Abstract
BackgroundThe estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations.ResultsHere we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females.ConclusionABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.
Highlights
The estimation of demographic parameters from genetic data often requires the computation of likelihoods
Estimation Procedure and Validation We computed a total of 338 summary statistics on the 11 populations and both mitochondrial DNA (mtDNA) and microsatellite datasets, which were reduced to 7 Partial Least Squares (PLS) components using specific R scripts of ABCtoolbox
ABCtoolbox allows a user to perform all the necessary steps of a full Approximate Bayesian Computation (ABC) analysis, like parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results
Summary
The estimation of demographic parameters from genetic data often requires the computation of likelihoods. The likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. The quantity of interest is the posterior distribution of the parameters θ, which is given by Bayes theorem as π (θ|D)~f(D|θ)π (θ), where f(D|θ) is the likelihood of the data. A simple rejection algorithm has been proposed [2,3,4] to estimate the likelihood: a candidate parameter vector θ is simulated from a prior distribution and accepted if the corresponding vector of summary
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