A Bayesian approach is presented for mapping a quantitative trait locus (QTL) using the
‘Fernando and Grossman’ multivariate Normal approximation to QTL inheritance. For this
model, a Bayesian implementation that includes QTL position is problematic because standard
Markov chain Monte Carlo (MCMC) algorithms do not mix, i.e. the QTL position gets stuck in
one marker interval. This is because of the dependence of the covariance structure for the QTL
effects on the adjacent markers and may be typical of the ‘Fernando and Grossman’ model. A
relatively new MCMC technique, simulated tempering, allows mixing and so makes possible
inferences about QTL position based on marginal posterior probabilities. The model was
implemented for estimating variance ratios and QTL position using a continuous grid of allowed
positions and was applied to simulated data of a standard granddaughter design. The results
showed a smooth mixing of QTL position after implementation of the simulated tempering
sampler. In this implementation, map distance between QTL and its flanking markers was
artificially stretched to reduce the dependence of markers and covariance. The method generalizes
easily to more complicated applications and can ultimately contribute to QTL mapping in
complex, heterogeneous, human, animal or plant populations.
Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations