Bayesian inference of population expansions in domestic bovines

The past population dynamics of four domestic and one wild species of bovine were estimated using Bayesian skyline plots, a coalescent Markov chain Monte Carlo method that does not require an assumed parametric model of demographic history. Four domestic species share a recent rapid population expansion not visible in the wild African buffalo (Syncerus caffer). The estimated timings of the expansions are consistent with the archaeological records of domestication.     

Exploring the demographic history of DNA sequences using the generalized skyline plot.

We present an intuitive visual framework, the generalized skyline plot, to explore the demographic history of sampled DNA sequences. This approach is based on a genealogy inferred from the sequences and provides a nonparametric estimate of effective population size through time. In contrast to previous related procedures, the generalized skyline plot is more applicable to cases where the underlying tree is not fully resolved and the data is not highly variable. This is achieved by the grouping of adjacent coalescent intervals. We employ a small-sample Akaike information criterion to objectively choose the optimal grouping strategy. We investigate the performance of our approach using simulation and subsequently apply it to HIV-1 sequences from central Africa and mtDNA sequences from red pandas.     

Inferring population decline and expansion from microsatellite data: a simulation-based evaluation of the Msvar method

Reconstructing the demographic history of populations is a central issue in evolutionary biology. Using likelihood-based methods coupled with Monte Carlo simulations, it is now possible to reconstruct past changes in population size from genetic data. Using simulated data sets under various demographic scenarios, we evaluate the statistical performance of Msvar, a full-likelihood Bayesian method that infers past demographic change from microsatellite data. Our simulation tests show that Msvar is very efficient at detecting population declines and expansions, provided the event is neither too weak nor too recent. We further show that Msvar outperforms two moment-based methods (the M-ratio test and Bottleneck) for detecting population size changes, whatever the time and the severity of the event. The same trend emerges from a compilation of empirical studies. The latest version of Msvar provides estimates of the current and the ancestral population size and the time since the population started changing in size. We show that, in the absence of prior knowledge, Msvar provides little information on the mutation rate, which results in biased estimates and/or wide credibility intervals for each of the demographic parameters. However, scaling the population size parameters with the mutation rate and scaling the time with current population size, as coalescent theory requires, significantly improves the quality of the estimates for contraction but not for expansion scenarios. Finally, our results suggest that Msvar is robust to moderate departures from a strict stepwise mutation model.     

Complex population dynamics and the coalescent under neutrality

Estimates of the coalescent effective population size N(e) can be poorly correlated with the true population size. The relationship between N(e) and the population size is sensitive to the way in which birth and death rates vary over time. The problem of inference is exacerbated when the mechanisms underlying population dynamics are complex and depend on many parameters. In instances where nonparametric estimators of N(e) such as the skyline struggle to reproduce the correct demographic history, model-based estimators that can draw on prior information about population size and growth rates may be more efficient. A coalescent model is developed for a large class of populations such that the demographic history is described by a deterministic nonlinear dynamical system of arbitrary dimension. This class of demographic model differs from those typically used in population genetics. Birth and death rates are not fixed, and no assumptions are made regarding the fraction of the population sampled. Furthermore, the population may be structured in such a way that gene copies reproduce both within and across demes. For this large class of models, it is shown how to derive the rate of coalescence, as well as the likelihood of a gene genealogy with heterochronous sampling and labeled taxa, and how to simulate a coalescent tree conditional on a complex demographic history. This theoretical framework encapsulates many of the models used by ecologists and epidemiologists and should facilitate the integration of population genetics with the study of mathematical population dynamics.     

Diversification of montane species via elevation shifts: the case of the Kaçkar cricket Phonochorion (Orthoptera)

Localized up‐down altitudinal shifts and subsequent isolation–admixture of montane species in response to glacial cycles has been proposed as a mechanism for the high diversity along Anatolian mountains. However, specific predictions of the proposed mechanism (the elevation shift model) have yet to be tested. Here, we provide a first assessment of this model for promoting inter‐ and intraspecific genetic diversity in the bush‐cricket genus Phonochorion endemic to the West Lesser Caucasus hotspot. Mitochondrial genes were analysed by Bayesian Markov Chain Monte Carlo inferences and coalescent simulations. Timing of diversification was estimated using a multispecies coalescent model. Divergence with gene flow was tested using an isolation with migration model. Population genetic parameters and genetic structuring were determined using Bayesian coalescent methods and spatial analysis. Demographic history was assessed using mismatch distributions and extended Bayesian skyline plots. Speciation events corresponded both to the Miocene and Pleistocene while intraspecific divergence was Pleistocene based. There was evidence for moderate levels of gene flow between species during diversification; however, incomplete lineage sorting could explain the data as well as gene flow. Overall diversification patterns within the genus Phonochorion agree with the predictions of the elevations shift model. Genetic patterns of diversification were driven mainly by Pleistocene glacial cycles and reflected the nature and distribution of sky islands. There was also some albeit weak evidence of demographic expansions coinciding with glacial cooling. However, evidence for divergence with gene flow was inconclusive.     

Joint inference of microsatellite mutation models, population history and genealogies using transdimensional Markov Chain Monte Carlo

We provide a framework for Bayesian coalescent inference from microsatellite data that enables inference of population history parameters averaged over microsatellite mutation models. To achieve this we first implemented a rich family of microsatellite mutation models and related components in the software package BEAST. BEAST is a powerful tool that performs Bayesian MCMC analysis on molecular data to make coalescent and evolutionary inferences. Our implementation permits the application of existing nonparametric methods to microsatellite data. The implemented microsatellite models are based on the replication slippage mechanism and focus on three properties of microsatellite mutation: length dependency of mutation rate, mutational bias toward expansion or contraction, and number of repeat units changed in a single mutation event. We develop a new model that facilitates microsatellite model averaging and Bayesian model selection by transdimensional MCMC. With Bayesian model averaging, the posterior distributions of population history parameters are integrated across a set of microsatellite models and thus account for model uncertainty. Simulated data are used to evaluate our method in terms of accuracy and precision of estimation and also identification of the true mutation model. Finally we apply our method to a red colobus monkey data set as an example.     

Interglacial refugia preserved high genetic diversity of the Chinese mole shrew in the mountains of southwest China

The mountains of southwest China (MSC) harbor extremely high species diversity; however, the mechanism behind this diversity is unknown. We investigated to what degree the topography and climate change shaped the genetic diversity and diversification in these mountains, and we also sought to identify the locations of microrefugia areas in these mountains. For these purposes, we sampled extensively to estimate the intraspecific phylogenetic pattern of the Chinese mole shrew (Anourosorex squamipes) in southwest China throughout its range of distribution. Two mitochondrial genes, namely, cytochrome b (CYT B) and NADH dehydrogenase subunit 2 (ND2), from 383 archived specimens from 43 localities were determined for phylogeographic and demographic analyses. We used the continuous-diffusion phylogeographic model, extensive Bayesian skyline plot species distribution modeling (SDM) and approximate Bayesian computation (ABC) to explore the changes in population size and distribution through time of the species. Two phylogenetic clades were identified, and significantly higher genetic diversity was preserved in the southern subregion of the mountains. The results of the SDM, continuous-diffusion phylogeographic model, extensive Bayesian skyline plot and ABC analyses were congruent and supported that the Last Interglacial Maximum (LIG) was an unfavorable period for the mole shrews because of a high degree of seasonality; A. squamipes survived in isolated interglacial refugia mainly located in the southern subregion during the LIG and rapidly expanded during the last glacial period. These results furnished the first evidence for major Pleistocene interglacial refugia and a latitudinal effect in southwest China, and the results shedding light on the higher level of species richness in the southern subregion.     

Joint inference of population assignment and demographic history

A new approach to assigning individuals to populations using genetic data is described. Most existing methods work by maximizing Hardy-Weinberg and linkage equilibrium within populations, neither of which will apply for many demographic histories. By including a demographic model, within a likelihood framework based on coalescent theory, we can jointly study demographic history and population assignment. Genealogies and population assignments are sampled from a posterior distribution using a general isolation-with-migration model for multiple populations. A measure of partition distance between assignments facilitates not only the summary of a posterior sample of assignments, but also the estimation of the posterior density for the demographic history. It is shown that joint estimates of assignment and demographic history are possible, including estimation of population phylogeny for samples from three populations. The new method is compared to results of a widely used assignment method, using simulated and published empirical data sets.     

Demographic Divergence History of Pied Flycatcher and Collared Flycatcher Inferred from Whole-Genome Re-sequencing Data

Profound knowledge of demographic history is a prerequisite for the understanding and inference of processes involved in the evolution of population differentiation and speciation. Together with new coalescent-based methods, the recent availability of genome-wide data enables investigation of differentiation and divergence processes at unprecedented depth. We combined two powerful approaches, full Approximate Bayesian Computation analysis (ABC) and pairwise sequentially Markovian coalescent modeling (PSMC), to reconstruct the demographic history of the split between two avian speciation model species, the pied flycatcher and collared flycatcher. Using whole-genome re-sequencing data from 20 individuals, we investigated 15 demographic models including different levels and patterns of gene flow, and changes in effective population size over time. ABC provided high support for recent (mode 0.3 my, range <0.7 my) species divergence, declines in effective population size of both species since their initial divergence, and unidirectional recent gene flow from pied flycatcher into collared flycatcher. The estimated divergence time and population size changes, supported by PSMC results, suggest that the ancestral species persisted through one of the glacial periods of middle Pleistocene and then split into two large populations that first increased in size before going through severe bottlenecks and expanding into their current ranges. Secondary contact appears to have been established after the last glacial maximum. The severity of the bottlenecks at the last glacial maximum is indicated by the discrepancy between current effective population sizes (20,000–80,000) and census sizes (5–50 million birds) of the two species. The recent divergence time challenges the supposition that avian speciation is a relatively slow process with extended times for intrinsic postzygotic reproductive barriers to evolve. Our study emphasizes the importance of using genome-wide data to unravel tangled demographic histories. Moreover, it constitutes one of the first examples of the inference of divergence history from genome-wide data in non-model species.     

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.