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A Restricted Model Space Approach for the Detection
of Epistasis in Quantitative Trait Loci Using Markov
Chain Monte Carlo Model Composition
Edward L. Boone
1
,
, Susan J. Simmons
2
, and Karl Ricanek
2
1
Virginia Commonwealth University, Richmond, Virginia, U.S.A.
2
University of North Carolina Wilmington, Wilmington, North Carolina, U.S.A.
elboone@vcu.edu,
{
simmonssj,ricanekk
}
@uncw.edu
Abstract.
Epistasis or the interaction between loci on a genome that controls
a quantitative trait is of great interest to geneticists. This work presents a pow-
erful Bayesian method utilizing Markov chain Monte Carlo model composition
approach using restricted spaces is developed for identifying epistatic effects in
Recombinant Inbred Lines (RIL) in plant studies. This method produces both pos-
terior activation probabilities and posterior conditional activation probabilities.
The method is verified through a simulation study and applied to an
Arabidopsis
thaliana
data set with cotyledon as the quantitative trait.
Keywords.
Quantitative trait loci, Epistasis, Bayesian statistics, Markov chain
Monte Carlo model composition.
1
Introduction
Quantitative Trait Loci (QTL) analysis determines which region(s) on a genome ex-
plains or controls a quantitative trait. However, in many instances an iteraction between
regions or loci may provide a better explanation for a trait than regions having a strictly
additive influence. This interaction between loci on a genome is known as
epistasis
.To
study QTL in plant species, organisms generated by recombinant inbreeding are often
used. Recombinant Inbred Lines (RIL) are plants that have been repeatedly mated with
siblings and themselves in order to create an inbred line whose genetic structure is a
combination of the original parent lines. These RILs provide a mechanism to reduce
environmental and individual effects. Furthermore, by utilizing RILs, the alleles at each
loci are homozygous and help simplify the search for QTL. For a complete review of
RILs see Broman [1].
Several methods have been developed to detect and evaluate epistatic effects for con-
tinuous traits. Multiple Interval Mapping (MIM) proposed by [10] is based on fitting a
multiple regression model that has both main effect terms as well as interactions and
employs a non-Bayesian search method. Carlborg et al. [5] use a genetic algorithm to
search for the loci and epistatic effects. Hensen et al. [9] propose a theoretical frame-
work for higher order interactions. Kao et al. [11] use the framework of [6] to partition
Corresponding author.
