Plant Genome II Conference
Town & Country Conference Center, San Diego, CA, January, 1994.
PG-II: Quantitative Trait Mapping
Quantitative Trait Mapping
Rebecca W. Doerge and Gary A. Churchill
Biometrics Unit, Cornell University, Ithaca, NY 14853
A general framework for mapping quantitative trait loci
(QTL) has been developed based an augmented data formulation of
the likelihood. In this approach, the observable data, marker
genotypes and quantitative phenotypes, are augmented by computing
the conditional expectation of the QTL genotypes in each
individual given the model parameters. The augmented data
likelihood is trivial to maximize. The two steps of conditional
expectation and maximization are applied iteratively to yield a
maximized likelihood for the observed data. This algorithm is
shown to be a special case of the expectation-maximization
algorithm (EM). Our approach to QTL mapping has several
advantages over the standard interval mapping approach. One of
these being that, although our method can be used to assign
likelihoods to intervals on a map where the order of the markers
is fixed and known, the recombination fractions between markers
are not fixed and may be simultaneously estimated with the other
model parameters. Perhaps the greatest advantage of the
augmented data approach is that its conceptual simplicity allows
us to readily extend it to more complex situations than currently
available methods can handle. We illustrate this generality by
deriving an EM algorithm for mapping in a system where the
quantitative trait has a bivariate normal mixture distribution
with three classes. Our working model, involves two major genes
that govern the trait of interest plus quantitative modifiers
that may be genetic and/or environmental. Interaction between
the two genes is complex, involving dominance relationships and
epistatic interactions among the different alleles.
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