A penalized likelihood method for mapping epistatic quantitative trait loci with one-dimensional genome searches

Epistasis is a common and important phenomenon, as indicated by results from a number of recent experiments. Unfortunately, the discovery of epistatic quantitative trait loci (QTL) is difficult since one must search for multiple QTL simultaneously in two or more dimensions. Such a multidimensional search necessitates many statistical tests, and a high statistical threshold must be adopted to avoid false positives. Furthermore, the large number of (interaction) parameters in comparison with the number of observations results in a serious danger of overfitting and overinterpretation of the data. In this article we present a new statistical framework for mapping epistasis in inbred line crosses. It is based on reducing the high dimensionality of the problem in two ways. First, epistatic QTL are mapped in a one-dimensional genome scan for high interactions between QTL and the genetic background. Second, the dimension of the search is bounded by penalized likelihood methods. We use simulated backcross data to illustrate the new approac