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Doctoral Thesis
Full name
Alfredo Ribeiro de Freitas
Knowledge Area
Date of Defense
Piracicaba, 1991
Title in Portuguese
Comparação de métodos para estimação de componentes de variância e parâmetros afins de múltiplos caracteres em bovinos
Keywords in Portuguese
Abstract in Portuguese
O trabalho objetivou comparar os métodos: Variância Quadràtica Mínima não Viciada, MIVQUE(o), Máxima Verossimilhança, (ML) e ML Restrita (REML), quanto aos aspectos computacionais, estimativas de variâncias genéticas (gii), residuais (rii) e herdabilidade ('H POT.2'), na análise univariada (ANOVA) do peso à desmama e aos doze meses em bovinos. O método da ML, da REML e um método iterativo de HENDERSON (IHSM), com a inclusão da matriz de parentesco entre touros, foram avaliados em modelo multivariado (MANOVA). Os resultados de ambas análises foram comparados aos obtidos pelo método 3 (h3) na ANOVA. ML e REML convergiram com o mesmo número de iterações, porém, o REML foi mais exigente computacionalmente. Os valores foram os mesmos em todos métodos. Comparando ao ML e REML, MIVQUE (o) e h3 subestimaram g ii e r ii em ambas análises. Estes resultados podem ser atribuídos a deficiências destes: o não controle de vícios devidos a seleção, impossibilidade de uso de carácteres múltiplos e do parentesco entre touros, limitando seus usos no melhoramento animal. O metodo IHSM, proporcionou valores maiores para g ii e r ii, comparado aos obtidos por ML e REML, porém, as suas boas características e facilidade de uso, justificam investigações adicionais. Os métodos ML e REML proporcionaram estimativas semelhantes na MANOVA, mostrando que variâncias e covariâncias apropriadas foram estimadas
Title in English
Comparison of methods for estimating components of variance and related parameters of multiple traits in cattle
Keywords in English

Abstract in English
The objective of this study was to evaluate the efficiency of the approximate Minimum Variance Quadratic Unbiased Estimation (MIVQUE(o)), Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML) estimation variance components methods, considering their computational aspects, genetic (gii) and residual (rii) variance components estimates and other genetic and phenotypic parameters estimates, from univariate analysis of variance (ANOVA), for body weights at weaning (Y1) and at 12 months of age. The ML and REML methods and another approximate MIVQUE method (IHSM) were also evaluated with Y1 and Y2 in a multitrait model (MANOVA) including the numerator relationship matrix among sires. Results of both analyses were compared to those obtained by method 3 (H3) of HENDERSON (1963), traditionally used in the estimation of genetic parameters in Brazil. The body weight data were from 526 females and 599 males Canchim calves, born at the Canchim farm, in São Carlos, State of São Paulo. The mathematic model included, in addition to the mean, the fixed effects of sex, year of birth, season of birth, year x season interaction and age of dam and the random effects of sires. The relationship among sires ranged from 0.0 to 50.0%, with a mean of 1.9%, and the progeny families were of paternal half-sibs. Considering the computational aspects, the ML and REML methods converged ln the ANOVA with seven and six iterations, respectively, while in the MANOVA, the IHSM, ML and REML methods converged with 13, 40 and 40 iterations, respectively. The rg and h2 estimates converged faster than the variance-covariance estimates, and this property is important for checking the convergence or process at each iteration. The higher estimate of gii for Y1 in the ANOVA was obtained by the REML method, followed in decreasing order, by those obtained by the ML, H3 and MIVOUE(o) methods, while for Y2, decreasing gii values were furnished by REML, H3, ML and MIVOUE(o) methods. With the MANOVA, for both traits, the higher gii estimate was obtained by IHSM, followed by those from REML and ML. Heritability (h2) estimates obtained with the ANOVA, based on intra-class correlation among paternal half-sibs, by the MIVOUE(o), H3, ML and REML methods were 0.49 ± 0.10, 0.66 ± 0.13, 0.74 ± 0.15 and 0.78 ± 0.16 for Y1 and 0.28 ± 0.11, 0.39 ± 0.10 ± 0.38 ± 0.10 and 0.43 ± 0.14 for Y2, respectively. With the MANOVA analyses, h2 values were 0.80 ± 0.15, 0.72 ± 0.15 and 0.69 ± 0.14 for Y1 and 0.48 ± 0.12, 0.34 ± 0.11 and 0.37 ± 0.10 for Y2, as obtained by the IHSM, ML and REML methods, respectively. The rg estimates were close to 1.0 in all cases, showing that the same group of genes influences the two variables: the phenotypic correlations (r̂F) were close to 0.72, except that obtained by the REML method in the MANOVA (r̂F = 0.87), and the residual correlations were the same in all the cases (0.68). Environmental correlations obtained by MIVOUE(o), H3, ML and REML with the ANOVA analyses, were 0.62, 0.51, 0.34 and 0.29, respectively. Since the rii estimates for each trait were similar for all methods, this range in the values of r̂E reflects the influence of the underestimated gii values obtained by the ML and REML. With the MANOVA, the r̂E values obtained from IHSM, ML and REML, were 0.45, 0.45 and 0.68, respectively. ln both analyses, the ratio r̂ii / ĝii was close to 4.5 for Y1 and Y2, explaining the lower h2 estimates obtained for Y2 as compared to those that for Y1. These results showed that uncontrollable environmental variations such as weight losses and/or absence of weight gains from weaning to 12 months of age, affected Y2 more intensively, masking possible genetic differences among the individuals. The IHSM method produced overestimated values of gii, rii and h2 as compared to the others methods. Despite its iterative nature, the IHSM method demanded less computational labor and the possibility of working with multiple traits, the control of bias due to selection and the use of relationships among sires, justify additional investigations before recommendation for practical use. With the ANOVA and, more emphasized, with the MANOVA, the MIVOUE(o) and H3 methods estimated lower values of rg and h2 as compared to the ones obtained by the ML and REML methods. These results showed that deficiencies of the H3 method like the use of explicit solution, that generally do not maximize the Iikelihood of the parameters, the uncontrolled bias due to selection and the impossibility of handling multiple traits and the relationship among sires, limits its use in animal breeding problems. The MIVOUE(o) method, besides the deficiencies of the H3 method, uses pseudo-variances rather than true variances, and its efficiency reduces as the ratio rii / gii gets away from zero. With the MANOVA and the inclusion of the numerator relationship matrix among sires, the ML and REML methods produced similar results for the genetic parameters, disappearing the differences between them observed with the ANOVA. This showed that, with the multivariate analysis, appropriate variances and covariances are known, or at best, well estimated. Although the ML and REML are computationally demanding methods, there are several linear models and programming techniques that reduce the computational labor associated with variance components algorithims. So, hopefully, these two methods, including multiple traits and the relationship among the individuals, may be spreadly used ln animal breeding in our Country.
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