Efficient Approximate Bayesian Computation Coupled With Markov Chain Monte Carlo Without Likelihood

Abstract

Approximate Bayesian computation (ABC) techniques permit inferences in complex demographic models, but are computationally inefficient. A Markov chain Monte Carlo (MCMC) approach has been proposed (Marjoram et al. 2003), but it suffers from computational problems and poor mixing. We propose several methodological developments to overcome the shortcomings of this MCMC approach and hence realize substantial computational advances over standard ABC. The principal idea is to relax the tolerance within MCMC to permit good mixing, but retain a good approximation to the posterior by a combination of subsampling the output and regression adjustment. We also propose to use a partial leastsquares (PLS) transformation to choose informative statistics. The accuracy of our approach is examined in the case of the divergence of two populations with and without migration. In that case, our ABC-MCMC approach needs considerably lower computation time to reach the same accuracy than conventional ABC. We then apply our method to a more complex case with the estimation of divergence times and migration rates between three African populations.W ITH the advent of large-scale genotyping techniques (e.g., Green et al. 2006;Levy et al. 2007), genetic data can be produced at an unprecedented scale (Altshuler et al. 2005;Bustamante et al. 2005), and the genetic variability of individuals and populations can now routinely be examined at hundreds of loci across the genome (Rosenberg et al. 2002;Williamson et al. 2005;Becquet and Przeworski 2007;Frazer et al. 2007). These large data sets offer the hope to better understand the evolutionary forces that have shaped the diversity of many species, including humans, and to identify genome regions involved in past selective events (Anisimova and Liberles 2007;Nielsen et al. 2007). However, the demographic history of the populations needs to be accounted for to disentangle its effects from those of selection (Haddrill et al. 2005;Nielsen et al. 2005;Biswas and Akey 2006). It therefore seems important to be able to properly estimate this past demography from neutral genetic data or to estimate demography and selection simultaneously (e.g., Williamson et al. 2005). The statistical estimation of mutation and demographic parameters has drastically improved in the last 10 years, particularly with the use of Bayesian and full-likelihood approaches (Beaumont et al. 2002;Marjoram and Tavare 2006). However, these methods are still restricted to relatively simple models whose likelihood can be computed or to small data sets that can be analyzed in a reasonable amount of time. The handling of large data sets and the estimation of demographic parameters under realistic models remain problematic, and goodness-of-fit methods have been often used in those cases (see, e.g., Marth et al. 2004;Schaffner et al. 2005;Plagnol and Wall 2006).The approximate Bayesian computation (ABC) framework (Tavare et al. 1997;Pritchard et al. 1999;Beaumont et al. 2002), which is based on a simple rejection algorithm, has bee...

Population divergence with or without admixture: selecting models using an ABC approach

“…We also found that applying the regression step decreased the dependence on the tolerance level d (Figure 4). This limited dependency on d was also found when using ABC algorithms to estimate parameters within a single model Excoffier et al, 2005;Sousa et al, 2009;Wegmann et al, 2009). The fact that the regression step decreases the dependence on the acceptance rate means that the number of simulations needed to separate models can be significantly reduced without losing much power (Figure 4).…”

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

“…Recently there has been a great increase in the application of ABC methods for problems in population genetics, and this has largely been driven by the availability of useful software packages (for example, ABCtoolbox package (Wegmann et al, 2009), ABC package (Csillery et al, 2012) or DIY-ABC (Cornuet et al, 2008)). These authors have developed a number of important enhancements to the original rejection and regression algorithms (reviewed in Beaumont (2010)).…”

Advances in Computer Simulation of Genome Evolution: Toward More Realistic Evolutionary Genomics Analysis by Approximate Bayesian Computation

“…These processes determine the evolutionary history of genomes and despite the fact that they have been widely studied (e.g., Chain and Feulner 2014), they are still very challenging to implement jointly in current analytical methods. For example, it is known that the computation of a likelihood function based on a relatively complex model of evolution can be intractable, thus restricting the use of likelihoodbased inference to simple evolutionary scenarios and models (e.g., Marjoram et al 2003;Wegmann et al 2009). Therefore, in order to deal with complex evolutionary models, statistical approaches based on computer simulations such as approximate Bayesian computation (ABC) (e.g., Beaumont 2010;Sunnaker et al 2013), that avoid the need for a likelihood function, are being established.…”