Genotype-environment interaction effects on weight gain in cattle using reaction norms

The existence of genotype-environment interaction (GEI) using reaction norm models and their impact on the genetic evaluation of Nellore sires for body weight at 120, 210, 365 and 450 days of age was verified. Three models were used: animal model (AM) that disregards GEI and the one-step reaction norm model with homogeneous and heterogeneous residual variance (1SRNMH_het). Bayes Inference via Gibbs Sampling was used to estimate the variance components. The AM model better fits to weights at 120 and 210 days of age, while 1SRNMH_het was more adequate for body weights at 365 and 450 days of age, suggesting the existence of GEI. The posterior means of direct heritability were 0.33±0.01 and 0.36±0.01 and maternal heritability of 0.21±0.01 and 0.19±0.01 for body weights at 120 and 210 days of age, respectively. For body weights at 365 and 450 days of age, posterior means of heritability varied along the environmental gradient, but the ranking of sires based on breeding values was not changed by different environmental gradients. All rank correlations were greater than 0.80, strongly suggesting a scale effect of GEI. Despite the evidence of GEI on post-weaning weight gain, it did not change the ranking of sires. Therefore, it did not have a relevant impact on the genetic evaluation of sires because they are robust to environmental changes.


Introduction
The selection of individuals in a given environment may not be valid to achieve the expected genetic gain in another environment, suggesting a possible influence of the genotype-environment interaction (GEI).
GEI occur when the genotype responds differently to changes in the environment (Kolmodin et al., 2002). The GEI may lead to changes in phenotypes, as well as changes in the absolute and relative magnitude of genetic and environmental variances.
This implies that the performance of animals and their progeny can change according to the environmental conditions in which they are raised and selected (Mattar et al., 2011). Therefore, the study of this interaction in beef cattle in Brazil is justified, since the production systems are relatively diversified due to the extensive area, with climatic, historical and cultural differences between regions (Oliveira et al. 2020).
Among the available methodologies for estimation of GEI, models of linear reaction norms have been widely used for gain traits (Souza et al. 2016;Ambrosini, 2016;Tempelman, 2015 andHay &Roberts 2018).
The reaction norm (RN) is defined as the set of phenotypes produced by a given genotype under different environments (De Jong, 1995). This methodology is based on curves of each genotype under two or more different environments, thus making it possible to establish the magnitude of GEI in the measured characteristic.
In these methodology, the environmental variable is considered to be continuous and can be defined by the proper dataset. Since genetic parameters are estimated on an environmental gradient, GEI can be identified more precisely based on the genetic correlations between different points on the environmental axis or by the non-parallelism in the estimates of adaptive reaction norms (Pégolo et al. 2009). Environment descriptors and data structure can influence these results, as shown by Fikse et al. (2003), Kolmodin et al. (2002) and Calus et al. (2002). Pégolo et al. 2009 have demonstrated an important GEI in the 450-day weight trait of Nelore cattle analyzed by reaction norm models, leading to significant re-ranking of sires in different environments and show the need to consider GEI effects, not only in large scale (across countries), but also within a national analysis.
Considering the above, the aim of this study was to verify the existence of genotype-environment interaction effects on gain traits in Nellore herds from the Central-West region of Brazil using reaction norm models.
The objective of this paper was to evaluate the sensitivity of Nelore cattle to the environment by different models of reaction norms and to estimate the genetic progress in environmental gradient.

Methodology
The dataset consisted of 102,921 adjusted weights for 120, 210, 365 and 450 days of age of Nellore beef cattle population from the Central-West region of Brazil, which participates in the genetic evaluation program of Associação Nacional de Criadores e Pesquisadores(ANCP), for animals born in 1990 to 2014.
To guarantee connectivity in the genetic evaluation, only sires with a minimum of four progenies in at least two different states were considered for analysis. The calving months were grouped into two seasons, corresponding to months of the lowest (from April to September) and highest (from October to March) rainfall levels and the contemporary groups (CG) were defined by using information on herd, year, gender, and calving season. CGs with less than four individuals were excluded.
Initially, we use a standard animal model (AM) that disregards GEI to estimate variances components and predict the animal's breeding value. For the body weight traits at 120 (W120) and at 210 (W210) days. The model was described as = + 1 + 2 + 3 + :, where y= vector of observations; b = vector of fixed effects (contemporary group and linear and quadratic for dam's age); a = vector of direct additive genetic effects; m = vector of maternal additive genetic effects; p = vector of maternal permanent environmental effects, and  = vector of residual random errors associated with observations. X, Z1, Z2 and Z3 are incidence matrices related to b, a, m and p to y.
Posteriorly, The one-step hierarchical reaction norm model (RNM) were implemented based on the unknown covariate proposition of Su et al. (2006). In the sense, the covariate was characterized by the CG effects that were jointly estimated with the RN of the animals.
The RNM used in the analyses is described as: y = Xβ + Eh + Za + Hb + e, where y = the vector of records of weights; β = the vector of fixed effects (linear and quadratic for dam's age); h = the vector of random CG effects; a and b = the vectors of random intercept and slope coefficients of animal additive genetic RN, respectively; e = the random error vectors; and X, E, Z, and H = the incidence matrices. Once covariates associated with the RN are treated as unknown, each row of H has one nonzero element that is equal to the element h (contemporary group effect) associated with the corresponding record on y, and all other elements of this row are equal to zero (Su et al., 2006).
Two different alternative assumptions were adopted for residual variance in the models, the first was Homoscedasticity of variance (RNMHO) with ~(0,σ 2 ) with σ 2 residual variance. The second assumption was heteroscedasticity of residual variance for reaction norm model (RNMHE), where e ~ N(0,diag{ σ 2 ( n hj ) } wich each error term hasits specific residual variance as a function of the associated environmental covariate hj ). This exponential function on a residual heteroskedasticity parameter, n, was based on the structural model proposed by Cardoso et al. (2005) and posterior means of hj by the RNMHO model,hj , were used in the function to facilitate recognizable fully conditional posterior densities.
Bayesian inference was performed by Monte Carlo methods via Markov chains, using the GIBBS1F90 software (Misztal et al., 2014), which was run for a total of 500,000 iterations, after a burn-in period of 50,000 iterations. Samples were generated every 10 iterations (thin = 10), resulting in a total of 45,000 effective samples for inference. The convergence was checked by Geweke's Z criterion (Geweeke, 1992) To determine the best fitting model, the Deviance Information Criterion (DIC), conditional predictive ordinate (CPO) criterion and pseudo-Bayes factors (BF) were used. Further details about these criteria can be seen in Cardoso et al. (2005).
Heritability was estimated from the ratio of the genetic variance to the phenotypic variance (genetic and environmental), as follows:ℎ 2 | = 2 | 2 | + 2 | , where 2 | = residual variance of environment X, obtained by 2 | = 2 η′X in a heteroscedastic model and 2 in a homoscedastic model, in which η = degree of heterogeneity of residual variance across environments (X). For the weights at 120 and 210 days, the maternal effect was also included to estimate the heritability.
Maternal heritability (ℎ 2 ),estimated only for weights at 120 and 210 days, was estimated from the ratio of the maternal effect variance ( 2 | ) to the phenotypic variance (genetic and residual variance) + the maternal effect variance, as follows: The correlation (̂, ) between intercept (a) and slope (b) of reaction norms was obtained by dividing the covariance between a and b ( , ) by the square root of their variances ( 2 2 ) : The breeding value of animals (G) was calculated by the sum between the intercept and the slope and the environmental gradient (X), as: G|X=a+bX.
Subsequently, for each trait, the ranking of sires based on breeding values was plotted against the different environmental gradients. For this, only sires with a minimum of 10 progenies were considered.
The levels of environmental gradients were redefined as low, medium and high. The low gradient was in the first quartile, that is, the lowest 25% values of contemporary groups (averages of -12,744 for W365 and -27,6033 for W450). The medium gradient is defined as the environmental average, that is, X = 0. The high gradient is composed of the highest 25% values of contemporary groups, that is, the third quartile (averages from 29.985 for W365 and 26.30 for W450).
For the evaluation of the genetic merits of sires with ten or more progenies for robustness and plasticity, a posterior mean for their slope was obtained, standardized and then classified as: Extremely robust (ER), with values within one standard deviation; Robust (R), with values greater than one and less than two standard deviations; Plastic (P), with values above and equal to two and less than three standard deviations; Extremely plastic (EP), with values equal to and above three standard deviations.

Results
The posterior means and standard deviations (SD), minimum and maximum values and number of records for body weights at 120 (W120), 210 (W210), 365 (W365) and 450 (W450) days of age are shown in Table 1. The coefficients of variation between body weights were similar: 0.16 for W120 and W210 and 0.18 for W365 and W450. The Geweke's Z criterion, posterior means of additive genetic, residual and (co)variances components associated with covariance functions obtained using Markov chains are shown in Table 2. Geweke's Z criterion for all parameters of variance and covariance in the all models analyzed were less than 0.05, were observed, these results showed that the sizes of the Markov chains were satisfactory for estimation of posterior means of variance components in the all models. According to the statistical criteria used (CPO: conditional predictive ordinate, DIC: Deviance Information Criterion, and BF: pseudo-Bayes factors), there were differences between models for pre-and post-weaning traits (Table 3). For the pre-weaning phase, the animal model (including a residual variance) was the most adequate based on the CPO and DIC criteria, while the reaction norm model with heterogeneous residual variance better fits to the data for the post-weaning phase.   Source: Authors.
Estimates of posterior means of the additive genetic correlations between environmental gradients for post-weaning traits (Figures 2 and 3) showed that more similar environmental gradients (near) are more correlated, whereas more extreme gradients (distant) are less correlated. This indicates that most of the gene groups that express in similar environments are the same, which did not occurr between extreme environments. Consequently, for the same body weight that is expressed in contrasting environments, the additive gene action has different effects, suggesting an effect of the genotype-environment interaction.

Discussion
The use of a covariance function in the model of reaction norms to describe the additive genetic variance for the environmental gradient levels did not fit well worked for W120 and W210. Thus, the criterias statistical CPO and DIC used pointed to the animal model as the most indicated for these characteristics, indicating absence of IGA for both traits. The fact that the animal model has met the criteria for good model performance may be related to the principle of parsimony, in which there is a occurrence to choose less parameterized models.
Howewer, the reaction norm model with heterogeneous residual variance was chosen for the estimation of GEI for W365 and W450. The existence of genotype-environment interaction effect on weight gain in post-weaning phase and absence in pre-weaning were verified.
This differs from Ambrosini et al. (2016), Souza et al. (2016) and Mattar et al. (2011), who evaluated Nellore, Tabapuã and Canchim breeds, respectively, in which the one-step reaction norm model with homogeneous residual variance was the bestfit model. However, the results found in the present study agree with other authors, who determined the residual heteroscedasticity for reaction norms in different species (Cardoso & Tempelman, 2015 in Angus cattle, Knap & Su, 2008 in swine, Pollott &Greeff, 2004 in sheep andCalus et al., 2002 in dairy cattle).
Heritability estimates for W120 and W210 reveal the possibility of relevant genetic gains through selection for these body weights by additive gene action. Thus, for W120 and W210, considerable genetic gains are expected at weaning, as well as gains for maternal ability of progeny by the selection of the most positive sires.
Posterior means of heritability for W365 were 0.42±0.02; 0.47±0.02 and 0.60±0.02 in low, medium and high environmental gradients, respectively. Estimates for W450 were 0.37±0.05; 0.38±0.05 and 0.44±0.05 in low, medium and high environmental gradients, respectively. In general, all posterior means of heritability in both body weights and levels were high, revealing good responses to selection for these traits. However, more accurate responses to selection were found in more favorable environments. The increase of posterior means of heritability in relation to high environmental gradients agrees with other studies of growth traits in cattle (Mattar et al., 2011, Corrêa et al. 2009and Santos et al. 2019).
The correlations between the intercept and slope were 0.66±0.03 and 0.24±0.04 for W365 and W450, respectively.
These values demonstrate that, not necessarily, sires with higher intercept values are also the most sensitive to environmental change.
For both W365 and W450, most of sires were classified as robust and extremely robust (representing more than 90% for the two traits), that is, with a slope close to zero. This indicates that they respond similarly to different environments, consequently their breeding values are very similar even under contrasting environments.
The effects of the robustness of sires can also be seen in Table 5, in which the Spearman correlations between the AM and RNMH models were all significant (P<0.01), but of high magnitude even under extreme environments. Therefore, no change is expected in the ranking of sires evaluated under different environmental gradients classified as low, medium and high (RNM) compared to the traditional animal model (AM).
These results corroborate with Ambrosini et al. (2016), who also did not observe considerable changes in ranking of sires as most of them were robust. The results differ from Corrêa et al. (2009), who found negative correlations between extreme environments and Mattar et al. (2011), who found low correlations between extreme gradients. High values also indicate low magnitude of GEI, also reported by Cardoso et al. (2011).
The existence of a scale effect of GEI is verified, with changes in genetic parameters in different environmental gradients, but without changing the ranking of sires within them.

Conclusion
In this way, it is conclude that the existence of genotype-environment interaction effect on the body weight gain in Nellore herds from the Central-West region was verified in the post-weaning phase, but not in the pre-weaning phase. The reaction norm model with heterogeneous residual variance was the most adequate to describe the genotype-environment interaction for body weight in the post-weaning phase. In this sense, despite the evidence of genotype-environment interaction in the post-weaning phase, it did not change the ranking of sires. Therefore, it did not have a relevant impact on the genetic evaluation of sires because they are robust to environmental changes.