Genetics, Vol. 167, 989-999, June 2004, Copyright © 2004
doi:10.1534/genetics.103.021683

Modifying the Schwarz Bayesian Information Criterion to Locate Multiple Interacting Quantitative Trait Loci

Magorzata Bogdan^*,, Jayanta K. Ghosh^, and R. W. Doerge^,,1

^* Institute of Mathematics, Wroclaw University of Technology, 50-370 Wroclaw, Poland
Indian Statistical Institute, Calcutta 700035, India
Department of Statistics, Purdue University, West Lafayette, Indiana 47907
Department of Agronomy, Purdue University, West Lafayette, Indiana 47907

¹ Corresponding author: Department of Statistics, 1399 Math Bldg., Purdue University, West Lafayette, Indiana 47907.
E-mail: doerge{at}purdue.edu

The problem of locating multiple interacting quantitative trait loci (QTL) can be addressed as a multiple regression problem, with marker genotypes being the regressor variables. An important and difficult part in fitting such a regression model is the estimation of the QTL number and respective interactions. Among the many model selection criteria that can be used to estimate the number of regressor variables, none are used to estimate the number of interactions. Our simulations demonstrate that epistatic terms appearing in a model without the related main effects cause the standard model selection criteria to have a strong tendency to overestimate the number of interactions, and so the QTL number. With this as our motivation we investigate the behavior of the Schwarz Bayesian information criterion (BIC) by explaining the phenomenon of the overestimation and proposing a novel modification of BIC that allows the detection of main effects and pairwise interactions in a backcross population. Results of an extensive simulation study demonstrate that our modified version of BIC performs very well in practice. Our methodology can be extended to general populations and higher-order interactions.

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