Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

Variância intrapessoal para ajuste da distribuição de nutrientes em estudos epidemiológicos

O objetivo do estudo foi apresentar a fração da variância intrapessoal para ajuste da distribuição de nutrientes de adultos e idosos. Utilizaram-se dados de inquérito populacional com amostra representativa (n = 511) de indivíduos com 19 anos ou mais do município de São Paulo, SP, em 2007. A fração da variância intrapessoal foi obtida pelo método proposto pela Iowa State University. Observaram-se diferenças nas frações das variâncias intrapessoais de nutrientes segundo sexo. Esses valores devem ser utilizados para ajustar a distribuição da ingestão de nutrientes, pois sua não utilização pode resultar em viés na análise e interpretação de dados.

Evaluating gene by sex and age interactions on cardiovascular risk factors in Brazilian families

Background: In family studies, it is important to evaluate the impact of genes and environmental factors on traits of interest. In particular, the relative influences of both genes and the environment may vary in different strata of the population of interest, such as young and old individuals, or males and females. Methods: In this paper, extensions of the variance components model are used to evaluate heterogeneity in the genetic and environmental variance components due to the effects of sex and age (the cutoff between young and old was 43 yrs). The data analyzed were from 81 Brazilian families (1,675 individuals) of the Baependi Family Heart Study. Results: The models allowing for heterogeneity of variance components by sex suggest that genetic and environmental variances are not different in males and females for diastolic blood pressure, LDL-cholesterol, and HDL-cholesterol, independent of the covariates included in the models. However, for systolic blood pressure, fasting glucose and triglycerides, the evidence for heterogeneity was dependent on the covariates in the model. For instance, in the presence of sex and age covariates, heterogeneity in the genetic variance component was suggested for fasting glucose. But, for systolic blood pressure, there was no evidence of heterogeneity in any of the two variance components. Except for the LDL-cholesterol, models allowing for heterogeneity by age provide evidence of heterogeneity in genetic variance for triglycerides and systolic and diastolic blood pressure. There was evidence of heterogeneity in environmental variance in fasting glucose and HDL-cholesterol. Conclusions: Our results suggest that heterogeneity in trait variances should not be ignored in the design and analyses of gene-finding studies involving these traits, as it may generate additional information about gene effects, and allow the investigation of more sophisticated models such as the model including sex-specific oligogenic variance components.

Genetic parameters for pre-weaning traits in Braunvieh cattle

The objective of this study was to estimate genetic parameters for pre-weaning traits of Braunvieh cattle raised under tropical conditions in Brazil. The weight and weight gain parameters were birth weight (BW, N = 9955), weight at 120 days of age (W120, N = 5901), weaning weight at 205 days (WW, N = 6970), weight gain from birth to 205 days (GAIN205, N = 6013), weight gain from birth to 120 days (GAIN120, N = 5135), and weight gain from 120 to 205 days (GAIN85, N = 4482). Variance components were estimated using the animal model with the MTDFREML software. The relationship matrix included 35,188 animals; phenotypic measures were available for 18,688. Direct and maternal heritability increased from birth to weaning, with estimates of 0.23 +/- 0.037, 0.25 +/- 0.050, 0.41 +/- 0.059 for direct heritability for BW, W120 and WW, respectively, 0.08 +/- 0.012, 0.15 +/- 0.032, 0.22 +/- 0.036 for maternal genetic effects, and 0.18, 0.14 and 0.16 for total heritability estimates. For pre-weaning gains, estimates of heritability were 0.36 +/- 0.059, 0.30 +/- 0.059, 0.12 +/- 0.035 for direct genetic effects of the traits GAIN205, GAIN120 and GAIN85, respectively, 0.23 +/- 0.038, 0.17 +/- 0.037, 0.03 +/- 0.029 for estimates of maternal heritability, and 0.12, 0.13, 0.16 for total heritability, respectively. Genetic correlations between weights were greater between measures taken at shorter intervals. This information can be used to optimize the design of programs for genetic improvement of Braunvieh cattle raised under tropical conditions.

Genetic parameters for productive life traits and reproductive efficiency traits at 6 years in Nellore cattle

The objective of the present study was to estimate (co)variance components for length of productive life (LPL) and some alternative reproductive traits of 6-year-old Nellore cattle. The data set contained 57,410 records for age at first calving from Nellore females and was edited to remove animal records with uncertain paternity and cows with just one piece of calving information. Only animals with age at first calving ranging from 23 to 48 months and calving intervals between 11 and 24 months were kept for analysis. LPL and life production ( LP) were used to describe productive life. LPL was defined as the number of months a cow was kept in the herd until she was 6 years old, given that she was alive at first calving and LP was defined as total number of calves in that time. Four traits were used to describe reproductive traits: two breeding efficiencies on original scale were estimated using Wilcox and Tomar functions (BEW and BET, respectively), and two breeding efficiencies transformed (ASBEW and ASBET, respectively), using the function [arcsine (square root (BEi/100))]. Estimates of heritability for measures of LPL and LP were low and ranged from 0.04 to 0.05. Estimates of heritability for breeding efficiencies on original and transformed scales oscillated from 0.18 to 0.32. Estimates of genetic correlations ranged from -0.57 to 0.79 for LPL and other traits and from 0.28 to 0.63 for LP and other traits.

Additive genetic relationship of longevity with fertility and production traits in Nellore cattle based on bivariate models

Survival or longevity is an economically important trait in beef cattle. The main inconvenience for its inclusion in selection criteria is delayed recording of phenotypic data and the high computational demand for including survival in proportional hazard models. Thus, identification of a longevity-correlated trait that could be recorded early in life would be very useful for selection purposes. We estimated the genetic relationship of survival with productive and reproductive traits in Nellore cattle, including weaning weight (WW), post-weaning growth (PWG), muscularity (MUSC), scrotal circumference at 18 months (SC18), and heifer pregnancy (HP). Survival was measured in discrete time intervals and modeled through a sequential threshold model. Five independent bivariate Bayesian analyses were performed, accounting for cow survival and the five productive and reproductive traits. Posterior mean estimates for heritability (standard deviation in parentheses) were 0.55 (0.01) for WW, 0.25 (0.01) for PWG, 0.23 (0.01) for MUSC, and 0.48 (0.01) for SC18. The posterior mean estimates (95% confidence interval in parentheses) for the genetic correlation with survival were 0.16 (0.13-0.19), 0.30 (0.25-0.34), 0.31 (0.25-0.36), 0.07 (0.02-0.12), and 0.82 (0.78-0.86) for WW, PWG, MUSC, SC18, and HP, respectively. Based on the high genetic correlation and heritability (0.54) posterior mean estimates for HP, the expected progeny difference for HP can be used to select bulls for longevity, as well as for post-weaning gain and muscle score.

Genetic parameters for postweaning traits in Braunvieh cattle

Genetic parameters for traits related to postweaning growth in Braunvieh cattle, reared under tropical and sub-tropical conditions in Brazil, were studied. Weight traits were weight at 365 days of age (W365, N = 4055), at 450 days (W450, N = 3453), and at 550 days (W550, N = 1946), while weight gains were gain from weaning to 365 days of age (WGW365, N = 3060), from weaning to 450 days (WGW450, N = 2764), from weaning to 550 days (WGW550, N = 1531), from 365 to 550 days of age (WG365550, N = 1528), from 365 to 450 days (WG365450, N = 2401), and from 450 to 550 days (WG450550, N = 1563). A full animal model was used for estimating the variance components, using the MTDFREML software. The dataset contained 18,688 animals with phenotypic measures and 35,188 animals in the relationship matrix. Heritability estimates for postweaning weights decreased with age. For W365, W450 and W550, respectively, the direct heritability estimates were 0.29 +/- 0.061, 0.25 +/- 0.057, 0.16 +/- 0.060, maternal heritability was 0.20 +/- 0.035, 0.18 +/- 0.035, 0.13 +/- 0.052, and total heritability was 0.30, 0.35, 0.26. In this breed, maternal influence was found to be important up to 550 days of age. The greater genetic correlations between weights were observed for weights measured at shorter intervals. A large environmental effect was observed for weight gain between weaning and 550 days; this effect was greater for the gains between 365 and 550 days.

Comparison of different nonlinear functions to describe Nelore cattle growth

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co) variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand`s check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co) variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.

Models for genetic evaluation of Nelore cattle mature body weight

Records of 18,770 Nelore animals, born from 1975 to 2002, in 8 herds participating in the Nelore Cattle Breeding Program, were analyzed to estimate genetic parameters for mature BW. The mature BW were analyzed as a single BW taken closest to 4.5 yr of age for each cow in the data file, considering BW starting from 2 (W2Y_S), 3 (W3Y_S), or 4 (W4Y_S) yr of age or as repeated records, including all BW starting from 2 (W2Y_R), 3 (W3Y_R), or 4 (W4Y_R) yr of age. The variance components were estimated by restricted maximum likelihood, fitting univariate and bivariate animal models, including weaning weight. The heritability estimates were 0.29, 0.34, 0.36, 0.41, 0.44, and 0.46 for W2Y_S, W3Y_S, W4Y_S, W2Y_R, W3Y_R, and W4Y_R, respectively. The repeatability estimates for W2Y_R, W3Y_R, and W4Y_R were 0.59, 0.64, and 0.72, respectively. Larger accuracy values associated with the EBV were obtained in the repeated records models. The results indicated the bivariate repeated records model as the most appropriate for analyzing mature BW.

Assessment of inbreeding depression in a Guzerat dairy herd: Effects of individual increase in inbreeding coefficients on production and reproduction

Influences of inbreeding on daily milk yield (DMY), age at first calving (AFC), and calving intervals (CI) were determined on a highly inbred zebu dairy subpopulation of the Guzerat breed. Variance components were estimated using animal models in single-trait analyses. Two approaches were employed to estimate inbreeding depression: using individual increase in inbreeding coefficients or using inbreeding coefficients as possible covariates included in the statistical models. The pedigree file included 9,915 animals, of which 9,055 were inbred, with an average inbreeding coefficient of 15.2%. The maximum inbreeding coefficient observed was 49.45%, and the average inbreeding for the females still in the herd during the analysis was 26.42%. Heritability estimates were 0.27 for DMY and 0.38 for AFC. The genetic variance ratio estimated with the random regression model for CI ranged around 0.10. Increased inbreeding caused poorer performance in DMY, AFC, and CI. However, some of the cows with the highest milk yield were among the highly inbred animals in this subpopulation. Individual increase in inbreeding used as a covariate in the statistical models accounted for inbreeding depression while avoiding overestimation that may result when fitting inbreeding coefficients.

Testicular traits as selection criteria for young Nellore bulls

The objective of this study was to evaluate the possible use of biometric testicular traits as selection criteria for young Nellore bulls using Bayesian inference to estimate heritability coefficients and genetic correlations. Multitrait analysis was performed including 17,211 records of scrotal circumference obtained during andrological assessment (SCAND) and 15,313 records of testicular volume and shape. In addition, 50,809 records of scrotal circumference at 18 mo (SC18), used as an anchor trait, were analyzed. The (co) variance components and breeding values were estimated by Gibbs sampling using the Gibbs2F90 program under an animal model that included contemporary groups as fixed effects, age of the animal as a linear covariate, and direct additive genetic effects as random effects. Heritabilities of 0.42, 0.43, 0.31, 0.20, 0.04, 0.16, 0.15, and 0.10 were obtained for SC18, SCAND, testicular volume, testicular shape, minor defects, major defects, total defects, and satisfactory andrological evaluation, respectively. The genetic correlations between SC18 and the other traits were 0.84 (SCAND), 0.75 (testicular shape), 0.44 (testicular volume), -0.23 (minor defects), -0.16 (major defects), -0.24 (total defects), and 0.56 (satisfactory andrological evaluation). Genetic correlations of 0.94 and 0.52 were obtained between SCAND and testicular volume and shape, respectively, and of 0.52 between testicular volume and testicular shape. In addition to favorable genetic parameter estimates, SC18 was found to be the most advantageous testicular trait due to its easy measurement before andrological assessment of the animals, even though the utilization of biometric testicular traits as selection criteria was also found to be possible. In conclusion, SC18 and biometric testicular traits can be adopted as a selection criterion to improve the fertility of young Nellore bulls.

Performance of balanced two-stage empirical predictors of realized cluster latent values from finite populations: A simulation study

Predictors of random effects are usually based on the popular mixed effects (ME) model developed under the assumption that the sample is obtained from a conceptual infinite population; such predictors are employed even when the actual population is finite. Two alternatives that incorporate the finite nature of the population are obtained from the superpopulation model proposed by Scott and Smith (1969. Estimation in multi-stage surveys. J. Amer. Statist. Assoc. 64, 830-840) or from the finite population mixed model recently proposed by Stanek and Singer (2004. Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 1119-1130). Predictors derived under the latter model with the additional assumptions that all variance components are known and that within-cluster variances are equal have smaller mean squared error (MSE) than the competitors based on either the ME or Scott and Smith`s models. As population variances are rarely known, we propose method of moment estimators to obtain empirical predictors and conduct a simulation study to evaluate their performance. The results suggest that the finite population mixed model empirical predictor is more stable than its competitors since, in terms of MSE, it is either the best or the second best and when second best, its performance lies within acceptable limits. When both cluster and unit intra-class correlation coefficients are very high (e.g., 0.95 or more), the performance of the empirical predictors derived under the three models is similar. (c) 2007 Elsevier B.V. All rights reserved.

QTL mapping for yield components in a tropical maize population using microsatellite markers

QTL mapping provides usefull information for breeding programs since it allows the estimation of genomic locations and genetic effects of chromossomal regions related to the expression of quantitative traits. The objective of this study was to map QTL related to several agronomic important traits associated with grain yield: ear weight (EW), prolificacy (PROL), ear number (NE), ear length (EL) and diameter (ED), number of rows on the ear (NRE) and number of kernels per row on the ear (NKPR). Four hundred F-2:3 tropical maize progenies were evaluated in five environments in Piracicaba, Sao Paulo, Brazil. The genetic map was previously estimated and had 117 microssatelite loci with average distance of 14 cM. Data was analysed using Composite Interval Mapping for each trait. Thirty six QTL were mapped and related to the expression of EW (2), PROL (3), NE (2), EL (5), ED (5), NRE (10), NKPR (5). Few QTL were mapped since there was high GxE interaction. Traits EW, PROL and EN showed high genetic correlation with grain yield and several QTL mapped to similar genomic regions, which could cause the observed correlation. However, further analysis using apropriate statistical models are required to separate linked versus pleiotropic QTL. Five QTL (named Ew1, Ne1, Ed3, Nre3 and Nre10) had high genetic effects, explaining from 10.8% (Nre3) to 16.9% (Nre10) of the phenotypic variance, and could be considered in further studies.

Validation of the Deardorff model for estimating energy balance components for a sugarcane crop

The quantification of the available energy in the environment is important because it determines photosynthesis, evapotranspiration and, therefore, the final yield of crops. Instruments for measuring the energy balance are costly and indirect estimation alternatives are desirable. This study assessed the Deardorff's model performance during a cycle of a sugarcane crop in Piracicaba, State of São Paulo, Brazil, in comparison to the aerodynamic method. This mechanistic model simulates the energy fluxes (sensible, latent heat and net radiation) at three levels (atmosphere, canopy and soil) using only air temperature, relative humidity and wind speed measured at a reference level above the canopy, crop leaf area index, and some pre-calibrated parameters (canopy albedo, soil emissivity, atmospheric transmissivity and hydrological characteristics of the soil). The analysis was made for different time scales, insolation conditions and seasons (spring, summer and autumn). Analyzing all data of 15 minute intervals, the model presented good performance for net radiation simulation in different insolations and seasons. The latent heat flux in the atmosphere and the sensible heat flux in the atmosphere did not present differences in comparison to data from the aerodynamic method during the autumn. The sensible heat flux in the soil was poorly simulated by the model due to the poor performance of the soil water balance method. The Deardorff's model improved in general the flux simulations in comparison to the aerodynamic method when more insolation was available in the environment.

Boosting the suppressive effects of Ascaris suum components in IFN-γ-deficient mice

High molecular weight components from Ascaris suum extract suppress ovalbumin-specific immunity in mice. In IFN-γ-deficient mice, ovalbumin-specific delayed-type hypersensitivity reactions are more strongly downregulated by these suppressive components. Here, the cellularity of the delayed-type hypersensitivity reaction in IFN-γ-deficient mice and the increased downregulation induced by Ascaris suum components were analyzed. IL-12p40-dependent neutrophilic influx was predominant. Suboptimal doses of the suppressive fraction from this nematode completely inhibited the hypersensitivity reaction, thus indicating intensification of the immunosuppression under conditions of intense recruitment of IFN-γ-independent neutrophils.