Approximate Bayesian computation for modular inference problems with many parameters: the example of migration rates. Journal Article


Author(s): Aeschbacher, Simon; Futschik, Andreas; Beaumont, Mark A
Article Title: Approximate Bayesian computation for modular inference problems with many parameters: the example of migration rates.
Affiliation IST Austria
Abstract: We propose a two-step procedure for estimating multiple migration rates in an approximate Bayesian computation (ABC) framework, accounting for global nuisance parameters. The approach is not limited to migration, but generally of interest for inference problems with multiple parameters and a modular structure (e.g. independent sets of demes or loci). We condition on a known, but complex demographic model of a spatially subdivided population, motivated by the reintroduction of Alpine ibex (Capra ibex) into Switzerland. In the first step, the global parameters ancestral mutation rate and male mating skew have been estimated for the whole population in Aeschbacher et al. (Genetics 2012; 192: 1027). In the second step, we estimate in this study the migration rates independently for clusters of demes putatively connected by migration. For large clusters (many migration rates), ABC faces the problem of too many summary statistics. We therefore assess by simulation if estimation per pair of demes is a valid alternative. We find that the trade-off between reduced dimensionality for the pairwise estimation on the one hand and lower accuracy due to the assumption of pairwise independence on the other depends on the number of migration rates to be inferred: the accuracy of the pairwise approach increases with the number of parameters, relative to the joint estimation approach. To distinguish between low and zero migration, we perform ABC-type model comparison between a model with migration and one without. Applying the approach to microsatellite data from Alpine ibex, we find no evidence for substantial gene flow via migration, except for one pair of demes in one direction.
Keywords: Alpine ibex; approximate Bayesian computation; divide and conquer; migration rates; pairwise estimation
Journal Title: Molecular Ecology
Volume: 22
Issue 4
ISSN: 0962-1083
Publisher: Wiley  
Date Published: 2013-02-01
Start Page: 987
End Page: 1002
DOI: 10.1111/mec.12165
Notes: We thank Nick Barton, Jitka Polechová and three anonymous reviewers for helpful comments on the manuscript. We are grateful to Iris Biebach and Lukas Keller for providing genetic data and for help in reconstructing the demographic data. We thank Markus Brülisauer, Erwin Eggenberger, Flurin Filli, Bernhard Nievergelt, Marc Rosset, Urs Zimmermann, Martin Zuber, the staff from Tierpark Langenberg, Tierpark Dählhölzli (Bern), Wildpark Peter and Paul (St. Gallen), Wildtier Schweiz and the Swiss Federal Office for the Environment for providing information on population history and reintroduction, and Barbara Oberholzer for double-checking the reintroduction history. We thank Walter Abderhalden, Iris Biebach, Michael Blum, Kati Csilléry, Lukas Keller and Christian Willisch for discussion. This study has made use of the computational resources provided by IST Austria and the Edinburgh Compute and Data Facility (ECDF; http://www.ecdf.ed.ac.uk). The ECDF is partially supported by the eDIKT initiative (http://www.edikt.org.uk). S.A. acknowledges financial support by IST Austria, the Janggen-Pöhn Foundation, St. Gallen, the Roche Research Foundation, Basel, the University of Edinburgh in the form of a Torrance Studentship, and the Austrian Science Fund (FWF P21305-N13).
Open access: no