118 DHGLMF90: A software tool using double hierarchical generalized linear models for estimating the genetic heterogeneity of residual variance

Abstract In animal breeding, there is a growing interest in selecting animals that exhibit uniform responses to environmental conditions, aiming for product consistency as a desirable breeding objective. This could be achieved by modeling heteroskedastic residuals when estimating breeding values through a hierarchical single-trait model that includes a mean and dispersion part. The latter could be influenced by genetic and non-genetic features. Bayesian methods can estimate heteroskedastic residuals using the Metropolis-Hastings algorithm, which is a slow and inefficient approach. Double hierarchical generalized linear models (DHGLM) provide a faster alternative to Bayesian methods. This study aimed to develop software named DHGLMF90 to implement DHGLM using a highly efficient algorithm to accurately estimate heterogeneous residual variances and breeding values, particularly suited for handling large datasets. We improved the reweighted least squares algorithm (IRWLS) to enhance convergence properties compared with prior implementations. IRWLS iteratively computes variance components and leverages them for a bivariate model, covering both the mean and dispersion part of the original model. In DHGLMF90, variance component estimation is performed using REML through BLUPF90+. The software was tested using both simulated and real datasets, the latter from previous studies. Additionally, the simulations were replicated to ensure a comprehensive evaluation of the DHGLMF90 performance. Results indicated that, in most cases, there were no significant differences in estimation compared with results obtained from previous studies. DHGLMF90 converged in order of magnitude faster than Bayesian methods. Future developments will include analyzing datasets with genomic information and multiple-trait models.