Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection

The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subsets was used. Number of markers ranged from 1,200 to 5,925 and number of animals ranged from 1,200 to 5,865. Methods were also applied to real data comprising 3081 individuals genotyped for 45181 SNPs. Results from simulated data showed that the iterative solver was substantially faster than direct methods for larger numbers of markers. Use of a direct solver may allow for computing (co)variances of SNP effects. When applied to real data, performance of the iterative method varied substantially, depending on the level of ill-conditioning of the coefficient matrix. From results with real data, Gentleman-Givens rotations would be the method of choice in this particular application as it provided an exact solution within a fairly reasonable time frame (less than two hours). It would indeed be the preferred method whenever computer resources allow its use

Genetic relationship among reproductive traits in Nellore cattle

In order to achieve improvements in production efficiency in livestock, herds of high sexual precocity and good fertility are needed. These traits increase the availability of animals in herd, either for sale or selection, allowing both greater selective intensity and greater genetic progress. This study aimed at estimating genetic parameters for reproductive traits measured directly in females in order to verify whether they could be used as selection criteria for genetic improvement in Nellore cows, as well as estimating the genetic relationship among these traits and scrotal circumference (SC), the traditional selection criterion for sexual precocity in cattle. In addition to SC, stayability (STAY), number of calvings at 53 months (NC53) and heifers rebreeding (HR) were studied. The (co)variances and genetic parameters were estimated using Bayesian inference. STAY, NC53 and HR were analyzed assuming a threshold model, whereas SC was analyzed with a linear model. Heritability estimated for NC53 was 0.22, and this trait was strongly and positively correlated with STAY, meaning selection for NC53 would improve productive longevity of Nellore cows. Correlations estimated between HR and STAY (approximate to 0.97) and between HR and NC53 (approximate to 0.99) allow an improvement on HR rates if selection was applied to traits related to longevity. Genetic correlations among SC and female reproductive traits were positive but weak, suggesting the need to use reproductive traits directly measured in females in order to obtain greater improvements in sexual precocity and longevity.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Efeitos da Heterogeneidade de Variância Residual entre Grupos de Contemporâneos na Avaliação Genética de Bovinos de Corte Effects of Heterogeneity of Residual Variance among Contemporary Groups on Genetic Evaluation of Beef Cattle

O objetivo deste estudo foi investigar, por meio de dados simulados, o efeito da heterogeneidade de variância residual entre grupos de contemporâneos (GC) sobre as avaliações genéticas de bovinos de corte, e comparar o uso de uma avaliação genética ponderada (R<FONT FACE=Symbol>&sup1;</FONT>Isigmae²) em relação à avaliação que pressupõe homogeneidade de variância (R=Isigmae²). A característica estudada foi ganho de peso pós-desmame corrigido para 345 dias, sendo esta simulada com variância fenotípica de 300 kg² e herdabilidade igual a 0,4. A estrutura de um conjunto real de dados foi utilizada para fornecer os GC e os pais referentes às observações de cada animal. Cinco níveis de heterogeneidade de variância residual foram considerados de forma que os componentes de variância fossem, na média, iguais aos da situação de homogeneidade de variância. Na medida em que níveis mais acentuados de heterogeneidade de variância residual foram considerados, os animais foram selecionados dos GC com maior variabilidade, especialmente com pressão de seleção intensa. Em relação à consistência de predição, os produtos e as vacas tiveram seus valores genéticos preditos mais afetados pela heterogeneidade de variância residual do que os touros. O fator de ponderação utilizado reduziu, mas não eliminou o efeito da heterogeneidade de variância. As avaliações genéticas ponderadas apresentaram resultados iguais ou superiores àqueles obtidos pelas avaliações que assumiram homogeneidade de variância. Mesmo quando não necessário, o uso de avaliações ponderadas produziu resultados não inferiores às avaliações que assumiram homogeneidade de variância.<br>The objective of this study was to investigate, via simulated data, the effect of heterogeneity of residual variance among contemporary groups (CG) on genetic evaluation of beef cattle, and to compare a weighted genetic evaluation procedure (R<FONT FACE=Symbol>&sup1;</FONT>Isigmae²) with one that assumes homogeneity of variances (R = Isigmae²). Different data sets of postweaning weight gain, adjusted to 345 days, were simulated with and without heterogeneity of residual variance, using a phenotypic variance of 300 kg² and a true heritability of 0.4. A real data set was used to provide the CG and parents related to each animal observation. Results showed that, when high levels of heterogeneity of residual variance were considered, animals were selected from CG with higher variability, especially with intense selection. With respect to prediction consistency, non parent animals and cows had their predicted breeding values more affected by heterogeneity of residual variance than sires. The weighed factor used reduced, but did not eliminate, the effect of heterogeneity of residual variance. The results of weighted genetic evaluations were similar or superior to those from evaluations that assumed homogeneity of variances. Even when the variances were homogeneous, the weighed genetic evaluations yielded results that were not inferior than those from the usual evaluations, which assumed homogeneity of variances