Hierarchical Bayesian models for genotype × environment estimates in post-weaning gain of Hereford bovine via reaction norms

Abstract

-It was evaluated statistical models with different assumptions to define the one that best describes the presence of genotype × environment interaction on adjusted post-weaning weight gain (PWG345) of Hereford cattle, through the study of reactions norms to the environment, obtained by random regression using a Bayesian approach.Four reaction norms hierarchical models (RNHM) were used through the INTERGEN program. The RNHM K uses the solutions of contemporary groups previously estimated by the standard animal model (AM) and considers them as environmental level for predicting the reaction norms and the RNHM S , which jointly estimate these two sets of unknowns.For both models, two versions were considered, one with a homogeneous (hm) and another with a heterogeneous (ht) residual variance. Based on the deviance information criterion and Bayes factor, RNHM s hm showed the best fit to the data, and by the deviance based on conditional predictive ordinate, the best fit was the RNHM K ht, whereas, by all the three criteria used, the worst fit was obtained by using the standard animal model. Heritabilities estimated on RNHM were increasing in the environmental gradients for PWG345, at -60 kg, 0 and +60 kg. The genetic correlation estimated between the level and slope of reaction norms was high, from 0.97 to 0.99, characterizing a scale effect on genotype × environment interaction. The reaction norms hierarchical models are efficient to describe the changes in variance components due to the environment and to describe the presence of genotype × environment interaction on PWG345 trait of Hereford cattle.Key Words: adaptability, Bayesian inference, environmental sensitivity, genetic evaluation, random regression Modelos hierárquicos bayesianos para estimativas de interação genótipo × ambiente em ganho pós-desmama de bovinos Hereford via normas de reaçãoRESUMO -Avaliaram-se modelos estatísticos com diferentes pressuposições para definir o que melhor descreva a presença de interação genótipo × ambiente no ganho de peso pós-desmama ajustado (GPD345) de bovinos Hereford, mediante o estudo de normas de reação ao ambiente, obtidas por regressão aleatória, usando uma abordagem bayesiana. Quatro modelos hierárquicos de normas de reação (MHNR) foram empregados por meio do programa INTERGEN. O MHNR K utiliza as soluções de grupos contemporâneos estimadas previamente pelo modelo animal padrão (MA) e as considera como nível ambiental para predizer as normas de reação e o MHNR S , que estima simultaneamente esses dois conjuntos de incógnitas.Para ambos os modelos, foram consideradas duas versões, uma com variância residual homogênea (hm) e outra heterogênea (ht). Pelo critério de informação da deviance e fator de Bayes, o MHRN S hm apresentou melhor ajuste aos dados e, pela deviance baseada na ordenada preditiva condicional, o melhor ajuste foi do MHNR K ht, enquanto, pelos três critérios, o pior ajuste foi obtido pelo modelo animal padrão. As herdabilidades estimadas nos MHNR foram crescentes nos gradientes ambientais em ...

Multiple-breed reaction norm animal model accounting for robustness and heteroskedastic in a Nelore–Angus crossed population

“…The a posteriori mean estimates of PWG heritability from the MAMRNH model for different AN and NE breed groups were all directly proportional to the environmental gradient (Figure 2). Similar results have been found in other studies of post-weaning gain in beef cattle (Corrêa et al, 2009;Cardoso et al, 2011;Mattar et al, 2011;Cardoso and Tempelman, 2012;Santana et al, 2013), and in dairy cattle for production and reproductive traits (Kolmodin et al, 2002;Shariati et al, 2007). These results indicate that heritability increases as environmental conditions improve.…”

“…Despite being opposite in sign, these results were similar to those obtained by Cardoso et al (2011), where residual variance increased slightly (scaling factor = 1.007) as the environmental gradient indicated conditions that were more conducive to growth. Indications robustness and heteroscedasticity were similar to those obtained without considering G × E interaction for MAMH and by Oliveira et al (2011).…”

“…Similar substantial correlations between intercept and slope were also observed in previous studies of beef cattle where reaction norms were modeled. Examples from these studies include: Cardoso and Tempelman (2012) for Angus (0.95), Cardoso et al (2011) for Hereford (0.97), Mattar et al (2011) for Canchim (0.90) and Santana et al (2013) for tropical composite (0.94). In contrast, the 95% posterior probability support interval for r abðANÞ included zero, implying a nonsignificant correlation in our AN sample (Table 4).…”

“…Through covariance functions it is possible to determine prediction of breeding values in response to continuous gradations in the production environment (Kirkpatrick et al, 1990). This approach also allows modeling of heterogeneous genetic and environmental variances and has been used successfully to identify G × E interaction effects on performance of dairy (Kolmodin et al, 2002;Shariati et al, 2007;Strandberg et al, 2009) and beef (Corrêa et al, 2009;Cardoso et al, 2011;Mattar et al, 2011;Cardoso and Tempelman, 2012;Santana et al, 2013) cattle. Hierarchical Bayes models have the flexibility necessary to fit these models (Sorensen and Gianola, 2002).…”

Phenotypic plasticity of composite beef cattle performance using reaction norms model with unknown covariate

“…In general, higher direct heritabilities were observed in extreme favorable environments (Figure 2 Several authors studying the postweaning performance of beef cattle reported changes in genetic parameters across the environmental gradient, with the observation of a higher proportion of phenotypic variation due to genetic factors in more favorable environments (Corrêa et al, 2009;Cardoso et al, 2011;Mattar et al, 2011). Heritability is a property of the population and of the environment to which the animal is exposed, whereas environmental variance depends on production and management conditions.…”