Bayesian inference in genetic parameter estimation of visual scores in Nellore beef-cattle

The aim of this study was to estimate the components of variance and genetic parameters for the visual scores which constitute the Morphological Evaluation System (MES), such as body structure (S), precocity (P) and musculature (M) in Nellore beef-cattle at the weaning and yearling stages, by using threshold Bayesian models. The information used for this was gleaned from visual scores of 5,407 animals evaluated at the weaning and 2,649 at the yearling stages. The genetic parameters for visual score traits were estimated through two-trait analysis, using the threshold animal model, with Bayesian statistics methodology and MTGSAM (Multiple Trait Gibbs Sampler for Animal Models) threshold software. Heritability estimates for S, P and M were 0.68, 0.65 and 0.62 (at weaning) and 0.44, 0.38 and 0.32 (at the yearling stage), respectively. Heritability estimates for S, P and M were found to be high, and so it is expected that these traits should respond favorably to direct selection. The visual scores evaluated at the weaning and yearling stages might be used in the composition of new selection indexes, as they presented sufficient genetic variability to promote genetic progress in such morphological traits.

Genetic parameter estimates for buffalo milk yield, milk quality and mozzarella production and Bayesian inference analysis of their relationships

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Genetic parameters for buffalo milk yield and milk quality traits using Bayesian inference

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

Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

Genetic parameters by Bayesian inference for dual purpose Jaffarabadi buffaloes

Knowledge of genetic parameters is essential for improved reproductive management and increased yield. Quantitative analysis of genetic parameters is lacking for many breeds of buffaloes. This article provides the first estimate of genetic parameters for dual purpose (meat and milk) Brazilian Jaffarabadi buffaloes, using Bayesian inference. Data on milk yield (MY), lactation length (LL), weight at 205 days (W205) and 365 (W365) days of age, and average daily gain (ADG) from 205 to 365 days of age were collected in two herds. Bivariate analyses (using the program MTGSAM) were performed with the Gibbs sampler to obtain estimates of variance and covariance. Average lactation milk yield and lactation length were 1 620.2 +/- 450.9 kg and 257.6 +/- 46.8 days, respectively, and the mean values for weight traits (kg) were 181.6 +/- 63.3 (W205), 298.04 +/- 116.1 (W365), and 0.73 +/- 0.35 (ADG). Heritability estimates (modes) were 0.16 for MY, 0.10 for LL, 0.43 for W205, 0.48 for W365 and 0.32 for ADG. There was a high genetic correlation (0.96) between milk yield and lactation length and very high genetic correlations (0.99) between the three growth traits. Our data suggest that both milk production and growth traits have clear potential for yield improvement through direct selection in this dual purpose breed. The selection for weight at an early age would be successful and selection for MY can be performed in the first lactation.

Genetic Parameters for Reproductive Traits of Crossbred Buffaloes from Brazil, Estimated by Bayesian Inference

The objective of the study was to estimate heritability for calving interval (CI) and age at first calving (AFC) and also calculate repeatability for CI in buffaloes using Bayesian inference. The Brazilian Buffaloes Genetic Improvement Program provided the database. Data consists on information from 628 females and four different herds, born between 1980 and 2003. In order to estimate the variance, univariate analyses were performed employing Gibbs sampler procedure included in the MTGSAM software. The model for CI included the random effects direct additive and permanent environment factors, and the fixed effects of contemporary groups and calving orders. The model for AFC included the direct additive random effect and contemporary groups as a fixed effect. The convergence diagnosis was obtained using Geweke that was implemented through the Bayesian Output Analysis package in R software. The estimated averages were 433.2 days and 36.7months for CI and AFC, respectively. The means, medians and modes for the calculated heritability coefficients were similar. The heritability coefficients were 0.10 and 0.42 for CI and AFC respectively, with a posteriori marginal density that follows a normal distribution for both traits. The repeatability for CI was 0.13. The low heritability estimated for CI indicates that the variation in this trait is, to a large extent, influenced by environmental factors such as herd management policies. The age at first calving has clear potential for yield improvement through direct selection in these animals.

Genetic Correlation for Pre-Weaning and Post-Weaning Traits of Mediterranean Buffaloes from Brazil, Estimated By Bayesian Inference

The aim of this study was to estimate genetic, environmental and phenotypic correlation between birth weight (BW) and weight at 205 days age (W205), BW and weight at 365 days age (W365) and W205-W365, using Bayesian inference. The Brazilian Program for Genetic Improvement of Buffaloes provided the data that included 3,883 observations from Mediterranean breed buffaloes. With the purpose to estimate variance and covariance, bivariate analyses were performed using Gibbs sampler that is included in the MTGSAM software. The model for BW, W205 and W365 included additive direct and maternal genetic random effects, maternal environmental random effect and contemporary group as fixed effect. The convergence diagnosis was achieved using Geweke, a method that uses an algorithm implemented in R software through the package Bayesian Output Analysis. The calculated direct genetic correlations were 0.34 (BW-W205), 0.25 (BW-W365) and 0.74 (W205-W365). The environmental correlations were 0.12, 0.11 and 0.72 between BW-W205, BW-W365 and W205-W365, respectively. The phenotypic correlations were low for BW-W205 (0.01) and BW-W365 (0.04), differently than the obtained for W205-W365 with a value of 0.67. The results indicate that BW trait have low genetic, environmental and phenotypic association with the two others traits. The genetic correlation between W205 and W365 was high and suggests that the selection for weight at around 205 days could be beneficial to accelerate the genetic gain.

Genetic Parameters for Growth Traits of Mediterranean Buffaloes from Brazil, Estimated By Bayesian Inference

Quantitative analysis of growth genetic parameters is not available for many breeds of buffaloes making selection and breeding decisions an empirical process that lacks robustness. The objective of this study was to estimate heritability for birth weight (BW), weight at 205 days (W205) and 365 days (W365) of age using Bayesian inference. The Brazilian Program for Genetic Improvement of Buffaloes provided the data. For the traits BW, W205 and W365 of Brazilian Mediterranean buffaloes 5169, 3792 and 3883 observations have been employed for the analysis, respectively. In order to obtain the estimates of variance, univariate analyses were conducted using the Gibbs sampler included in the MTGSAM software. The model for BW, W205 and W365 included additive direct and maternal genetic random effects, random maternal permanent environmental effect and contemporary group that was treated as a fixed effect. The convergence diagnosis was performed employing Geweke, a method that uses an algorithm from the Bayesian Output Analysis package that was implemented using R software environment. The average values for weight traits were 37.6 +/- 4.7 kg for BW, 192.7 +/- 40.3 kg for W205 and 298.6 +/- 67.4 kg for W365. The heritability posterior distributions for direct and maternal effects were symmetric and close to those expected in a normal distribution. Direct heritability estimates obtained using the modes were 0.30 (BW), 0.52 (W205) and 0.54 (W365). The maternal heritability coefficient estimates were 0.31, 0.19 and 0.21 for BW, W205 and W365, respectively. Our data suggests that all growth traits and mainly W205 and W365, have clear potential for yield improvement through direct genetic selection.

Genetic Parameters for Milk Yield and Lactation Length of Crossbred Buffaloes from Brazil by Bayesian Inference

The objective of the study was to estimate heritability and repeatability for milk yield (MY) and lactation length (LL) in buffaloes using Bayesian inference. The Brazilian genetic improvement program of buffalo provided the data that included 628 females, from four herds, born between 1980 and 2003. In order to obtain the estimates of variance, univariate analyses were performed with the Gibbs sampler, using the MTGSAM software. The model for MY and LL included direct genetic additive and permanent environment as random effects, and contemporary groups, milking frequency and calving number as fixed effects. The convergence diagnosis was performed with the Geweke method using an algorithm implemented in R software through the package Bayesian Output Analysis. Average for milk yield and lactation length was 1,546.1 +/- 483.8 kg and 252.3 +/- 42.5 days, respectively. The heritability coefficients were 0.31 (mode), 0.35 (mean) and 0.34 (median) for MY and 0.11 (mode), 0.10 (mean) and 0.10 (median) for LL. The repeatability coefficient (mode) were 0.50 and 0.15 for MY and LL, respectively. Milk yield is the only trait with clear potential for genetic improvement by direct genetic selection. The repeatability for MY indicates that selection based on the first lactation could contribute for an improvement in this trait.

Bayesian inference for two-parameter gamma distribution assuming different noninformative priors

In this paper distinct prior distributions are derived in a Bayesian inference of the two-parameters Gamma distribution. Noniformative priors, such as Jeffreys, reference, MDIP, Tibshirani and an innovative prior based on the copula approach are investigated. We show that the maximal data information prior provides in an improper posterior density and that the different choices of the parameter of interest lead to different reference priors in this case. Based on the simulated data sets, the Bayesian estimates and credible intervals for the unknown parameters are computed and the performance of the prior distributions are evaluated. The Bayesian analysis is conducted using the Markov Chain Monte Carlo (MCMC) methods to generate samples from the posterior distributions under the above priors.

The zero-inflated Conway-Maxwell-Poisson distribution: Bayesian inference, regression modeling and influence diagnostic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimation of genetic parameters for milk yield in Murrah buffaloes by Bayesian inference

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Genetic analysis of visual scores and their relationships to mature female weight in Nellore breed

Dados de 79.884 animais da raça Nelore foram utilizados para estimar parâmetros genéticos e avaliar as relações entre os escores de conformação, precocidade e musculatura obtidos à desmama e ao sobreano e o peso das fêmeas à idade adulta. Utilizou-se o método da máxima verossimilhança restrita, em análise multicaracterísticas, com modelo que incluiu os efeitos genéticos aditivos direto e residual, como aleatórios, e os efeitos fixos de grupo de contemporâneos e, como covariáveis, a idade do animal à pesagem e a idade da mãe ao parto (exceto para o peso das fêmeas à idade adulta). Os grupos contemporâneos à desmama foram definidos pelas variáveis: sexo, rebanho, ano e mês de nascimento, grupo de manejo ao nascimento e à desmama. Na definição de grupo contemporâneo ao sobreano também foi incluída a variável grupo de manejo ao sobreano. Para o peso das fêmeas à idade adulta, o grupo de contemporâneos foi composto por rebanho, ano de nascimento, grupo de manejo ao sobreano, ano e estação da pesagem. Os efeitos genético materno e de ambiente permanente materno também foram incluídos no modelo para análise dos escores de conformação, precocidade e musculatura à desmama. As estimativas de herdabilidade direta obtidas foram 0,18 ± 0,02 para o escore de conformação; 0,21 ± 0,01 para o escore de precocidade; 0,22 ± 0,01 para o escore de musculatura à desmama e 0,24 ± 0,01 para o escore de conformação; 0,27 ± 0,01 para o escore de precocidade; e 0,26 ± 0,01 para o escore de musculatura ao sobreano e 0,42 ± 0,02 para o peso das fêmeas à idade adulta. As correlações genéticas estimadas entre os escores visuais medidos à desmama e ao sobreano foram positivas, variando de média a alta magnitude (0,56 ± 0,03 a 0,85 ± 0,01). Por outro lado, as correlações genéticas estimadas entre os escores visuais e o peso das fêmeas à idade adulta foram positivas e moderadas, variando de 0,21 ± 0,03 a 0,35 ± 0,03. Os resultados obtidos indicam que a seleção de animais com maiores escores visuais, principalmente ao sobreano, deve promover aumento do peso das fêmeas à idade adulta.

Genetic correlations between heifer subsequent rebreeding and age at first calving and growth traits in Nellore cattle by Bayesian inference

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