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

A procedure to take into account the nongenetic relationship between matern al effects in adjacent generations is presented. It considers a correlation between maternal environments provided by a dam and its daughters (lambda) . The dispersion structure of the maternal animal model was modified to inc lude a correlation matrix (E) that relates the maternal permanent environme ntal effects. The structures of the E matrix and its inverse (E-1) are desc ribed. Both matrices are completely defined by the correlation coefficient lambda. An algorithm to compute these matrices from pedigree information wa s also developed. Furthermore, a Bayesian analysis of this model including the lambda parameter was developed using Gibbs sampling, with Metropolis st eps 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 estima te of the environment relationship between the maternal effects of dams and daughters by the lambda parameter. The same Bayesian analysis was also car ried out with weaning weight data of the Bruna dels Pirineus breed. The pos terior means (standard deviation) of(co)variance ratios were .214 (.081) fo r direct heritability (h(d)(2)), .107 (.033) for maternal heritability (h(m )(2)), .047 (.020) for the proportion of variance due to maternal environme ntal effects (C-m(2)), and -.034 (.043)for the genetic correlation between direct and maternal effects (Tdm) The posterior mean of lambda parameter wa s -.190, and 76% of its marginal posterior distribution took negative value s. As occurred with simulated data, considering the maternal environmental correlation in the analysis implied higher h(m)(2) estimates, lower c(m)(2) and h(d)(2) estimates, and less negative values for the marginal posterior distribution of r(dm). These results were considered as evidence of the en vironmental antagonism between maternal effects provided by a dam and its d aughters to weaning weight of their progeny in the Bruna dels Pirineus bree d.