Reaction norms of direct and maternal effects for weight at 205 days in Polled Nellore cattle in north-eastern Brazil

This study investigated the presence of genotype-environment interaction (GEI) for body weight adjusted to 205 days of age (W205) in Polled Nellore cattle raised in north-eastern Brazil using reaction norm (RN) models. The reaction norm hierarchical models (RNHM) included the fixed (linear and quadratic) effect of cow’s age, random effect of contemporary group (CG), RN level and slope for additive direct and maternal genetic effects and permanent maternal environmental effect. The one-step reaction norm model with homogeneous residual variance (RNHM1sHm) yielded the best adjustment compared to the others. Based on this model, the estimates of direct additive and maternal variances and increased with environment improvement (35.34±7.92 kg2 to 134.42±25.97 kg2 and 12.76±5.38 kg2 to 58.22±19.74 kg2 for low and high-quality environments, respectively). The estimates of heritability direct additive and maternal too increased with environmental improvement (0.08±0.02 to 0.24±0.04 and 0.03±0.01 to 0.10±0.04). The correlation between the intercept and the slope of RNHM indicates that animals with higher genetic values respond more efficiently to environmental improvements, representing a scale effect for W205. These results allowed us to characterize the GEI for W205 and showed that specific evaluation should be performed with low, intermediary and high production levels.


Introduction
Genotype-environment interaction (GEI) implies that similar genotypes respond differently to environmental changes, which might cause a reclassification or changes in ranking genetic values (Falconer & Mackay 1996).In livestock genetic improvement, this effect can lead to discrepancies in breeding values once the best bloodstock raised in a specific production system might produce an inferior offspring in other environments (Lynch & Walsh 1998) Brazil has a wide range of environments for animal production since it covers nearly half of South America and encompasses distinct biomes and climate conditions.This is particularly true in north-eastern Brazil, which includes areas with favourable conditions for animal production as well as less favoured ones, near to central region and under the influence of semiarid climate.Therefore, it is important to study genotype-environment interaction (GEI) in this region and necessary to include GEI in estimates of genetic values in order to maximize response to selection.
Usually, reaction norm models (RNM) have been used to assess GEI in several economically important breeds, such as dairy cattle (Bohmanova et al. 2008, Streit et al. 2012) and beef cattle (Ambrosini et al. 2012, Corrêa et al. 2009, Fördös et al. 2010, Mattar et al. 2011, Vostry et al. 2009, Szabó et al. 2010).The utilization of RNM in identification of high-quality individuals might potentially change the current paradigm of selection strategies, once the predictions of genetic values can differ for the same candidate to selection in distinct environments (Mattar et al. 2011).
Reaction norm models (RNM) allow us to describe the gradual and continuous variation of genetic breeding values related to economically important traits throughout an environmental gradient.Although this approach remains overlooked in routine genetic assessments in Brazil, many authors (Ambrosini et al. 2012, Alencar et al. 2005, Fridrich et al. 2008, Espasandin et al. 2011) verified the presence of GEI in different populations.Additionally, a model including the maternal effect in GEI studies via RNM has not been performed yet.Therefore, GEI and maternal effects were assessed in the present study for weights adjusted at 205 days in Polled Nellore cattle raised in north-eastern Brazil based on reaction norms using a Bayesian approach.

Material and methods
The work was carried out with records of Polled Nellore animals born from 1975 to 2007 in north-eastern Brazil.The initial database was provided by ABCZ, the Brazilian Association of Zebu Breeders, and comprised 35 221 records.Nonetheless, those individuals without weight data (8 637), disconnected (143), measured outside the interval from 80 kg to 280 kg (164), born from cows below 1.9 years-old and over 25 years-old (171) or with less than 3 progenies (8 390) and from breeders with less than 5 progenies (624), as well as contemporary groups with less than 5 observations and average weight above +3 standard deviations (6 948) were excluded.Therefore, 10 144 records were used for analysis of weights adjusted at 205 days of age (W205).
The routines created by Cardoso (2008) in SAS v9 (SAS Institute Inc., Cary, NC, USA) were used to prepare the dataset for RN analyses.Afterwards, the connectivity of contemporary groups (CG) was tested based on the total number of genetic links (minimum of 10) using the software AMC (Roso & Schenkel 2006).The connectivity of CG resulted in a main archipelago (CG with the highest number of genetic links and interconnected CG) with 10 144 animals in 1 094 CG and 143 animals in 91 disconnected CG.Only the main archipelago was used for the analysis.
The CG was formed so that all animals shared a common production environment, including herd, year, birth period and sex.The birth periods were grouped into four classes (period 1: May, June and July; period 2: August, September and October; period 3: November, December and January; and period 4: February, March and April).
The software INTERGEN (Embrapa Pecuária Sul, Bagé, RS, Brazil) was used with a standard animal model (AM) to obtain the estimates of mean environmental effects according to CG and to provide a comparative analysis in relation to RNM.This software adjusts Bayesian hierarchical models with parameters defined in structured levels or stages comprising the diversity of animal performance data.In the case of RNM, the individual genetic value is obtained by a function of the mean environmental level corresponding to the solution of CG to which the record belongs, i.e., there is a specific genetic value for each animal in each environmental level (Cardoso & Tempelman 2012).
Initially, a standard animal model (AM) that disregards GEI was adopted to estimate individual genetic values and to obtain the estimates of mean environmental effects based on CG: where y ij is the record of animal i in environment j, β is the vector of fixed effects (linear and quadratic for cow's age), x i ' is the incidence vector, X j is the random CG environmental effect, a i is the additive genetic value of animal Г ., m i is the maternal genetic value of animal Г .
, ep i is the maternal permanent environmental effect; and e ij is the residual error.
In addition, two methodologies were implemented to describe the reaction norm hierarchical models (RNHM).Firstly, we used the model proposed by Kolmodin et al. (2002) assuming the environment solutions of AM as co-variables in two-step RNHM (RNHM 2s ), as follows: where ф is the fixed regression coefficient, a i is the additive genetic value for the RN intercept or level in animal i, m is the maternal genetic value for the RN intercept or level in animal i, ep i is the permanent maternal environmental effect, b 1i is the random regression coefficient or direct RN slope of animal i in the environment represented by X ˆj, b 2i is the random regression coefficient or maternal RN slope of animal i in the environment represented by X ˆj ; X j is the predictor obtained in ( 1) and e ij is the residual error.
Secondly, the one-step RNHM (RNHM 1S ) proposed by Su et al. (2006) was used.Albeit similar to the previous model ( 2), RNHM 1S is distinguished by the simultaneous estimation of CG solutions and intercepts and slopes of RN.In this model, the CG effects are regarded as unknown covariables in RNM, in which the estimates for environmental effects were used as a covariant to obtain the slope of the animal RN, that is X j and b i are jointly estimated as follows: Two different assumptions were adopted for the residual variance in tested models: (a) homoscedasticity for AM, RNHM 2S (RNHM 2S Hm) and RNHM 1S (RNHM 1S Hm) where e i ~N(0,σ 2 e ) is the residual variance; and (b) heteroscedasticity for RNHM 2S (RNHM 2S He) and RNHM 1S (RNHM 1S He), with e i ~N(0,σ 2 ej ) and σ 2 ej = σ 2 e η x j , where η is the heterogeneity parameter of residual variance at X j environmental level, following the structural model proposed by Cardoso et al. (2005).
The direct additive and maternal genetic variances in environment X, σ 2 A |X and σ 2 m |X, were obtained by: a are the additive genetic variance components estimated for the RN intercept, σ 2 m are the maternal genetic variance components estimated for the RN intercept, σ 2 b are the variance components estimated for the RN slope, and σ 2 ab are the estimate of covariance components between RN intercept and slope.
The heritabilities were estimated by the ratio between genetic variance and phenotypical (genetic+environmental) variance, as follows: where σ 2 e |X is the residual variance in environment X, obtained by σ 2 e |X=σ 2 e η ˆX in the heteroscedastic model and by σ 2 e in the homoscedastic model.A Bayesian approach (Gianola & Fernando 1986) via Markov Chain Monte Carlo (MCMC) method (Blasco 2001) was implemented to obtain the parameter estimates according to the following procedure (Figure 1): a) a pilot sample was analysed with 55 000 cycles, 5 500 burn-in and thinning of 5; b) using the variance component obtained in (a) and R package (R Development Core Team 2008) -Bayesian Output Analysis -BOA (Smith 2007), the test by Raftery & Lewis (1992) was applied to determine the new chain size and thinning; moreover, and c) the burn-in was evaluated according to Heidelberger & Welch (1983).
The final analyses comprised runs with chains from 330 000 to 660 000 cycles.A posteriori means, standard deviations and percentiles (0.025 and 0.975) of parameter values were obtained from their marginal posterior densities obtained through KDE procedure available in SAS (SAS Institute Inc., Cary, NC, USA) The Geweke's convergence diagnostic for Markov chains (Geweke, 1992) was performed.This is a standard Z-test for equality of the means of the conditional data distribution logarithm, denoted by l (j)  i = log p (y|θ (j) , M i ) in the first 10 % and the last 50 % of the Markov chain, similarly to the statistics proposed by Brooks and Roberts (1998): where , n A = 66,000, n B = 330,000, n* = 330,001, and with Ŝ i A (0) and, Ŝ i B (0) where the respective estimates of spectral density at frequency zero was obtained by the procedure SPECTRA in SAS (SAS Institute Inc., Cary, NC, USA), for the first n A and the last n B cycles in the MCMC of length m.Extreme absolute values of the Z i score in a two-tailed test reject the convergence test.
The following criteria were used to verify the best adjusted model: Deviance Information Criterion (DIC) (Spiegelhalter et al. 2002); Conditional Predictive Ordinate Deviance (CPO) (Gelfand 1996) and Bayes Factors (BF), described as the deviance based on the Monte Carlo estimator (Newton & Raftery 1994).These deviations represent the degree of separation of the evaluated model in relation to a hypothetically perfectly adjusted model, in which the lowest values indicate the best adjustment.
Amongst the tested MNR, RNHM 1S Hm yielded improved data adjustment, being the best model in two out of the three analysed criteria (DIC and CPO).The RNHM 1S Hm was inferior only by BF and had the second best adjustment under this criterion (Table 1).Reaction norm models based on homogeneous and heterogeneous residual variance were previously used to assess standardized post-weaning weight gain in Angus (Cardoso & Tempelman 2012), Devon (Corrêa et al. 2009), Hereford (Cardoso et al. 2011) and Canchim (Mattar et al. 2011) cattle.These authors compared homoscedastic RNHM to heteroscedastic RNHM and AM and concluded that the former yielded the best adjustments.Markov chains with 660 000 iterations and burn-in of 60 000 (10 % discarded) were obtained in homoscedastic RNHM (chosen model), generating posterior samples at every 113 cycles.Besides the Geweke's test (Geweke 1992), the chain convergence was also evaluated by line graphs of the sample values in all co-variance components against the chain cycle (data not shown).
In RNHM 1S Hm, the environmental gradient solutions ranged from −54 to 60 kg, characterizing low and high-quality environments (management levels).The direct and maternal heritability estimates in AM were 0.35±0.03and 0.10±0.02,respectively (Figure 2).These values were higher than the estimated ones by RNHM 1S Hm in all RN levels, and also superior to the values reported by Cardoso & Tempelman (2004) (0.19±0.02) and Corrêa et al. (2009) (0.13±0.017) for direct heritability of standardized post-weaning weight gain (PWG365) in AM.However, it should be pointed out that both reports were based on Bos taurus breeds raised in southern Brazil, where the production system is completely different from that performed in the north-eastern region.
On the other hand, the direct heritability estimated by AM in the present study was inferior while maternal heritability was higher to those reported by Malhado et al. (2005) based on restricted likelihood for W205 in Polled Nellore from Bahia state, north-eastern Brazil (0.24±0.04 and 0.20±0.06,respectively).The mean a posteriori correlation between RN slope and intercept was 0.81±0.10 and 0.70±0.15,for direct and maternal effect, respectively.This result indicates that animals with higher direct and maternal genetic values responded more efficiently to environmental improvements, i.e. they comprise more responsive genotypes of high plasticity, characterizing a scale effect of GEI (Falconer & Mackay 1996).Scale effects have also been reported by Mattar et al. (2011) in Canchim cattle and by Kolmodin et al. (2002) in protein production of Nordic dairy cattle.Such effect can be observed at all environmental levels, with a special increase in the genetic values of breeders in high-quality production systems (Figure 3).
The scores of some breeders have also changed along the environmental gradient, both for direct and maternal genetic values (Figures 3A and 3B).This kind of interaction is a major handicap for selection, once it results in inadequate choice of breeders to certain environments, thus jeopardizing the effectiveness of genetic improvement.
The slope of RN ranged from −0.36 to 0.23 degrees for the direct effect with a higher incidence of robust and intermediary genotypes (−0.20 and 0.20 degrees), observed in 99.35 % (10 100) of animals.Plastic genotypes (−0.36 to −0.21 and 0.21 to 0.23 degrees) were identified in only 0.65 % (44) of animals.
In the case of maternal effect, the slope values were less variable (−0.15 to 0.14 degrees) thus indicating less variation of the genotypic values across different environments.Nonetheless, the RN for both direct and maternal effects in the 10 breeders with the largest offspring revealed changes in genetic values according to environmental gradient even in less plastic genotypes (Figure 3A and 3B).
These results demonstrate the importance of including GEI in genetic assessments to reach the best performance in distinct environments by selecting highly productive robust genotypes or giving preference to plastic genotypes that respond positively to environment improvements.Spearman's ranking correlations of breeders with highest genetic values ranged from 0.48 to 0.93 in each environment and model when 5 % of top-ranked breeders were chosen (above the diagonal) and from 0.51 to 0.97 when 10 % of top-ranked breeders (below the diagonal) were used (Table 2).The lowest correlation values were observed when the animal model was compared to RN models, thus confirming the interaction between genotype and environment (GEI).No considerable changes in ranking were observed when comparing low, medium and high levels of RNHM 1S Hm.Slight differences were detected between the results based on 5 % and 10 % top-ranked breeders (Table 2).When only 5 % of the top-ranked breeders were taken into account, the greatest difference in classification was observed between low-level RNHM and high-level RNHM (0.48), followed by correlation between AM and low-level RNHM (0.60) and medium-level RNHM and highlevel RNHM (0.67).The correlation values considering 10 % of the best breeders behaved similarly, ranged from 0.52 to 0.97.The highest difference in this case was obtained between AM and low-level RNHM (0.52) and between low-level RNHM and high-level RNHM (0.61).
Both results, based on 5 % or 10 % top-ranked breeders, indicate changes in ranking.
In Devon cattle, Corrêa et al. (2010) obtained Spearman's correlation values for standard post-weaning weight at 365 days varying from 0.12 to 0.98 and from 0.75 to 0.99 for the best 5 % and 10 % breeders, respectively.According to these authors, these values implied moderate to high ranking changes.Different scores were also reported in dairy cattle by Kolmodin et al. (2002), indicating that classification of low-performance ranks would be beneficial only if performed in a specific environment.
Genetic correlations between genetic values at distinct environments were narrower for direct effect in RNHM 1S Hm (0.33 to 1.00) and higher for maternal effect (−0.24 to 1.00) (Figure 4), which characterizes GEI.The present results differ from those reported by Corrêa et al. (2009), who described negative genetic correlations among environmental gradient levels in standard post-weaning weight gain at 365 days.On contrary, Mattar et al. (2011) observed values between 0.24 and 1.00, suggesting that animals were more responsive to improvement of environmental conditions.Both studies show that the genetic pool required for productivity in each environmental level should be different.The application of reaction norm models in GEI studies of Polled Nellore cattle from northeastern Brazil is new and allowed us to identify GEI in this population.A scale effect was observed, with differentiated responses of genotypes in relation to the environmental gradient that determined changes in animal ranking.These changes were more accentuated in high-quality production systems; as the environmental conditions improve, the differences between genetic values increase once animals are able to express their full genetic potential.Genotype-environment interaction (GEI) is present for both direct and maternal effects in Polled Nellore cattle from north-eastern Brazil, both for direct and maternal effect.The assumption of one-step homogeneous residual variance in the reaction norm hierarchical model (RNHM 1S Hm) yielded the best adjustment to data.Scale effects in GEI and ranking changes along the environmental gradient were observed, as confirmed by the correlation variation among breeders of high genetic values.The inclusion of this methodology in improvement programs might increase selection effectiveness, leading to faster genetic progress in this economically important breed.

Figure 1
Figure 1 Flowchart showing the stages required to analyses in the INTERGEN software

Figure 2
Figure 2 Direct and maternal heritability values of weight at 205 days of age (W205) in animal model (AM) and onestep homoscedastic hierarchical reaction norms models (RNHM 1S Hm) according to environmental gradient

Figure 3
Figure 3 Reaction norm for direct (A) and maternal (B) effect in W205 along the environmental gradient in the ten most used breeders

Figure 4
Figure 4 Response surface graph of correlations between direct (A) and maternal (B) genetic values and environmental gradient

Table 2
Spearman's correlations among classifications of Polled Nellore breeders with the highest genetic values raised in north-eastern Brazil (5 % above the diagonal and 10 % below the diagonal) according to animal model (AM) and one-step hierarchical reaction norms model (RNHM 1S Hm) at different environmental levels.