Estimation of genetic parameters and breeding values in shrimp Fenneropenaeus chinensis using the REML/BLUP procedure

An analysis of a selection experiment was used to assess the impact of various animal model structures on REML estimates of variance components.The analyses were carried out based on 162 d body mass (BM) of 1 287 animals from 21 paternal half-sib groups of Fenneropenaeus chinensis.Estimated breeding values (EBV) of BM of all individuals were estimated using eight statistical models (A,AB,ABC,ABDC,ABMFC,ABMDC,ABFDC and ABMFDC) and BLUP (best linear unbiased prediction).These models were designed involving factors such as sex,spawn date as fixed effects,maternal genetic effects,full-sib family effects as random effects,mean BM of families at tagging and age at recording (covariate).The results demonstrate the importance of correct interpretation of effects in the data set,particularly those that can influence resemblance between relatives.The data structure and the particular model that was applied markedly influenced the magnitude of variance component estimates.Models based on few effects obtained upward biased estimates of additive genetic variance.The accuracy of genetic parameters and breeding value estimated by ABFDC model was higher than other models.The results imply that additive genetic direct value,full-sib family effects,and covariance effects besides sex and spawn date as fixed effects were very important for estimating genetic parameters and breeding value of body mass.This model had a heritability estimate of 162 d BM of 0.44.The comparison of the efficiency of selection based on breeding values or phenotypic value revealed great difference:average breeding value of the best 24 families selected by the 162 d BM breeding value and phenotype were 0.577 g and 0.366 g,respectively,representing a 36.57% higher efficiency in the former.In conclusion,selection based on breeding value was more effective than selection based on phenotypic value.Our results indicate that effects influencing the magnitude of estimates should be taken into account when estimating heritability and breeding values for BM.     

Covariance function diagnostics for spatial linear models

Case deletion diagnostics are developed for detecting observations that are influential in estimating the covariance function of a spatial random field. Diagnostics are developed within the context of universal kriging. Computational formulae are given that make the procedures feasible and the diagnostics are illustrated in an example.     

On a stronger-than-best property for best prediction

The minimum mean squared error (MMSE) criterion is a popular criterion for devising best predictors. In case of linear predictors, it has the advantage that no further distributional assumptions need to be made, other then about the first- and second-order moments. In the spatial and Earth sciences, it is the best linear unbiased predictor (BLUP) that is used most often. Despite the fact that in this case only the first- and second-order moments need to be known, one often still makes statements about the complete distribution, in particular when statistical testing is involved. For such cases, one can do better than the BLUP, as shown in Teunissen (J Geod. doi: 10.1007/s00190-007-0140-6, 2006), and thus devise predictors that have a smaller MMSE than the BLUP. Hence, these predictors are to be preferred over the BLUP, if one really values the MMSE-criterion. In the present contribution, we will show, however, that the BLUP has another optimality property than the MMSE-property, provided that the distribution is Gaussian. It will be shown that in the Gaussian case, the prediction error of the BLUP has the highest possible probability of all linear unbiased predictors of being bounded in the weighted squared norm sense. This is a stronger property than the often advertised MMSE-property of the BLUP.