Maternal animal model with correlation between maternal environmental effects of related dams

A procedure to take into account the nongenetic relationship between maternal effects in adjacent generations is presented. It considers a correlation between maternal environments provided by a dam and its daughters (λ). The dispersion structure of the maternal animal model was modified to include a correlation matrix (E) that relates the maternal permanent environmental effects. The structures of the E matrix and its inverse (E -1 ) are described. Both matrices are completely defined by the correlation coefficient λ. An algorithm to compute these matrices from pedigree information was also developed. Furthermore, a Bayesian analysis of this model including the λ parameter was developed using Gibbs sampling, with Metropolis steps for the nonstandard conditional distributions. With simulated data, the proposed model reduced the bias in all estimates of dispersion parameters when an antagonism between the maternal effects received by a daughter and its future maternal environment existed. This model also provides an estimate of the environmental relationship between the maternal effects of dams and daughters by the λ parameter. The same Bayesian analysis was also carried out with weaning weight data of the Bruna dels Pirineus breed. The posterior means (standard deviation) of (co)variance ratios were .214 (.081) for direct heritability (h 2d ), .107 (.033) for maternal heritability (h 2m ), .047 (.020) for the proportion of variance due to maternal environmental effects (c 2m ), and -.034 (.043) for the genetic correlation between direct and maternal effects (r dm ). The posterior mean of λ parameter was -.190, and 76% of its marginal posterior distribution took negative values. As occurred with simulated data, considering the maternal environmental correlation in the analysis implied higher h 2m estimates, lower c 2m and h 2m estimates, and less negative values for the marginal posterior distribution of r dm . These results were considered as evidence of the environmental antagonism between maternal effects provided by a dam and its daughters to weaning weight of their progeny in the Bruna dels Pirineus breed.