Bayesian analysis of genetic change due to selection using Gibbs sampling

Summary - A method of analysing response to selection using a Bayesian perspective is presented. The following measures of response to selection were analysed: 1) total response in terms of the difference in additive genetic means between last and first generations; 2) the slope (through the origin) of the regression of mean additive genetic value on generation; 3) the linear regression slope of mean additive genetic value on generation. Inferences are based on marginal posterior distributions of the above-defined measures of genetic response, and uncertainties about fixed effects and variance components are taken into account. The marginal posterior distributions were estimated using the Gibbs sampler. Two simulated data sets with heritability levels 0.2 and 0.5 having 5 cycles of selection were used to illustrate the method. Two analyses were carried out for each data set, with partial data (generations 0-2) and with the whole data. The Bayesian analysis differed from a traditional 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 at high heritability values and using all the data for the analysis. The Bayesian approach correctly assessed the degree of uncertainty associated with insufficient information in the data. A Bayesian analysis using 2 different sets of prior distributions for the variance components showed that inferences differed only when the relative amount of information contributed by the data was small.

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