Test for simultaneous divergence using approximate Bayesian computation

Comparative phylogeographic studies often reveal disparate levels of sequence divergence between lineages spanning a common geographic barrier, leading to the conclusion that isolation was nonsynchronous. However, only rarely do researchers account for the expected variance associated with ancestral coalescence and among-taxon variation in demographic history. We introduce a flexible approximate Bayesian computational (ABC) framework that can test for simultaneous divergence (TSD) using a hierarchical model that incorporates idiosyncratic differences in demographic history across taxon pairs. The method is tested across a range of conditions and is shown to be accurate even with single-locus mitochondrial DNA (mtDNA) data. We apply this method to a landmark dataset of putative simultaneous vicariance, eight geminate echinoid taxon pairs thought to have been split by the Isthmus of Panama 3.1 million years ago. The ABC posterior estimates are not consistent with a history of simultaneous vicariance given these data. Subsequent ABC estimates under a constrained model that assumes two divergence times across the eight taxon pairs suggests simultaneous divergence 3.1 million years ago in seven of the taxon pairs and a more recent divergence in the remaining taxon pair. These ABC estimates on the simultaneous divergence of the seven taxon pairs correspond to a DNA substitution rate of approximately 1.59% per lineage per million years at the mtDNA cytochrome oxidase I gene. This ABC framework can easily be modified to analyze single taxon-pair datasets and/or be expanded to include multiple loci, migration, recombination, and other idiosyncratic demographic histories. The flexible aspect of ABC and its built-in evaluation of estimator bias and statistical power has the potential to greatly enhance statistical rigor in phylogeographic studies.     

Interpreting scratch assays using pair density dynamics and approximate Bayesian computation

Quantifying the impact of biochemical compounds on collective cell spreading is an essential element of drug design, with various applications including developing treatments for chronic wounds and cancer. Scratch assays are a technically simple and inexpensive method used to study collective cell spreading; however, most previous interpretations of scratch assays are qualitative and do not provide estimates of the cell diffusivity, D, or the cell proliferation rate, λ. Estimating D and λ is important for investigating the efficacy of a potential treatment and provides insight into the mechanism through which the potential treatment acts. While a few methods for estimating D and λ have been proposed, these previous methods lead to point estimates of D and λ, and provide no insight into the uncertainty in these estimates. Here, we compare various types of information that can be extracted from images of a scratch assay, and quantify D and λ using discrete computational simulations and approximate Bayesian computation. We show that it is possible to robustly recover estimates of D and λ from synthetic data, as well as a new set of experimental data. For the first time, our approach also provides a method to estimate the uncertainty in our estimates of D and λ. We anticipate that our approach can be generalized to deal with more realistic experimental scenarios in which we are interested in estimating D and λ, as well as additional relevant parameters such as the strength of cell-to-cell adhesion or the strength of cell-to-substrate adhesion.     

Estimating species trees using multiple-allele DNA sequence data

Several techniques, such as concatenation and consensus methods, are available for combining data from multiple loci to produce a single statement of phylogenetic relationships. However, when multiple alleles are sampled from individual species, it becomes more challenging to estimate relationships at the level of species, either because concatenation becomes inappropriate due to conflicts among individual gene trees, or because the species from which multiple alleles have been sampled may not form monophyletic groups in the estimated tree. We propose a Bayesian hierarchical model to reconstruct species trees from multiple-allele, multilocus sequence data, building on a recently proposed method for estimating species trees from single allele multilocus data. A two-step Markov Chain Monte Carlo (MCMC) algorithm is adopted to estimate the posterior distribution of the species tree. The model is applied to estimate the posterior distribution of species trees for two multiple-allele datasets--yeast (Saccharomyces) and birds (Manacus-manakins). The estimates of the species trees using our method are consistent with those inferred from other methods and genetic markers, but in contrast to other species tree methods, it provides credible regions for the species tree. The Bayesian approach described here provides a powerful framework for statistical testing and integration of population genetics and phylogenetics.     

Estimating species trees from unrooted gene trees

In this study, we develop a distance method for inferring unrooted species trees from a collection of unrooted gene trees. The species tree is estimated by the neighbor joining (NJ) tree built from a distance matrix in which the distance between two species is defined as the average number of internodes between two species across gene trees, that is, average gene-tree internode distance. The distance method is named NJ(st) to distinguish it from the original NJ method. Under the coalescent model, we show that if gene trees are known or estimated correctly, the NJ(st) method is statistically consistent in estimating unrooted species trees. The simulation results suggest that NJ(st) and STAR (another coalescence-based method for inferring species trees) perform almost equally well in estimating topologies of species trees, whereas the Bayesian coalescence-based method, BEST, outperforms both NJ(st) and STAR. Unlike BEST and STAR, the NJ(st) method can take unrooted gene trees to infer species trees without using an outgroup. In addition, the NJ(st) method can handle missing data and is thus useful in phylogenomic studies in which data sets often contain missing loci for some individuals.     

msBayes: Pipeline for testing comparative phylogeographic histories using hierarchical approximate Bayesian computation

Background  

Although testing for simultaneous divergence (vicariance) across different population-pairs that span the same barrier to gene flow is of central importance to evolutionary biology, researchers often equate the gene tree and population/species tree thereby ignoring stochastic coalescent variance in their conclusions of temporal incongruence. In contrast to other available phylogeographic software packages, msBayes is the only one that analyses data from multiple species/population pairs under a hierarchical model.     

Using approximate Bayesian computation to infer photosynthesis model parameters

We developed a method, namely Adaptive Population Monte Carlo Approximate Bayesian Computation (APMC), to estimate the parameters of Farquhar photosynthesis model. Treating the canopy as a big leaf, we applied this method to derive the parameters at canopy scale. Validations against observational data showed that parameters estimated based on the APMC optimization are un-biased for predicting the photosynthesis rate. We conclude that APMC has greater advantages in estimating the model parameters than those of the conventional nonlinear regression models.     

On optimal selection of summary statistics for approximate Bayesian computation

How best to summarize large and complex datasets is a problem that arises in many areas of science. We approach it from the point of view of seeking data summaries that minimize the average squared error of the posterior distribution for a parameter of interest under approximate Bayesian computation (ABC). In ABC, simulation under the model replaces computation of the likelihood, which is convenient for many complex models. Simulated and observed datasets are usually compared using summary statistics, typically in practice chosen on the basis of the investigator's intuition and established practice in the field. We propose two algorithms for automated choice of efficient data summaries. Firstly, we motivate minimisation of the estimated entropy of the posterior approximation as a heuristic for the selection of summary statistics. Secondly, we propose a two-stage procedure: the minimum-entropy algorithm is used to identify simulated datasets close to that observed, and these are each successively regarded as observed datasets for which the mean root integrated squared error of the ABC posterior approximation is minimized over sets of summary statistics. In a simulation study, we both singly and jointly inferred the scaled mutation and recombination parameters from a population sample of DNA sequences. The computationally-fast minimum entropy algorithm showed a modest improvement over existing methods while our two-stage procedure showed substantial and highly-significant further improvement for both univariate and bivariate inferences. We found that the optimal set of summary statistics was highly dataset specific, suggesting that more generally there may be no globally-optimal choice, which argues for a new selection for each dataset even if the model and target of inference are unchanged.     

Monte Carlo integration over stepping stone models for spatial genetic inference using approximate Bayesian computation

Approximate Bayesian computation (ABC) substitutes simulation for analytic models in Bayesian inference. Simulating evolutionary scenarios under Kimura’s stepping stone model (KSS) might therefore allow inference over spatial genetic process where analytical results are difficult to obtain. ABC first creates a reference set of simulations and would proceed by comparing summary statistics over KSS simulations to summary statistics from localities sampled in the field, but: comparison of which localities and stepping stones? Identical stepping stones can be arranged so two localities fall in the same stepping stone, nearest or diagonal neighbours, or without contact. None is intrinsically correct, yet some choice must be made and this affects inference. We explore a Bayesian strategy for mapping field observations onto discrete stepping stones. We make Sundial, for projecting field data onto the plane, available. We generalize KSS over regular tilings of the plane. We show Bayesian averaging over the mapping between a continuous field area and discrete stepping stones improves the fit between KSS and isolation by distance expectations. We make Tiler Durden available for carrying out this Bayesian averaging. We describe a novel parameterization of KSS based on Wright’s neighbourhood size, placing an upper bound on the geographic area represented by a stepping stone and make it available as m Vector. We generalize spatial coalescence recursions to continuous and discrete space cases and use these to numerically solve for KSS coalescence previously examined only using simulation. We thus provide applied and analytical resources for comparison of stepping stone simulations with field observations.     

Fitting models of continuous trait evolution to incompletely sampled comparative data using approximate Bayesian computation

In recent years, a suite of methods has been developed to fit multiple rate models to phylogenetic comparative data. However, most methods have limited utility at broad phylogenetic scales because they typically require complete sampling of both the tree and the associated phenotypic data. Here, we develop and implement a new, tree-based method called MECCA (Modeling Evolution of Continuous Characters using ABC) that uses a hybrid likelihood/approximate Bayesian computation (ABC)-Markov-Chain Monte Carlo approach to simultaneously infer rates of diversification and trait evolution from incompletely sampled phylogenies and trait data. We demonstrate via simulation that MECCA has considerable power to choose among single versus multiple evolutionary rate models, and thus can be used to test hypotheses about changes in the rate of trait evolution across an incomplete tree of life. We finally apply MECCA to an empirical example of body size evolution in carnivores, and show that there is no evidence for an elevated rate of body size evolution in the pinnipeds relative to terrestrial carnivores. ABC approaches can provide a useful alternative set of tools for future macroevolutionary studies where likelihood-dependent approaches are lacking.     

Identifying models of trait‐mediated community assembly using random forests and approximate Bayesian computation

Ecologists often use dispersion metrics and statistical hypothesis testing to infer processes of community formation such as environmental filtering, competitive exclusion, and neutral species assembly. These metrics have limited power in inferring assembly models because they rely on often‐violated assumptions. Here, we adapt a model of phenotypic similarity and repulsion to simulate the process of community assembly via environmental filtering and competitive exclusion, all while parameterizing the strength of the respective ecological processes. We then use random forests and approximate Bayesian computation to distinguish between these models given the simulated data. We find that our approach is more accurate than using dispersion metrics and accounts for uncertainty in model selection. We also demonstrate that the parameter determining the strength of the assembly processes can be accurately estimated. This approach is available in the R package CAMI; Community Assembly Model Inference. We demonstrate the effectiveness of CAMI using an example of plant communities living on lava flow islands.     

COMPUTER PROGRAMS: onesamp: a program to estimate effective population size using approximate Bayesian computation

The estimation of effective population size from one sample of genotypes has been problematic because most estimators have been proven imprecise or biased. We developed a web-based program, onesamp that uses approximate Bayesian computation to estimate effective population size from a sample of microsatellite genotypes. onesamp requires an input file of sampled individuals' microsatellite genotypes along with information about several sampling and biological parameters. onesamp provides an estimate of effective population size, along with 95% credible limits. We illustrate the use of onesamp with an example data set from a re-introduced population of ibex Capra ibex.     

Elucidating the spatio‐temporal dynamics of an emerging wildlife pathogen using approximate Bayesian computation

Emerging pathogens constitute a severe threat for human health and biodiversity. Determining the status (native or non‐native) of emerging pathogens, and tracing back their spatio‐temporal dynamics, is crucial to understand the eco‐evolutionary factors promoting their emergence, to control their spread and mitigate their impacts. However, tracing back the spatio‐temporal dynamics of emerging wildlife pathogens is challenging because (i) they are often neglected until they become sufficiently abundant and pose socio‐economical concerns and (ii) their geographical range is often little known. Here, we combined classical population genetics tools and approximate Bayesian computation (i.e. ABC) to retrace the dynamics of Tracheliastes polycolpus, a poorly documented pathogenic ectoparasite emerging in Western Europe that threatens several freshwater fish species. Our results strongly suggest that populations of T. polycolpus in France emerged from individuals originating from a unique genetic pool that were most likely introduced in the 1920s in central France. From this initial population, three waves of colonization occurred into peripheral watersheds within the next two decades. We further demonstrated that populations remained at low densities, and hence undetectable, during 10 years before a major demographic expansion occurred, and before its official detection in France. These findings corroborate and expand the few historical records available for this emerging pathogen. More generally, our study demonstrates how ABC can be used to determine the status, reconstruct the colonization history and infer key evolutionary parameters of emerging wildlife pathogens with low data availability, and for which samples from the putative native area are inaccessible.     

Using approximate Bayesian computation to estimate tuberculosis transmission parameters from genotype data

Tuberculosis can be studied at the population level by genotyping strains of Mycobacterium tuberculosis isolated from patients. We use an approximate Bayesian computational method in combination with a stochastic model of tuberculosis transmission and mutation of a molecular marker to estimate the net transmission rate, the doubling time, and the reproductive value of the pathogen. This method is applied to a published data set from San Francisco of tuberculosis genotypes based on the marker IS6110. The mutation rate of this marker has previously been studied, and we use those estimates to form a prior distribution of mutation rates in the inference procedure. The posterior point estimates of the key parameters of interest for these data are as follows: net transmission rate, 0.69/year [95% credibility interval (C.I.) 0.38, 1.08]; doubling time, 1.08 years (95% C.I. 0.64, 1.82); and reproductive value 3.4 (95% C.I. 1.4, 79.7). These figures suggest a rapidly spreading epidemic, consistent with observations of the resurgence of tuberculosis in the United States in the 1980s and 1990s.     

Leveraging whole genome sequencing data for demographic inference with approximate Bayesian computation

Accounting for historical demographic features, such as the strength and timing of gene flow and divergence times between closely related lineages, is vital for many inferences in evolutionary biology. Approximate Bayesian computation (ABC) is one method commonly used to estimate demographic parameters. However, the DNA sequences used as input for this method, often microsatellites or RADseq loci, usually represent a small fraction of the genome. Whole genome sequencing (WGS) data, on the other hand, have been used less often with ABC, and questions remain about the potential benefit of, and how to best implement, this type of data; we used pseudo‐observed data sets to explore such questions. Specifically, we addressed the potential improvements in parameter estimation accuracy that could be associated with WGS data in multiple contexts; namely, we quantified the effects of (a) more data, (b) haplotype‐based summary statistics, and (c) locus length. Compared with a hypothetical RADseq data set with 2.5 Mbp of data, using a 1 Gbp data set consisting of 100 Kbp sequences led to substantial gains in the accuracy of parameter estimates, which was mostly due to haplotype statistics and increased data. We also quantified the effects of including (a) locus‐specific recombination rates, and (b) background selection information in ABC analyses. Importantly, assuming uniform recombination or ignoring background selection had a negative effect on accuracy in many cases. Software and results from this method validation study should be useful for future demographic history analyses.     

Coestimation of recombination,substitution and molecular adaptation rates by approximate Bayesian computation

The estimation of parameters in molecular evolution may be biased when some processes are not considered. For example, the estimation of selection at the molecular level using codon-substitution models can have an upward bias when recombination is ignored. Here we address the joint estimation of recombination, molecular adaptation and substitution rates from coding sequences using approximate Bayesian computation (ABC). We describe the implementation of a regression-based strategy for choosing subsets of summary statistics for coding data, and show that this approach can accurately infer recombination allowing for intracodon recombination breakpoints, molecular adaptation and codon substitution rates. We demonstrate that our ABC approach can outperform other analytical methods under a variety of evolutionary scenarios. We also show that although the choice of the codon-substitution model is important, our inferences are robust to a moderate degree of model misspecification. In addition, we demonstrate that our approach can accurately choose the evolutionary model that best fits the data, providing an alternative for when the use of full-likelihood methods is impracticable. Finally, we applied our ABC method to co-estimate recombination, substitution and molecular adaptation rates from 24 published human immunodeficiency virus 1 coding data sets.     

Species trees from gene trees: reconstructing Bayesian posterior distributions of a species phylogeny using estimated gene tree distributions

The desire to infer the evolutionary history of a group of species should be more viable now that a considerable amount of multilocus molecular data is available. However, the current molecular phylogenetic paradigm still reconstructs gene trees to represent the species tree. Further, commonly used methods of combining data, such as the concatenation method, are known to be inconsistent in some circumstances. In this paper, we propose a Bayesian hierarchical model to estimate the phylogeny of a group of species using multiple estimated gene tree distributions, such as those that arise in a Bayesian analysis of DNA sequence data. Our model employs substitution models used in traditional phylogenetics but also uses coalescent theory to explain genealogical signals from species trees to gene trees and from gene trees to sequence data, thereby forming a complete stochastic model to estimate gene trees, species trees, ancestral population sizes, and species divergence times simultaneously. Our model is founded on the assumption that gene trees, even of unlinked loci, are correlated due to being derived from a single species tree and therefore should be estimated jointly. We apply the method to two multilocus data sets of DNA sequences. The estimates of the species tree topology and divergence times appear to be robust to the prior of the population size, whereas the estimates of effective population sizes are sensitive to the prior used in the analysis. These analyses also suggest that the model is superior to the concatenation method in fitting these data sets and thus provides a more realistic assessment of the variability in the distribution of the species tree that may have produced the molecular information at hand. Future improvements of our model and algorithm should include consideration of other factors that can cause discordance of gene trees and species trees, such as horizontal transfer or gene duplication.     

Analyzing tropical forest tree species abundance distributions using a nonneutral model and through approximate Bayesian inference

The neutral theory of biodiversity challenges the classical niche-based view of ecological communities, where species attributes and environmental conditions jointly determine community composition. Functional equivalence among species, as assumed by neutral ecological theory, has been recurrently falsified, yet many patterns of tropical tree communities appear consistent with neutral predictions. This may mean that neutral theory is a good first-approximation theory or that species abundance data sets contain too little information to reject neutrality. Here we present a simple test of neutrality based on species abundance distributions in ecological communities. Based on this test, we show that deviations from neutrality are more frequent than previously thought in tropical forest trees, especially at small spatial scales. We then develop a nonneutral model that generalizes Hubbell's dispersal-limited neutral model in a simple way by including one additional parameter of frequency dependence. We also develop a statistical method to infer the parameters of this model from empirical data by approximate Bayesian computation. In more than half of the permanent tree plots, we show that our new model fits the data better than does the neutral model. Finally, we discuss whether observed deviations from neutrality may be interpreted as the signature of environmental filtering on tropical tree species abundance distributions.     

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC. AVAILABILITY: The software DIY ABC is freely available at http://www.montpellier.inra.fr/CBGP/diyabc.     

利用近似贝氏计算推论台湾海峡沿岸秋茄种群的拓殖路线

由于地理关系,台湾海峡两岸的红树植物组成具有高度的相似性,都以耐寒性较强的秋茄为优势种。中国台湾(以下简称"台湾")与大陆仅一水之隔,因此台湾的秋茄种群来源最有可能来自东南沿海种群,然而台湾南、北红树植物种群的拓殖路线以及与大陆东南沿海种群的遗传关系的研究至今仍未见报道。通过SSR分子标记,利用近似贝氏计算(Approximate Bayesian Computation)推测海峡两岸4个分布区域秋茄的起源及其拓殖路线。结果表明4个区域的种群出现明显分化,大陆东南北部种群与其他种群间分化程度最高。通过推测台湾北部种群起源可追溯到29000—48400a前,早于末次冰期时间,且台湾北部种群遗传结构与大陆东南南部种群最相近,推测它们可能共同起源于南方祖先。大陆东南沿海南北种群的溯祖时间约为15.1万年至25.2a年前,约为更新世中期末,则意味东南沿海南、北种群的遗传分化可能受到更新世后期气候变化与海侵海退的影响而出现隔离,或东南沿海南、北种群可能来自不同的起源。而台湾南部种群与台湾北部种群的相似性,表明台湾南部种群是由北部种群拓殖而来,近似贝氏计算亦支持这个假说。因而,可以推测海峡两岸秋茄的拓殖路线是从大陆东南南方种群随黑潮迁移至台湾北部,再从北部拓殖到台湾南部。利用近似贝氏计算推论台湾海峡两岸红树林种群起源及拓殖路线,为未来我国东南沿海红树林植物的生物地理研究提供参考。