Originally published as Genetics Published Articles Ahead of Print on February 2, 2009.

Genetics, Vol. 181, 1507-1519, April 2009, Copyright © 2009
doi:10.1534/genetics.108.098129

Approximate Bayesian Computation Without Summary Statistics: The Case of Admixture

Vitor C. Sousa^*,,1, Marielle Fritz, Mark A. Beaumont and Lounès Chikhi^*,**

^* Instituto Gulbenkian de Ciência, Rua da Quinta Grande, P-2780-156 Oeiras, Portugal, Centro de Biologia Ambiental, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal, Laboratoire de Statistiques et Probabilités, UMR C5583 Université Paul Sabatier, 31062 Toulouse Cédex 09, France, University of Reading, Whiteknights, RG6 6BX Reading, United Kingdom and ^** Laboratoire Evolution et Diversité Biologique, UMR CNRS/UPS 5174 Université Paul Sabatier, 31062 Toulouse Cédex 09, France

¹ Corresponding author: Instituto Gulbenkian de Ciência, Rua da Quinta Grande, No. 6, P-2780-156 Oeiras, Portugal.
E-mail: vitorsousa{at}igc.gulbenkian.pt

In recent years approximate Bayesian computation (ABC) methods have become popular in population genetics as an alternative to full-likelihood methods to make inferences under complex demographic models. Most ABC methods rely on the choice of a set of summary statistics to extract information from the data. In this article we tested the use of the full allelic distribution directly in an ABC framework. Although the ABC techniques are becoming more widely used, there is still uncertainty over how they perform in comparison with full-likelihood methods. We thus conducted a simulation study and provide a detailed examination of ABC in comparison with full likelihood in the case of a model of admixture. This model assumes that two parental populations mixed at a certain time in the past, creating a hybrid population, and that the three populations then evolve under pure drift. Several aspects of ABC methodology were investigated, such as the effect of the distance metric chosen to measure the similarity between simulated and observed data sets. Results show that in general ABC provides good approximations to the posterior distributions obtained with the full-likelihood method. This suggests that it is possible to apply ABC using allele frequencies to make inferences in cases where it is difficult to select a set of suitable summary statistics and when the complexity of the model or the size of the data set makes it computationally prohibitive to use full-likelihood methods.

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