If not accounted for, genotype x environment (G×E) interactions can decrease the accuracy of genetic evaluations and the efficiency of breeding schemes. These interactions are reflected by genetic correlations between countries lower than 1. In countries that are characterized by a heterogeneity of production systems, they are also likely to exist within country, especially when production systems are diverse, as is the case in South Africa. We illustrate several alternative approaches to assess the existence of G×E interactions for production traits and age at first calving in Holsteins in South Africa. Data from 257,836 first lactation cows were used. First, phenotypes that were collected in different regions were considered as separate traits and various multivariate animal models were fitted to calculate the estimates of heritability for each region and the genetic correlations between them. Second, a random regression approach using long-term averages of climatic variables at the herd level in a reaction norm model, was used as an alternative way to account for G×E interactions. Genetic parameter estimates and goodness-of-fit measures were compared. Genetic correlations between regions as low as 0.80 or even lower were found for production traits, which reflect strong G×E interactions within South Africa that can be linked to the production systems (pasture vs total mixed ration). A random regression model including average rainfall during several decades in the herd surroundings gave the best goodness-of-fit for production traits. This can be related to a preference for total mixed ration on farms with limited rainfall. For age at first calving, the best model was based on a random regression on maximum relative humidity and maximum temperature in summer. Our results indicate that G×E interactions can be accounted for when genetic evaluations of production traits are performed in South Africa, by either considering production records in different regions as different correlated traits or using a reaction norm model based on herd management characteristics. From a statistical point of view, climatic variables such as average rainfall over a long period can be included in a random regression model as proxies of herd production systems and climate.

中文翻译：

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两种方法来解释南非荷斯坦牛第一次产犊时基因型与环境相互作用的生产性状和年龄

如果不考虑，基因型 x 环境 (G×E) 相互作用会降低遗传评估的准确性和育种计划的效率。这些相互作用反映在低于 1 的国家之间的遗传相关性上。在以生产系统异质性为特征的国家，它们也可能存在于国内，特别是当生产系统多样化时，如南非的情况。我们说明了几种替代方法来评估南非荷斯坦牛首次产犊时生产性状和年龄的 G×E 相互作用的存在。使用了来自 257,836 头初产奶牛的数据。第一的，在不同地区收集的表型被认为是单独的性状，并拟合了各种多变量动物模型来计算每个地区的遗传力估计值以及它们之间的遗传相关性。其次，在反应范数模型中使用牛群水平气候变量的长期平均值的随机回归方法被用作解释 G×E 相互作用的替代方法。比较了遗传参数估计和拟合优度测量。对于生产性状，发现区域之间的遗传相关性低至 0.80 甚至更低，这反映了与生产系统（牧场与总混合日粮）相关的南非境内强烈的 G×E 相互作用。一个随机回归模型，包括畜群周围几十年的平均降雨量，给出了生产性状的最佳拟合优度。这可能与降雨量有限的农场偏爱全混合日粮有关。对于第一次产犊的年龄，最好的模型是基于夏季最大相对湿度和最高温度的随机回归。我们的结果表明，在南非进行生产性状的遗传评估时，可以通过将不同地区的生产记录视为不同的相关性状或使用基于畜群管理特征的反应规范模型来解释 G×E 相互作用。从统计的角度来看，