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.     

Testing comparative phylogeographic models of marine vicariance and dispersal using a hierarchical Bayesian approach

Background  

Marine allopatric speciation is an enigma because pelagic larval dispersal can potentially connect disjunct populations thereby preventing reproductive and morphological divergence. Here we present a new hierarchical approximate Bayesian computation model (HABC) that tests two hypotheses of marine allopatric speciation: 1.) "soft vicariance", where a speciation involves fragmentation of a large widespread ancestral species range that was previously connected by long distance gene flow; and 2.) peripatric colonization, where speciations in peripheral archipelagos emerge from sweepstakes colonizations from central source regions. The HABC approach analyzes all the phylogeographic datasets at once in order to make across taxon-pair inferences about biogeographic processes while explicitly allowing for uncertainty in the demographic differences within each taxon-pair. Our method uses comparative phylogeographic data that consists of single locus mtDNA sequences from multiple co-distributed taxa containing pairs of central and peripheral populations. We use the method on two comparative phylogeographic data sets consisting of cowrie gastropod endemics co-distributed in the Hawaiian (11 taxon-pairs) and Marquesan archipelagos (7 taxon-pairs).     

Estimating species trees using approximate Bayesian computation

Development of methods for estimating species trees from multilocus data is a current challenge in evolutionary biology. We propose a method for estimating the species tree topology and branch lengths using approximate Bayesian computation (ABC). The method takes as data a sample of observed rooted gene tree topologies, and then iterates through the following sequence of steps: First, a randomly selected species tree is used to compute the distribution of rooted gene tree topologies. This distribution is then compared to the observed gene topology frequencies, and if the fit between the observed and the predicted distributions is close enough, the proposed species tree is retained. Repeating this many times leads to a collection of retained species trees that are then used to form the estimate of the overall species tree. We test the performance of the method, which we call ST-ABC, using both simulated and empirical data. The simulation study examines both symmetric and asymmetric species trees over a range of branch lengths and sample sizes. The results from the simulation study show that the model performs very well, giving accurate estimates for both the topology and the branch lengths across the conditions studied, and that a sample size of 25 loci appears to be adequate for the method. Further, we apply the method to two empirical cases: a 4-taxon data set for primates and a 7-taxon data set for yeast. In both cases, we find that estimates obtained with ST-ABC agree with previous studies. The method provides efficient estimation of the species tree, and does not require sequence data, but rather the observed distribution of rooted gene topologies without branch lengths. Therefore, this method is a useful alternative to other currently available methods for species tree estimation.     

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.     

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.     

Statistical hypothesis testing in intraspecific phylogeography: nested clade phylogeographical analysis vs. approximate Bayesian computation

Nested clade phylogeographical analysis (NCPA) and approximate Bayesian computation (ABC) have been used to test phylogeographical hypotheses. Multilocus NCPA tests null hypotheses, whereas ABC discriminates among a finite set of alternatives. The interpretive criteria of NCPA are explicit and allow complex models to be built from simple components. The interpretive criteria of ABC are ad hoc and require the specification of a complete phylogeographical model. The conclusions from ABC are often influenced by implicit assumptions arising from the many parameters needed to specify a complex model. These complex models confound many assumptions so that biological interpretations are difficult. Sampling error is accounted for in NCPA, but ABC ignores important sources of sampling error that creates pseudo-statistical power. NCPA generates the full sampling distribution of its statistics, but ABC only yields local probabilities, which in turn make it impossible to distinguish between a good fitting model, a non-informative model, and an over-determined model. Both NCPA and ABC use approximations, but convergences of the approximations used in NCPA are well defined whereas those in ABC are not. NCPA can analyse a large number of locations, but ABC cannot. Finally, the dimensionality of tested hypothesis is known in NCPA, but not for ABC. As a consequence, the 'probabilities' generated by ABC are not true probabilities and are statistically non-interpretable. Accordingly, ABC should not be used for hypothesis testing, but simulation approaches are valuable when used in conjunction with NCPA or other methods that do not rely on highly parameterized 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.     

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.     

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.     

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.     

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.     

Ginkgo: spatially-explicit simulator of complex phylogeographic histories

We present Ginkgo, a software package for agent-based, forward-time simulations of genealogies of multiple unlinked loci from diploid populations. Ginkgo simulates the evolution of one or more species on a spatially explicit landscape of cells. The user of the software can specify the geographical and environmental characteristics of the landscape, and these properties can change according to a prespecified schedule. The geographical elements modelled include the arrangement of cells and movement rates between particular cells. Each species has a function that can calculate a fitness score for any combination of an individual organism's phenotype and environmental characteristics. The user can control the number of fitness factors (the dimensionality of the cell-specific fitness factors and the individuals phenotypic vectors) and the weighting of each of these dimensions in the fitness calculation. Cell-specific fitness trait optima can be specified across the landscape to mimic differences in habitat. In addition to their differing fitness functions, species can differ in terms of their vagility and fecundity. Genealogies and occurrence data can be produced at any time during the simulation in NEXUS and ESRI Ascii Grid formats, respectively.     

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.     

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.     

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.     

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.     

MTML-msBayes: Approximate Bayesian comparative phylogeographic inference from multiple taxa and multiple loci with rate heterogeneity

Background  

MTML-msBayes uses hierarchical approximate Bayesian computation (HABC) under a coalescent model to infer temporal patterns of divergence and gene flow across codistributed taxon-pairs. Under a model of multiple codistributed taxa that diverge into taxon-pairs with subsequent gene flow or isolation, one can estimate hyper-parameters that quantify the mean and variability in divergence times or test models of migration and isolation. The software uses multi-locus DNA sequence data collected from multiple taxon-pairs and allows variation across taxa in demographic parameters as well as heterogeneity in DNA mutation rates across loci. The method also allows a flexible sampling scheme: different numbers of loci of varying length can be sampled from different taxon-pairs.     

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.     

A comparative phylogeographic study reveals discordant evolutionary histories of alpine ground beetles (Coleoptera,Carabidae)

Taiwan, an island with three major mountain ranges, provides an ideal topography to study mountain–island effect on organisms that would be diversified in the isolation areas. Glaciations, however, might drive these organisms to lower elevations, causing gene flow among previously isolated populations. Two hypotheses have been proposed to depict the possible refugia for alpine organisms during glaciations. Nunatak hypothesis suggests that alpine species might have stayed in situ in high mountain areas during glaciations. Massif de refuge, on the other hand, proposes that alpine species might have migrated to lower ice‐free areas. By sampling five sympatric carabid species of Nebria and Leistus, and using two mitochondrial genes and two nuclear genes, we evaluated the mountain–island effect on alpine carabids and tested the two proposed hypotheses with comparative phylogeographic method. Results from the phylogenetic relationships, network analysis, lineage calibration, and genetic structure indicate that the deep divergence among populations in all L. smetanai, N. formosana, and N. niitakana was subjected to long‐term isolation, a phenomenon in agreement with the nunatak hypothesis. However, genetic admixture among populations of N. uenoiana and some populations of L. nokoensis complex suggests that gene flow occurred during glaciations, as a massif de refuge depicts. The speciation event in N. niitakana is estimated to have occurred before 1.89 million years ago (Mya), while differentiation among isolated populations in N. niitakana, N. formosana, L. smetanai, and L. nokoensis complex might have taken place during 0.65–1.65 Mya. While each of the alpine carabids arriving in Taiwan during different glaciation events acquired its evolutionary history, all of them had confronted the existing mountain ranges.