January 2005, Volume 94, Number 1, Pages 119-128
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Original Article
An EM algorithm for mapping quantitative resistance loci

C Xu1, Y-M Zhang1 and S Xu1

1Department of Botany and Plant Sciences, University of California,
Riverside, CA 92521, USA

Correspondence to: S Xu, Department of Botany and Plant Sciences, University
of California, Riverside, CA 92521, USA. E-mail: xu{at}genetics.ucr.edu


Abstract

Many disease resistance traits in plants have a polygenic background and the
disease phenotypes are modified by environmental factors. As a consequence,
the phenotypic values usually show a quantitative variation. The phenotypes
of such disease traits, however, are often measured in discrete but ordered
categories. These traits are called ordinal traits. In terms of disease
resistance, they are called quantitative resistance traits, as opposed to
qualitative resistance traits, and are controlled by the quantitative
resistance loci (QRL). Classical quantitative trait locus mapping methods
are not optimal for ordinal trait analysis because the assumption of normal
distribution is violated. Methods for mapping binary trait loci are not
suitable either because there are more than two categories in ordinal
traits. We developed a maximum likelihood method to map these QRL. The
method is implemented via a multicycle expectation-conditional-maximization
(ECM) algorithm under the threshold model, where we can estimate both the
QRL effects and the thresholds that link the disease liability and the
categorical phenotype. The method is verified in simulated data under
various combinations of the parameters. An SAS program is available to
implement the multicycle ECM algorithm. The program can be downloaded from
our website at www.statgen.ucr.edu.

Heredity (2005) 94, 119-128. doi:10.1038/sj.hdy.6800583
Published online 15 September 2004

Keywords
ECM-algorithm; maximum likelihood; ordinal trait; quantitative resistance
locus

Full Text at Nature Heredity
http://info.nature.com/cgi-bin24/DM/y/hRWc0CfMvE0DS0XPb0A4

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