BAYESIAN-ANALYSIS OF GENETIC CHANGE DUE TO SELECTION USING GIBBS SAMPLING

A method of analysing response to selection using a Bayesian perspecti ve is presented. The following measures of response to selection were analysed: 1) total response in terms of the difference in additive gen etic means between last and first generations; 2) the slope (through t he origin) of the regression of mean additive genetic value on generat ion; 3) the linear regression slope of mean additive genetic value on generation. Inferences are based on marginal posterior distributions o f the above-defined measures of genetic response, and uncertainties ab out fixed effects and variance components are taken into account. The marginal posterior distributions were estimated using the Gibbs sample r. Two simulated data sets with heritability levels 0.2 and 0.5 having 5 cycles of selection were used to illustrate the method. Two analyse s were carried out for each data set, with partial data (generations 0 -2) and with the whole data. The Bayesian analysis differed from a tra ditional analysis based on best linear unbiased predictors (BLUP) with an animal model, when the amount of information in the data was small . Inferences about selection response were similar with both methods a t high heritability values and using all the data for the analysis. Th e Bayesian approach correctly assessed the degree of uncertainty assoc iated with insufficient information in the data. A Bayesian analysis u sing 2 different sets of prior distributions for the variance componen ts showed that inferences differed only when the relative amount of in formation contributed by the data was small.