Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations

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

Genotype by Environment Interaction for Holstein Milk Yield in Colombia, Mexico, and Puerto Rico

Components of (co)variance and genetic parameters were estimated by REML procedures from first lactation mature equivalent Holstein milk records from 54,604 Colombian, Mexican, and Puerto Rican cows and 198,079 US cows. The objective was to determine the cause of heterogeneous daughter response to sire selection for milk yield between the regions. Data from Latin America were partitioned by country and by herd-year SD class for milk to obtain five joint analyses between the US and Latin America, low herd-year SD, high herd year SD, Colombia, and Mexico. Sire and residual variances for milk were 41 and 29% smaller in Latin America than in the US, 47 and 58% smaller for low than for high herd-year SD, and 31 and 49% smaller for Colombia than for Mexico. Resultant heritabilities ranged from .20 to .29. Genetic correlations for milk yield between the US and Latin America, low and high herd-year SD, Colombia, and Mexico were .91, .82, .89, .78, and .90. Expected correlated responses for milk in Latin America, low and high herd-year SD, Colombia, and Mexico were 70, 53, 79.56, and 78% of the direct response in the US. The scaling effects of heterogeneous variance resulted in smaller daughter milk responses in Latin America compared with the US even when herd-year SD was similar

Effects of clinical ketosis on test day milk yields in Finnish Ayrshire cattle

A linear model for repeated measurements was used to estimate the effects of clinical ketosis on 722,198 test day milk yields collected from September 1, 1985 to January 31, 1988 on 60,851 Finnish Ayrshire cows of parity 17 d after diagnosis, and milk collected on nonketotic cows. For each parity separately, the statistical model included fixed effects (ketosis, calving season, year and season of milk sampling, and stage of lactation) and random effects (herd and permanent and temporary environments) on test day milk yields. The pattern underlying correlations between temporary environmental effects was accommodated in the statistical model. Compared with those for nonketotic cows, lactation curves of cows with ketosis showed a depression in early lactation; estimated milk loss was 44.3 kg for 17 d after diagnosis. The 305-d milk yield of cows diagnosed with ketosis was estimated to be 141.1 kg higher than that of cows free of ketosis. Although milk losses occurred after ketosis, ketotic cows yielded more milk over the entire lactation than did nonketotic cows; and yields would have been even higher if cows had not had ketosis