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The objective of this work was to evaluate the Nelore beef cattle, growth curve parameters using the Von Bertalanffy function in a nested Bayesian procedure that allowed estimation of the joint posterior distribution of growth curve parameters, their (co)variance components, and the environmental and additive genetic components affecting them. A hierarchical model was applied; each individual had a growth trajectory described by the nonlinear function, and each parameter of this function was considered to be affected by genetic and environmental effects that were described by an animal model. Random samples of the posterior distributions were drawn using Gibbs sampling and Metropolis-Hastings algorithms. The data set consisted of a total of 145,961 BW recorded from 15,386 animals. Even though the curve parameters were estimated for animals with few records, given that the information from related animals and the structure of systematic effects were considered in the curve fitting, all mature BW predicted were suitable. A large additive genetic variance for mature BW was observed. The parameter a of growth curves, which represents asymptotic adult BW, could be used as a selection criterion to control increases in adult BW when selecting for growth rate. The effect of maternal environment on growth was carried through to maturity and should be considered when evaluating adult BW. Other growth curve parameters showed small additive genetic and maternal effects. Mature BW and parameter k, related to the slope of the curve, presented a large, positive genetic correlation. The results indicated that selection for growth rate would increase adult BW without substantially changing the shape of the growth curve. Selection to change the slope of the growth curve without modifying adult BW would be inefficient because their genetic correlation is large. However, adult BW could be considered in a selection index with its corresponding economic weight to improve the overall efficiency of beef cattle production.

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To estimate the heritability for the probability that yearling heifers would become pregnant, we analyzed the records of 11,487 Nellore animals that participated in breeding seasons at three farms in the Brazilian states of São Paulo and Mato Grosso do Sul. All heifers were exposed to a bull at the age of about 14 mo. The probability of pregnancy was analyzed as a categorical trait, with a value of 1 (success) assigned to heifers that were diagnosed pregnant by rectal palpation about 60 d after the end of the breeding season of 90 d and a value of 0 (failure) assigned to those that were not pregnant at that time. The estimate of heritability, obtained by Method 9, was 0.57 with standard error of 0.01. The EPD was predicted using a maximum a posteriori threshold method and was expressed as deviations from 50% probability. The range in EPD was -24.50 to 24.55%, with a mean of 0.78% and a SD of 7.46%. We conclude that EPD for probability of pregnancy can be used to select heifers with a higher probability of being fertile. However, it is mainly recommended for the selection of bulls for the production of precocious daughters because the accuracy of prediction is higher for bulls, depending on their number of daughters.