Behaviour of the additive finite locus model

A finite locus model to estimate additive variance and the breeding values was implemented using Gibbs sampling. Four different distributions for the size of the gene effects across the loci were considered: i) uniform with loci of different effects, ii) uniform with all loci having equal effects, iii) exponential, and iv) normal. Stochastic simulation was used to study the influence of the number of loci and the distribution of their effect assumed in the model analysis. The assumption of loci with different and uniformly distributed effects resulted in an increase in the estimate of the additive variance according to the number of loci assumed in the model of analysis, causing biases in the estimated breeding values. When the gene effects were assumed to be exponentially distributed, the estimate of the additive variance was still dependent on the number of loci assumed in the model of analysis, but this influence was much less. When assuming that all the loci have the same gene effects or when they were normally distributed, the additive variance estimate was the same regardless of the number of loci assumed in the model of analysis. The estimates were not significantly different from either the true simulated values or from those obtained when using the standard mixed model approach where an infinitesimal model is assumed. The results indicate that if the number of loci has to be assumed a priori, the most useful finite locus models are those assuming loci with equal effects or normally distributed effects. (C) Inra/Elsevier, Paris.