Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

Genotype x environment interaction for age at first calving in Brazilian and Colombian Holsteins

The objective was to determine whether there is a genotype x environment interaction for age at first calving (AFC) in Holstein cattle in Brazil and Colombia. Data included 51,239 and 25,569 first-lactation records from Brazil and Colombia, respectively. Of 4230 sires in the data, 530 were North American sires used in both countries. Analyses were done using the REML bi-trait animal model, and AFC was considered as a distinct characteristic in each country. Fixed effects of contemporary group (herd-calving year), sire genetic group, and cow genetic group, and random effects of animal and residual variation were included in the model. Average AFC in Brazil and Colombia were 29.5 ± 4.0 and 32.1 ± 3.5 mo, respectively. Additive and residual genetic components and heritability coefficient for AFC in Brazil were 2.21 mo 2, 9.41 mo 2, and 0.19, respectively, whereas for Colombia, they were 1.02 mo 2, 6.84 mo 2, and 0.13, respectively. The genetic correlation of AFC between Brazil and Colombia was 0.78, indicating differences in ranking of sires consistent with a genotype x environment interaction. Therefore, in countries with differing environments, progeny of Holstein sires may calve at relatively younger or older ages compared with contemporary herdmates in one environment versus another.

Tendências genéticas para características relacionadas à velocidade de crescimento em bovinos nelore na região nordeste do brasil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Correlações genéticas de características de tamanho corporal e condição corporal com características de eficiência produtiva de fêmeas da raça Canchim

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interacción genotipo x ambiente sobre el peso al destete de bovinos nelore en Brasil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Evaluación genética de búfalos de la raza Murrah para la producción de leche en el día de control y a los 305 días de lactancia

There were analyzed 4757 complete lactations of the Murrah breed, daughters of 187 bulls, with the goal of verifying the viability upon employing the test-day (PDLC), on substitution of the milk yield at 305th day of lactation (PL305), in the genetic evaluations. The components of variance for the PDLC1 to PDLC9 and for the PL305 were estimated in uni-traits analysis according to maximum restricted likelihood method. The used model included the genetic direct additive random effects, of residual and permanent environment. There were considered as fixed effects, the contemporary group and the number of milkings and the age of the cow at the moment of parity co-variable (quadratic and linear effect). The contemporary groups were constituted by the herd-year-month of control for the PDLC and by herd-year-epoch of parity for PL305. The estimates of heritability for the PDLC and PL305 were 0.12 to 0.23 and 0.22, respectively. The correlations of order of the predicted genetic values for the 187 bulls, obtained between the PDLC and the PL305, were from moderate to high, varying from 67.74 to 83.12. From the minimum selection of the 10% of the best bulls relating to the predicted genetic value for the PL305, the coincidence among the classification of these animals was over 68%, when evaluated by the PDLC3,PDLC4,PDLC5 and PDLC6. Upon selecting the 5% of the best animals that coincidence presented a lower value.

Buffalo milk production in brazil and colombia: Genotype by environment interaction

The objective of this study was to determine whether there is a genotype by environment interaction (GxE) for dairy buffaloes in Brazil and Colombia. The (co)variance components were estimated by using a bi-trait repeatability animal model with the REML method. Each trait consisted in the milk yield obtained in both countries. Contemporary group (herd, year and season of parity) and age at parity (linear and quadratic covariate) fixed effects, along with the additive genetic, permanent environment, and the residual random effects were included in the model. Genetic, permanent environmental and residual variance and heritabilities were different for both countries. The genetic correlations for milk yield between Brazil and Colombia were low (between 0.10 and 0.13), indicating a GxE interaction between both countries. Knowing that this interaction influences the genetic progress of buffalo populations in Brazil and Colombia, we recommend choosing sires tested in the country they will be used, along with conducting joint genetic evaluations that consider GxE interaction effects.

Test-day model for milk yield of dairy buffaloes in colombia

The test-day model is the preferred method for genetic evaluations in dairy cattle. For this study, 28372 test-day records of 1220 lactations from 1997 to 2009 were used. The (co)variance components for milk in test-day were estimated using a Uni and multiple-traits repeated animal model with the Restricted Maximum Likelihood method (REML). The Contemporary Group (herd, year, and season of parity) and the age of parity (linear and quadratic) fixed effects, and the additive genetic, permanent environmental, and residual random effects were included in the model. The heritabilities ranged between 0.06 and 0.45 during lactation. The genetic correlations were greater than 0.93. In conclusion, the test-day model is appropriate for the genetic evaluation of dairy buffaloes in Colombia.

Genotype by environment interaction in different birth seasons for weight at 240, 365 and 450 days of age in Tabapuã cattle

The objective of this study was to evaluate the effect of genotype by environment interaction (GEI) on the weight of Tabapuã cattle at 240 (W240), 365 (W365) and 450 (W450) days of age. In total, 35,732 records of 8,458 Tabapuã animalswhich were born in the state of Bahia, Brazil, from 1975 to 2001, from 167 sires and 3,707 dams, were used. Two birth seasons were tested as for the environment effect: the dry (D) and rainy (R) ones. The covariance components were obtainedby a multiple-trait analysis using Bayesian inference, in which each trait was considered as being different in each season. Covariance components were estimated by software gibbs2f90. As for W240, the model was comprised of contemporary groups and cow age (in classes) as fixed effects; animal and maternal genetic additive, maternal permanent environmental and residual were considered as random effects. Concerning W365 and W450, the model included only the contemporary aged cow groups as fixed effects and the genetic additive and residual effects of the animal as the random ones. The GEI was assessed considering the genetic correlation, in which values below 0.80 indicated the presence of GEI. Regarding W365 and W450, the GEI was found in both seasons. As for post-weaning weight (W240), the effect of such interaction was not observed. ©2012 Sociedade Brasileira de Zootecnia.

Genetic correlations between mature cow weight and productive and reproductive traits in Nellore cattle

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Meat quality of young Nellore bulls with low and high residual feed intake

Fifty-nine Nellore bulls from low and high residual feed intake (RFI) levels were studied with the objective of evaluating meat quality traits. Animals were slaughtered when ultrasound-measured backfat thickness reached 4. mm, and samples of Longissimus were collected. A mixed model including RFI as fixed effect and herd and diet as random effects was used, and least square means were compared by t-test. More efficient animals consumed 0.730. kg dry matter/day less than less efficient animals, with similar performance. No significant differences in carcass weight, prime meat cuts proportion, chemical composition, pH, sarcomere length, or color were observed between RFI groups. Shear force, myofibrillar fragmentation index and soluble collagen content were influenced by RFI, with a higher shear force and soluble collagen content and a lower fragmentation index in low RFI animals. Feedlot-finished low RFI young Nellore bulls more efficiently convert feed into meat, presenting carcasses within quality standards. © 2012 Elsevier Ltd.

Principal components and factor analytic models for birth to mature weights in Nellore cattle

A total of 61,528 weight records from 22,246 Nellore animals born between 1984 and 2002 were used to compare different multiple-trait analysis methods for birth to mature weights. The following models were used: standard multivarite model (MV), five reduced-rank models fitting the first 1, 2, 3, 4 and 5 genetic principal components, and five models using factor analysis with 1, 2, 3, 4 and 5 factors. Direct additive genetic random effects and residual effects were included in all models. In addition, maternal genetic and maternal permanent environmental effects were included as random effects for birth and weaning weight. The models included contemporary group as fixed effect and age of animal at recording (except for birth weight) and age of dam at calving as linear and quadratic effects (for birth weight and weaning weight). The maternal genetic, maternal permanent environmental and residual (co)variance matrices were assumed to be full rank. According to model selection criteria, the model fitting the three first principal components (PC3) provided the best fit, without the need for factor analysis models. Similar estimates of phenotypic, direct additive and maternal genetic, maternal permanent environmental and residual (co)variances were obtained with models MV and PC3. Direct heritability ranged from 0.21 (birth weight) to 0.45 (weight at 6 years of age). The genetic and phenotypic correlations obtained with model PC3 were slightly higher than those estimated with model MV. In general, the reduced-rank model substantially decreased the number of parameters in the analyses without reducing the goodness-of-fit. © 2013 Elsevier B.V.

Linear and Poisson models for genetic evaluation of tick resistance in cross-bred Hereford x Nellore cattle

Cattle resistance to ticks is measured by the number of ticks infesting the animal. The model used for the genetic analysis of cattle resistance to ticks frequently requires logarithmic transformation of the observations. The objective of this study was to evaluate the predictive ability and goodness of fit of different models for the analysis of this trait in cross-bred Hereford x Nellore cattle. Three models were tested: a linear model using logarithmic transformation of the observations (MLOG); a linear model without transformation of the observations (MLIN); and a generalized linear Poisson model with residual term (MPOI). All models included the classificatory effects of contemporary group and genetic group and the covariates age of animal at the time of recording and individual heterozygosis, as well as additive genetic effects as random effects. Heritability estimates were 0.08 ± 0.02, 0.10 ± 0.02 and 0.14 ± 0.04 for MLIN, MLOG and MPOI models, respectively. The model fit quality, verified by deviance information criterion (DIC) and residual mean square, indicated fit superiority of MPOI model. The predictive ability of the models was compared by validation test in independent sample. The MPOI model was slightly superior in terms of goodness of fit and predictive ability, whereas the correlations between observed and predicted tick counts were practically the same for all models. A higher rank correlation between breeding values was observed between models MLOG and MPOI. Poisson model can be used for the selection of tick-resistant animals. © 2013 Blackwell Verlag GmbH.

Multivariate models for correlated count data

In this study, we deal with the problem of overdispersion beyond extra zeros for a collection of counts that can be correlated. Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial distributions have been considered. First, we propose a multivariate count model in which all counts follow the same distribution and are correlated. Then we extend this model in a sense that correlated counts may follow different distributions. To accommodate correlation among counts, we have considered correlated random effects for each individual in the mean structure, thus inducing dependency among common observations to an individual. The method is applied to real data to investigate variation in food resources use in a species of marsupial in a locality of the Brazilian Cerrado biome. © 2013 Copyright Taylor and Francis Group, LLC.

Genetic parameters for scrotal circumference, breeding soundness examination and sperm defects in young Nellore bulls

A total of 51,161 records of scrotal circumference measurements at 18 mo of age (SCI 8) and 17,648 records of sperm defects and breeding soundness of Nellore bulls (mean age of 22.5 mo), raised under extensive conditions, were analyzed to estimate coefficients of heritability and genetic correlations of morphological semen traits by Bayesian inference. The observed semen traits were classified as minor (MID). major (MAD), and total sperm defects (TD). The animals were classified according to breeding soundness as satisfactory and unsatisfactory potential breeders. The (co)variance components and breeding values were estimated by Gibbs sampling using the GIBBS2F90 program under an animal model that included contemporary group as fixed effect, age of animal as linear covariate, and direct additive genetic effects as random effects. Heritabilities of 0.40 ± 0.02, 0.16 ± 0.02, 0.04 ± 0.01, 0.15 ± 0.01, and 0.10 ± 0.01 were obtained for SCI8, MID, MAD, TD, and breeding soundness, respectively. The SC18 showed a positive and moderate correlation with breeding soundness (0.56 ± 0.04) and a negative and low correlation with MID (-0.23 ± 0.03), MAD (-0.16 ± 0.02), and TD (-0.24 ± 0.02). In conclusion, scrotal circumference showed the best response to selection among the traits studied and was favorably correlated with breeding soundness and sperm morphology in young Nellore bulls. © 2013 American Society of Animal Science. All rights reserved.