This article reviews key contributions in the area of statistics as
applied to the use of molecular marker technology and quantitative genetics in
the search for genes affecting quantitative traits responsible for specific
diseases and economically important agronomic traits. Since an exhaustive
literature review is not possible, the limited scope of this work is to
encourage further statistical work in this vast field by first reviewing human
and domestic species literature, and then concentrating on the statistical
developments for experimental breeding populations. Substantial gains have been
made over the years by both plant and animal breeders toward a long-term goal
of locating genes affecting quantitative traits (quantitative trait loci, QTLs)
for the eventual characterization and manipulation of these genes in order to
develop improved agronomically important traits. Our main concern is that the
care and expense that are required in generating both genetic marker data and
quantitative trait data should be accompanied by equal care in the statistical
analysis of the data. Through an example using an $F_2$ male genetic map of
mouse chromosome 10, and quantitative trait values measured on weight gain, we
implement much of the reviewed methodology for the purpose of detecting or
locating a QTL having an effect on weight gain.