in analytical techniques (e.g., genomics, biogeochemical analyses) have led to new applications and greater power in elucidating the environmental records contained within biological archives. Paleoecological and paleoclimate discoveries derived from biological archives, and integration with existing data from other paleoclimate data sources, will significantly expand our understanding of past, present, and future ecological change, alongside climate change, in a unique, globally significant region.

The bounded coalescent model: Conditioning a genealogy on a minimum root date

The coalescent model represents how individuals sampled from a population may have originated from a last common ancestor. The bounded coalescent model is obtained by conditioning the coalescent model such that the last common ancestor must have existed after a certain date. This conditioned model arises in a variety of applications, such as speciation, horizontal gene transfer or transmission analysis, and yet the bounded coalescent model has not been previously analysed in detail. Here we describe a new algorithm to simulate from this model directly, without resorting to rejection sampling. We show that this direct simulation algorithm is more computationally efficient than the rejection sampling approach. We also show how to calculate the probability of the last common ancestor occurring after a given date, which is required to compute the probability density of realisations under the bounded coalescent model. Our results are applicable in both the isochronous (when all samples have the same date) and heterochronous (where samples can have different dates) settings. We explore the effect of setting a bound on the date of the last common ancestor, and show that it affects a number of properties of the resulting phylogenies. All our methods are implemented in a new R package called BoundedCoalescent which is freely available online.

Bayesian inference of clonal expansions in a dated phylogeny

Microbial population genetics models often assume that all lineages are constrained by the same population size dynamics over time. However, many neutral and selective events can invalidate this assumption and can contribute to the clonal expansion of a specific lineage relative to the rest of the population. Such differential phylodynamic properties between lineages result in asymmetries and imbalances in phylogenetic trees that are sometimes described informally but which are difficult to analyze formally. To this end, we developed a model of how clonal expansions occur and affect the branching patterns of a phylogeny. We show how the parameters of this model can be inferred from a given dated phylogeny using Bayesian statistics, which allows us to assess the probability that one or more clonal expansion events occurred. For each putative clonal expansion event, we estimate its date of emergence and subsequent phylodynamic trajectory, including its long-term evolutionary potential which is important to determine how much effort should be placed on specific control measures. We demonstrate the applicability of our methodology on simulated and real data sets. Inference under our clonal expansion model can reveal important features in the evolution and epidemiology of infectious disease pathogens. [Clonal expansion; genomic epidemiology; microbial population genomics; phylodynamics.]

Genealogical structure changes as range expansions transition from pushed to pulled

Range expansions accelerate evolution through multiple mechanisms, including gene surfing and genetic drift. The inference and control of these evolutionary processes ultimately rely on the information contained in genealogical trees. Currently, there are two opposing views on how range expansions shape genealogies. In invasion biology, expansions are typically approximated by a series of population bottlenecks producing genealogies with only pairwise mergers between lineages-a process known as the Kingman coalescent. Conversely, traveling wave models predict a coalescent with multiple mergers, known as the Bolthausen-Sznitman coalescent. Here, we unify these two approaches and show that expansions can generate an entire spectrum of coalescent topologies. Specifically, we show that tree topology is controlled by growth dynamics at the front and exhibits large differences between pulled and pushed expansions. These differences are explained by the fluctuations in the total number of descendants left by the early founders. High growth cooperativity leads to a narrow distribution of reproductive values and the Kingman coalescent. Conversely, low growth cooperativity results in a broad distribution, whose exponent controls the merger sizes in the genealogies. These broad distribution and non-Kingman tree topologies emerge due to the fluctuations in the front shape and position and do not occur in quasi-deterministic simulations. Overall, our results show that range expansions provide a robust mechanism for generating different types of multiple mergers, which could be similar to those observed in populations with strong selection or high fecundity. Thus, caution should be exercised in making inferences about the origin of non-Kingman genealogies.

Model design for non-parametric phylodynamic inference and applications to pathogen surveillance

Inference of effective population size from genomic data can provide unique information about demographic history, and when applied to pathogen genetic data can also provide insights into epidemiological dynamics. The combination of non-parametric models for population dynamics with molecular clock models which relate genetic data to time has enabled phylodynamic inference based on large sets of time-stamped genetic sequence data. The methodology for non-parametric inference of effective population size is well-developed in the Bayesian setting, but here we develop a frequentist approach based on non-parametric latent process models of population size dynamics. We appeal to statistical principles based on out-of-sample prediction accuracy in order to optimize parameters that control shape and smoothness of the population size over time. We demonstrate the flexibility and speed of this approach in a series of simulation experiments, and apply the methodology to reconstruct the previously described waves in the seventh pandemic of cholera. We also estimate the impact of non-pharmaceutical interventions for COVID-19 in England using thousands of SARS-CoV-2 sequences. By incorporating a measure of the strength of these interventions over time within the phylodynamic model, we estimate the impact of the first national lockdown in the UK on the epidemic reproduction number.

Whole plastomes are not enough: phylogenomic and morphometric exploration at multiple demographic levels of the bee orchid clade Ophrys sect. Sphegodes

Plastid sequences have long dominated phylogeny reconstruction at all time depths, predicated on a usually untested assumption that they accurately represent the evolutionary histories of phenotypically circumscribed species. We combined detailed in situ morphometrics (124 plants) and whole-plastome sequencing through genome skimming (71 plants) in order to better understand species-level diversity and speciation in arguably the most challenging monophyletic group within the taxonomically controversial, pseudo-copulatory bee orchid genus Ophrys. Using trees and ordinations, we interpreted the data at four nested demographic levels-macrospecies, mesospecies, microspecies, and local population-seeking the optimal level for bona fide species. Neither morphological nor molecular discontinuities are evident at any level below macrospecies, the observed overlap among taxa suggesting that both mesospecies and microspecies reflect arbitrary division of a continuum of variation. Plastomes represent geographic location more strongly than taxonomic assignment and correlate poorly with morphology, suggesting widespread plastid capture and possibly post-glacial expansion from multiple southern refugia. As they are rarely directly involved in the speciation process, plastomes depend on extinction of intermediate lineages to provide phylogenetic signal and so cannot adequately document evolutionary radiations. The popular 'ethological' evolutionary model recognizes as numerous 'ecological species' (microspecies) lineages perceived as actively diverging as a result of density-dependent selection on very few features that immediately dictate extreme pollinator specificity. However, it is assumed rather than demonstrated that the many microspecies are genuinely diverging. We conversely envisage a complex four-dimensional reticulate network of lineages, generated locally and transiently through a wide spectrum of mechanisms, but each unlikely to maintain an independent evolutionary trajectory long enough to genuinely speciate by escaping ongoing gene flow. The frequent but localized microevolution that characterizes the Ophrys sphegodes complex is often convergent and rarely leads to macroevolution. Choosing between the contrasting 'discontinuity' and 'ethology' models will require next-generation sequencing of nuclear genomes plus ordination of corresponding morphometric matrices, seeking the crucial distinction between retained ancestral polymorphism-consistent with lineage divergence-and polymorphisms reflecting gene flow through 'hybridization'-more consistent with lineage convergence.

Assessing the evolutionary persistence of ecological relationships: A review and preview

Species interactions, such as pollination, parasitism and predation, form the basis of functioning ecosystems. The origins and resilience of such interactions therefore merit attention. However, fossils only occasionally document ancient interactions, and phylogenetic methods are blind to recent interactions. Is there some other way to track shared species experiences? "Comparative demography" examines when pairs of species jointly thrived or declined. By forging links between ecology, epidemiology, and evolutionary biology, this method sheds light on biological adaptation, species resilience, and ecosystem health. Here, we describe how this method works, discuss examples, and suggest future directions in hopes of inspiring interest, imitators, and critics.

Evolutionary Genomics of High Fecundity

Natural highly fecund populations abound. These range from viruses to gadids. Many highly fecund populations are economically important. Highly fecund populations provide an important contrast to the low-fecundity organisms that have traditionally been applied in evolutionary studies. A key question regarding high fecundity is whether large numbers of offspring are produced on a regular basis, by few individuals each time, in a sweepstakes mode of reproduction. Such reproduction characteristics are not incorporated into the classical Wright-Fisher model, the standard reference model of population genetics, or similar types of models, in which each individual can produce only small numbers of offspring relative to the population size. The expected genomic footprints of population genetic models of sweepstakes reproduction are very different from those of the Wright-Fisher model. A key, immediate issue involves identifying the footprints of sweepstakes reproduction in genomic data. Whole-genome sequencing data can be used to distinguish the patterns made by sweepstakes reproduction from the patterns made by population growth in a population evolving according to the Wright-Fisher model (or similar models). If the hypothesis of sweepstakes reproduction cannot be rejected, then models of sweepstakes reproduction and associated multiple-merger coalescents will become at least as relevant as the Wright-Fisher model (or similar models) and the Kingman coalescent, the cornerstones of mathematical population genetics, in further discussions of evolutionary genomics of highly fecund populations.

Counterbalancing the time-dependent effect on the human mitochondrial DNA molecular clock

BACKGROUND

The molecular clock is an important genetic tool for estimating evolutionary timescales. However, the detection of a time-dependent effect on substitution rate estimates complicates its application. It has been suggested that demographic processes could be the main cause of this confounding effect. In the present study, I propose a new algorithm for estimating the coalescent age of phylogenetically related sequences, taking into account the observed time-dependent effect on the molecular rate detected by others.

RESULTS

By applying this method to real human mitochondrial DNA trees with shallow and deep topologies, I obtained significantly older molecular ages for the main events of human evolution than were previously estimated. These ages are in close agreement with the most recent archaeological and paleontological records favoring the emergence of early anatomically modern humans in Africa 315 ± 34 thousand years ago (kya) and the presence of recent modern humans outside of Africa as early as 174 ± 48 thousand years ago. Furthermore, during the implementation process, I demonstrated that in a population with fluctuating sizes, the probability of fixation of a new neutral mutant depends on the effective population size, which is in better accordance with the fact that under the neutral theory of molecular evolution, the fate of a molecular mutation is mainly determined by random drift.

CONCLUSIONS

I suggest that the demographic history of populations has a more decisive effect than purifying selection and/or mutational saturation on the time-dependent effect observed for the substitution rate, and I propose a new method that corrects for this effect.

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

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

Measuring single cell divisions in human tissues from multi-region sequencing data

Both normal tissue development and cancer growth are driven by a branching process of cell division and mutation accumulation that leads to intra-tissue genetic heterogeneity. However, quantifying somatic evolution in humans remains challenging. Here, we show that multi-sample genomic data from a single time point of normal and cancer tissues contains information on single-cell divisions. We present a new theoretical framework that, applied to whole-genome sequencing data of healthy tissue and cancer, allows inferring the mutation rate and the cell survival/death rate per division. On average, we found that cells accumulate 1.14 mutations per cell division in healthy haematopoiesis and 1.37 mutations per division in brain development. In both tissues, cell survival was maximal during early development. Analysis of 131 biopsies from 16 tumours showed 4 to 100 times increased mutation rates compared to healthy development and substantial inter-patient variation of cell survival/death rates.

Bayesian Estimation of Population Size Changes by Sampling Tajima's Trees

The large state space of gene genealogies is a major hurdle for inference methods based on Kingman's coalescent. Here, we present a new Bayesian approach for inferring past population sizes, which relies on a lower-resolution coalescent process that we refer to as "Tajima's coalescent." Tajima's coalescent has a drastically smaller state space, and hence it is a computationally more efficient model, than the standard Kingman coalescent. We provide a new algorithm for efficient and exact likelihood calculations for data without recombination, which exploits a directed acyclic graph and a correspondingly tailored Markov Chain Monte Carlo method. We compare the performance of our Bayesian Estimation of population size changes by Sampling Tajima's Trees (BESTT) with a popular implementation of coalescent-based inference in BEAST using simulated and human data. We empirically demonstrate that BESTT can accurately infer effective population sizes, and it further provides an efficient alternative to the Kingman's coalescent. The algorithms described here are implemented in the R package phylodyn, which is available for download at https://github.com/JuliaPalacios/phylodyn.

Coalescent Theory of Migration Network Motifs

Natural populations display a variety of spatial arrangements, each potentially with a distinctive impact on genetic diversity and genetic differentiation among subpopulations. Although the spatial arrangement of populations can lead to intricate migration networks, theoretical developments have focused mainly on a small subset of such networks, emphasizing the island-migration and stepping-stone models. In this study, we investigate all small network motifs: the set of all possible migration networks among populations subdivided into at most four subpopulations. For each motif, we use coalescent theory to derive expectations for three quantities that describe genetic variation: nucleotide diversity, F_ST, and half-time to equilibrium diversity. We describe the impact of network properties on these quantities, finding that motifs with a high mean node degree have the largest nucleotide diversity and the longest time to equilibrium, whereas motifs with low density have the largest F_ST. In addition, we show that the motifs whose pattern of variation is most strongly influenced by loss of a connection or a subpopulation are those that can be split easily into disconnected components. We illustrate our results using two example data sets—sky island birds of genus Sholicola and Indian tigers—identifying disturbance scenarios that produce the greatest reduction in genetic diversity; for tigers, we also compare the benefits of two assisted gene flow scenarios. Our results have consequences for understanding the effect of geography on genetic diversity, and they can assist in designing strategies to alter population migration networks toward maximizing genetic variation in the context of conservation of endangered species.

On the joint distribution of tree height and tree length under the coalescent

Many statistics that examine genetic variation depend on the underlying shapes of genealogical trees. Under the coalescent model, we investigate the joint distribution of two quantities that describe genealogical tree shape: tree height and tree length. We derive a recursive formula for their exact joint distribution under a demographic model of a constant-sized population. We obtain approximations for the mean and variance of the ratio of tree height to tree length, using them to show that this ratio converges in probability to 0 as the sample size increases. We find that as the sample size increases, the correlation coefficient for tree height and length approaches (π2-6)∕[π2π2-18]≈0.9340. Using simulations, we examine the joint distribution of height and length under demographic models with population growth and population subdivision. We interpret the joint distribution in relation to problems of interest in data analysis, including inference of the time to the most recent common ancestor. The results assist in understanding the influences of demographic histories on two fundamental features of tree shape.

An efficient algorithm for generating the internal branches of a Kingman coalescent

Coalescent simulations are a widely used approach for simulating sample genealogies, but can become computationally burdensome in large samples. Methods exist to analytically calculate a sample's expected frequency spectrum without simulating full genealogies. However, statistics that rely on the distribution of the length of internal coalescent branches, such as the probability that two mutations of equal size arose on the same genealogical branch, have previously required full coalescent simulations to estimate. Here, we present a sampling method capable of efficiently generating limited portions of sample genealogies using a series of analytic equations that give probabilities for the number, start, and end of internal branches conditional on the number of final samples they subtend. These equations are independent of the coalescent waiting times and need only be calculated a single time, lending themselves to efficient computation. We compare our method with full coalescent simulations to show the resulting distribution of branch lengths and summary statistics are equivalent, but that for many conditions our method is at least 10 times faster.

Molecular evolution methods to study HIV-1 epidemics

Nucleotide sequences of HIV isolates are obtained routinely to evaluate the presence of resistance mutations to antiretroviral drugs. But, beyond their clinical use, these and other viral sequences include a wealth of information that can be used to better understand and characterize the epidemiology of HIV in relevant populations. In this review, we provide a brief overview of the main methods used to analyze HIV sequences, the data bases where reference sequences can be obtained, and some caveats about the possible applications for public health of these analyses, along with some considerations about their limitations and correct usage to derive robust and reliable conclusions.

Integrating restriction site-associated DNA sequencing (RAD-seq) with morphological cladistic analysis clarifies evolutionary relationships among major species groups of bee orchids

BACKGROUND AND AIMS

Bee orchids (Ophrys) have become the most popular model system for studying reproduction via insect-mediated pseudo-copulation and for exploring the consequent, putatively adaptive, evolutionary radiations. However, despite intensive past research, both the phylogenetic structure and species diversity within the genus remain highly contentious. Here, we integrate next-generation sequencing and morphological cladistic techniques to clarify the phylogeny of the genus.

METHODS

At least two accessions of each of the ten species groups previously circumscribed from large-scale cloned nuclear ribosomal internal transcibed spacer (nrITS) sequencing were subjected to restriction site-associated sequencing (RAD-seq). The resulting matrix of 4159 single nucleotide polymorphisms (SNPs) for 34 accessions was used to construct an unrooted network and a rooted maximum likelihood phylogeny. A parallel morphological cladistic matrix of 43 characters generated both polymorphic and non-polymorphic sets of parsimony trees before being mapped across the RAD-seq topology.

KEY RESULTS

RAD-seq data strongly support the monophyly of nine out of ten groups previously circumscribed using nrITS and resolve three major clades; in contrast, supposed microspecies are barely distinguishable. Strong incongruence separated the RAD-seq trees from both the morphological trees and traditional classifications; mapping of the morphological characters across the RAD-seq topology rendered them far more homoplastic.

CONCLUSIONS

The comparatively high level of morphological homoplasy reflects extensive convergence, whereas the derived placement of the fusca group is attributed to paedomorphic simplification. The phenotype of the most recent common ancestor of the extant lineages is inferred, but it post-dates the majority of the character-state changes that typify the genus. RAD-seq may represent the high-water mark of the contribution of molecular phylogenetics to understanding evolution within Ophrys; further progress will require large-scale population-level studies that integrate phenotypic and genotypic data in a cogent conceptual framework.

Mlcoalsim: Multilocus Coalescent Simulations

Coalescent theory is a powerful tool for population geneticists as well as molecular biologists interested in understanding the patterns and levels of DNA variation. Using coalescent Monte Carlo simulations it is possible to obtain the empirical distributions for a number of statistics across a wide range of evolutionary models; these distributions can be used to test evolutionary hypotheses using experimental data. The mlcoalsim application presented here (based on a version of the ms program, Hudson, 2002) adds important new features to improve methodology (uncertainty and conditional methods for mutation and recombination), models (including strong positive selection, finite sites and heterogeneity in mutation and recombination rates) and analyses (calculating a number of statistics used in population genetics and P-values for observed data). One of the most important features of mlcoalsim is the analysis of multilocus data in linked and independent regions. In summary, mlcoalsim is an integrated software application aimed at researchers interested in molecular evolution. mlcoalsim is written in ANSI C and is available at: http://www.ub.es/softevol/mlcoalsim .

Did Late Pleistocene climate change result in parallel genetic structure and demographic bottlenecks in sympatric Central African crocodiles, Mecistops and Osteolaemus?

The mid-Holocene has had profound demographic impacts on wildlife on the African continent, although there is little known about the impacts on species from Central Africa. Understanding the impacts of climate change on codistributed species can enhance our understanding of ecosystem dynamics and for formulating restoration objectives. We took a multigenome comparative approach to examine the phylogeographic structure of two poorly known Central African crocodile species-Mecistops sp. aff. cataphractus and Osteolaemus tetraspis. In addition, we conducted coalescent-based demographic reconstructions to test the hypothesis that population decline was driven by climate change since the Last Glacial Maximum, vs. more recent anthropogenic pressures. Using a hierarchical Bayesian model to reconstruct demographic history, we show that both species had dramatic declines (>97%) in effective population size in the 'period following the Last Glacial Maximum 1,500-18,000 YBP. Identification of genetic structuring showed both species have similar regional structure corresponding to major geological features (i.e., hydrologic basin) and that small observed differences between them are best explained by the differences in their ecology and the likely impact that climate change had on their habitat needs. Our results support our hypothesis that climatic effects, presumably on forest and wetland habitat, had a congruent negative impact on both species.

PHYLOGEOGRAPHY OF SPOTTED OWL (STRIX OCCIDENTALIS) POPULATIONS BASED ON MITOCHONDRIAL DNA SEQUENCES: GENE FLOW, GENETIC STRUCTURE, AND A NOVEL BIOGEOGRAPHIC PATTERN

Mitochondrial DNA control region sequences of spotted owls (Strix occidentalis) allowed us to investigate gene flow, genetic structure, and biogeographic relationships among these forest-dwelling birds of western North America Estimates of gene flow based on genetic partitioning and the phylogeography of haplotypes indicate substantial dispersal within three long-recognized subspecies. However, patterns of individual phyletic relationships indicate a historical absence of gene flow among the subspecies, which are essentially monophyletic. The pattern of haplotype coalescence enabled us to identify the approximate timing and direction of a recent episode of gene flow from the Sierra Nevada to the northern coastal ranges. The three subspecies comprise phylogenetic species, and the northern spotted owl (S. o. caurina) is sister to a clade of California (S. o. occidentalis) plus Mexican spotted owls (S o lucida); this represents a novel biogeographic pattern within birds. The California spotted owl had substantially lower nucleotide diversity than the other two subspecies; this result is inconsistent with present patterns of population density A causal explanation requires postulating a severe bottleneck or a selective sweep, either of which was confined to only one geographic region.

NO EVIDENCE OF BOTTLENECK IN THE POSTGLACIAL RECOLONIZATION OF EUROPE BY THE NOCTULE BAT (NYCTALUS NOCTULA)

During the Pleistocene, the habitat of the noctule bat (Nyctalus noctula) was limited to small refuge areas located in Southern Europe, whereas the species is now widespread across this continent. Using mtDNA (control region and ND1 gene) polymorphisms, we asked whether this recolonization occurred through bottlenecks and whether it was accompanied by population growth. Sequences of the second hypervariable domain of the control region were obtained from 364 noctule bats representing 18 colonies sampled across Europe. This yielded 108 haplotypes that were depicted on a minimum spanning tree that showed a starlike structure with two long branches. Additional sequences obtained from the ND1 gene confirmed that the different parts of the MST correspond to three clades which diverged before the Last Glacial Maximum (18,000 yrC¹⁴ BP), leading to the conclusion that the noctule bat survived in several isolated refugia. Partitioning populations into coherent geographical groups divided our samples (φ_CT = 0.17; P = 0.01) into a group of highly variable nursing colonies from central and eastern Europe and less variable, isolated colonies from western and southern Europe. Demographic analyses suggest that populations of the former group underwent demographic expansions either after the Younger Dryas (11,000-10,000 yrC¹⁴ BP), assuming a fast mutation rate for HV II, or during the Pleistocene, assuming a conventional mutation rate. We discuss the fact that the high genetic variability (h = 0.69-0.96; π = 0.006-0.013) observed in nursing colonies that are located some distance from potential Pleistocene refugia is probably due to the combined effect of rapid evolution of the control region in growing populations and a range shift of noctule populations parallel to the recovery of forests in Europe after the last glaciations.

Robustness results for the coalescent

A variety of convergence results for genealogical and line-of-descendent processes are known for exchangeable neutral population genetics models. A general convergence-to-the-coalescent theorem is presented, which works not only for a larger class of exchangeable models but also for a large class of non-exchangeable population models. The coalescence probability, i.e. the probability that two genes, chosen randomly without replacement, have a common ancestor one generation backwards in time, is the central quantity to analyse the ancestral structure.

Coalescent theory for seed bank models

We study the genealogical structure of samples from a population for which any given generation is made up of direct descendants from several previous generations. These occur in nature when there are seed banks or egg banks allowing an individual to leave offspring several generations in the future. We show how this temporal structure in the reproduction mechanism causes a decrease in the coalescence rate. We also investigate the effects of age-dependent neutral mutations. Our main result gives weak convergence of the scaled ancestral process, with the usual diffusion scaling, to a coalescent process which is equivalent to a time-changed version of Kingman's coalescent.

Convergence to the coalescent in populations of substantially varying size

Kingman's classical theory of the coalescent uncovered the basic pattern of genealogical trees of random samples of individuals in large but time-constant populations. Time is viewed as being discrete and is identified with non-overlapping generations. Reproduction can be very generally taken as exchangeable (meaning that the labelling of individuals in each generation carries no significance). Recent generalisations have dealt with population sizes exhibiting given deterministic or (minor) random fluctuations. We consider population sizes which constitute a stationary Markov chain, explicitly allowing large fluctuations in short times. Convergence of the genealogical tree, as population size tends to infinity, towards the (time-scaled) coalescent is proved under minimal conditions. As a result, we obtain a formula for effective population size, generalising the well-known harmonic mean expression for effective size.

The structured coalescent process with weak migration

The aim of this paper is to study genealogical processes in a geographically structured population with weak migration. The coalescence time for sampled genes from different colonies diverges to infinity as the migration rates among colonies are close to zero. We investigate the moment generating functions of the coalescence time, the number of segregating sites and the number of allele types in sampled genes when there is low migration. Employing a perturbation method, we obtain a system of recurrence relations for the approximate solutions of these moment generating functions and solve them in some cases.

Robustness results for the coalescent

A variety of convergence results for genealogical and line-of-descendent processes are known for exchangeable neutral population genetics models. A general convergence-to-the-coalescent theorem is presented, which works not only for a larger class of exchangeable models but also for a large class of non-exchangeable population models. The coalescence probability, i.e. the probability that two genes, chosen randomly without replacement, have a common ancestor one generation backwards in time, is the central quantity to analyse the ancestral structure.

Weak convergence to the coalescent in neutral population models

For a large class of neutral population models the asymptotics of the ancestral structure of a sample of n individuals (or genes) is studied, if the total population size becomes large. Under certain conditions and under a well-known time-scaling, which can be expressed in terms of the coalescence probabilities, weak convergence in DE([0,∞)) to the coalescent holds. Further the convergence behaviour of the jump chain of the ancestral process is studied. The results are used to approximate probabilities which are of certain interest in applications, for example hitting probabilities.

Weak convergence to the coalescent in neutral population models

For a large class of neutral population models the asymptotics of the ancestral structure of a sample of n individuals (or genes) is studied, if the total population size becomes large. Under certain conditions and under a well-known time-scaling, which can be expressed in terms of the coalescence probabilities, weak convergence in D E ([0,∞)) to the coalescent holds. Further the convergence behaviour of the jump chain of the ancestral process is studied. The results are used to approximate probabilities which are of certain interest in applications, for example hitting probabilities.

Structured coalescent with nonconservative migration

We study the ancestral process of a sample from a subdivided population with stochastically varying subpopulation sizes. The sizes of the subpopulations change very rapidly (almost every generation) with respect to the coalescent time scale. For haploid populations of sizeN, one coalescence time unit corresponds toNgenerations. Coalescence and migration events occur on the same time scale. We show that, when the total population size tends to infinity, the structured coalescent is obtained, thus confirming the robustness of the coalescent. Many population structure models have been shown to converge to the structured coalescent (see Herbots (1997), Hudson (1998), Nordborg (2001), Nordborg and Krone (2002), and Notohara (1990)).

Convergence to the coalescent in populations of substantially varying size

Kingman's classical theory of the coalescent uncovered the basic pattern of genealogical trees of random samples of individuals in large but time-constant populations. Time is viewed as being discrete and is identified with non-overlapping generations. Reproduction can be very generally taken as exchangeable (meaning that the labelling of individuals in each generation carries no significance). Recent generalisations have dealt with population sizes exhibiting given deterministic or (minor) random fluctuations. We consider population sizes which constitute a stationary Markov chain, explicitly allowing large fluctuations in short times. Convergence of the genealogical tree, as population size tends to infinity, towards the (time-scaled) coalescent is proved under minimal conditions. As a result, we obtain a formula for effective population size, generalising the well-known harmonic mean expression for effective size.

The structured coalescent process with weak migration

The aim of this paper is to study genealogical processes in a geographically structured population with weak migration. The coalescence time for sampled genes from different colonies diverges to infinity as the migration rates among colonies are close to zero. We investigate the moment generating functions of the coalescence time, the number of segregating sites and the number of allele types in sampled genes when there is low migration. Employing a perturbation method, we obtain a system of recurrence relations for the approximate solutions of these moment generating functions and solve them in some cases.

Coalescent theory for seed bank models

We study the genealogical structure of samples from a population for which any given generation is made up of direct descendants from several previous generations. These occur in nature when there are seed banks or egg banks allowing an individual to leave offspring several generations in the future. We show how this temporal structure in the reproduction mechanism causes a decrease in the coalescence rate. We also investigate the effects of age-dependent neutral mutations. Our main result gives weak convergence of the scaled ancestral process, with the usual diffusion scaling, to a coalescent process which is equivalent to a time-changed version of Kingman's coalescent.

Structured coalescent with nonconservative migration

We study the ancestral process of a sample from a subdivided population with stochastically varying subpopulation sizes. The sizes of the subpopulations change very rapidly (almost every generation) with respect to the coalescent time scale. For haploid populations of sizeN, one coalescence time unit corresponds toNgenerations. Coalescence and migration events occur on the same time scale. We show that, when the total population size tends to infinity, the structured coalescent is obtained, thus confirming the robustness of the coalescent. Many population structure models have been shown to converge to the structured coalescent (see Herbots (1997), Hudson (1998), Nordborg (2001), Nordborg and Krone (2002), and Notohara (1990)).

Post-data inference of coalescence times and segregating-site distribution in a two-island model with symmetric migration

In this paper, we present the distribution of the coalescence time of two DNA sequences (or genes) subject to symmetric migration between two islands, and conditional on the observed number of segregating sites in the sequences. The distribution for the segregating-site pattern is also obtained. Some surprising results emerge when both genes are initially on the same island. First, the post-data mean coalescence time is shown to be dependent on the migration parameter, as opposed to the pre-data mean. Second, both the post-data density and expectation for the coalescence time are shown to converge, in the weak-migration limit, to the corresponding panmictic results, as opposed to the pre-data situation where there is convergence in the density but not in the expectation. Finally, it is shown that there is convergence in the weak-migration limit in the distribution of the number of segregating sites but not in the expectation and variance. Numerical and graphical results for samples of size greater than two are also presented.

Expected coalescence time for a nonuniform allocation process

We study a process where balls are repeatedly thrown intonboxes independently according to some probability distributionp. We start withnballs, and at each step, all balls landing in the same box are fused into a single ball; the process terminates when there is only one ball left (coalescence). Letc:= ∑jpj2, the collision probability of two fixed balls. We show that the expected coalescence time is asymptotically 2c−1, under two constraints onpthat exclude a thin set of distributionsp. One of the constraints isc=o(ln−2n). This ln−2nis shown to be a threshold value: forc= ω(ln−2n), there existspwithc(p) =csuch that the expected coalescence time far exceedsc−1. Connections to coalescent processes in population biology and theoretical computer science are discussed.

A convergence theorem for markov chains arising in population genetics and the coalescent with selfing

A simple convergence theorem for sequences of Markov chains is presented in order to derive new ‘convergence-to-the-coalescent’ results for diploid neutral population models.

For the so-called diploid Wright-Fisher model with selfing probabilitysand mutation rate θ, it is shown that the ancestral structure ofnsampled genes can be treated in the framework of ann-coalescent with mutation rate ̃θ := θ(1-s/2), if the population sizeNis large and if the time is measured in units of (2-s)Ngenerations.

Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates

Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics and evolutionary biology. Kingman's coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. Major goals of demographic reconstruction include identifying driving factors of effective population size, and understanding the association between the effective population size and such factors. Building upon Bayesian nonparametric coalescent-based approaches, we introduce a flexible framework that incorporates time-varying covariates that exploit Gaussian Markov random fields to achieve temporal smoothing of effective population size trajectories. To approximate the posterior distribution, we adapt efficient Markov chain Monte Carlo algorithms designed for highly structured Gaussian models. Incorporating covariates into the demographic inference framework enables the modeling of associations between the effective population size and covariates while accounting for uncertainty in population histories. Furthermore, it can lead to more precise estimates of population dynamics. We apply our model to four examples. We reconstruct the demographic history of raccoon rabies in North America and find a significant association with the spatiotemporal spread of the outbreak. Next, we examine the effective population size trajectory of the DENV-4 virus in Puerto Rico along with viral isolate count data and find similar cyclic patterns. We compare the population history of the HIV-1 CRF02_AG clade in Cameroon with HIV incidence and prevalence data and find that the effective population size is more reflective of incidence rate. Finally, we explore the hypothesis that the population dynamics of musk ox during the Late Quaternary period were related to climate change. [Coalescent; effective population size; Gaussian Markov random fields; phylodynamics; phylogenetics; population genetics.

A convergence theorem for markov chains arising in population genetics and the coalescent with selfing

A simple convergence theorem for sequences of Markov chains is presented in order to derive new ‘convergence-to-the-coalescent’ results for diploid neutral population models.

For the so-called diploid Wright-Fisher model with selfing probability s and mutation rate θ, it is shown that the ancestral structure of n sampled genes can be treated in the framework of an n-coalescent with mutation rate ̃θ := θ(1-s/2), if the population size N is large and if the time is measured in units of (2-s)N generations.