The aim of this study was to estimate G*E interactions for production traits in the Holstein and Normande breeds in France. Genetic correlations between environments were very close to unity, except between very extreme environments for all breeds, models, and datasets, demonstrating that reranking of animals for production traits across environments does not exist in France. Such a result was previously reported in studies in France that used herd production level as definition of herd environment
 as well as in other studies
[9–11] that used different definitions of the environment. Yet, other studies did report genetic correlations less than one between environments, i.e., with reranking of animals. These studies dealt with data from different countries
[12–15], that is, for ranges of environments that were greater than in this national study.
Variable genetic variances across environments for production traits were found in this study and have been reported before
[9, 16]. Genetic variances increased with the capacity of the herd management to promote milk production. These results are in agreement with
[8, 9, 17], in which genetic variances increased with increasing production level.
In a G*E interaction study, the definition of the herd environment is crucial. Definitions used in the literature are extremely diverse; they depend on the scale of the study (experimental farm versus national or international studies) and on the traits analysed. In the case of production traits, definition of the herd environment can be based on specific features of the feeding system, such as the level of concentrate in the diet
[18, 19], grazing severity and silage quality
, features of the reproduction system, such as the calving system (seasonal or uniform)
, features of the herd structure, such as herd size
, features of the climate such, as temperature humidity index
, or features of genetic background (percent of Holstein genes)
. Many studies have described the environment based on observed performances of the animals, such as herd milk production level
[8, 21], fat and protein yields
, peak milk yield, or persistency
. In these cases, environmental and genetic factors are combined. In this study, herd environment was described based on HTD profiles. This definition focuses on the part of the production due to herd management only. This improves the study of G*E interactions because environmental and genetic factors are no longer confounded in the definition of the environment. Moreover, HTD profiles are available from national databases and do not require extra recording, in contrast to many herd management descriptors. Using HTD profiles allows analysis of large datasets. Finally, HTD profiles summarize all impacts of environment on production and offer a general overview of the environment, whereas some other herd management descriptors reduce environment to a limited number of features (temperature, average performances, herd size).
Summarizing HTD profiles descriptors by first PC scores allowed correlations between the 21 descriptors to be taken into account and a focus on the main causes of variability among HTD profiles. However, by limiting the analysis to the first PC scores, part of the diversity of HTD profiles that reflect differences in herd management (i.e., environment diversity) was not accounted for, regardless of the model used (multiple-trait, single-trait or reaction norm model). In fact, the three herd clusters used to describe the environment in the multiple-trait model were built based on the first 10 PC scores only, which explained about 76% of the total variance in HTD profiles. Moreover, we selected paragon herds for each cluster, which reduced the within-environment diversity. For the reaction norm models, the environment was described only through one or two PC scores. This may seem reductive but reaction norm models based on three PC scores gave poorer goodness of fit in terms of the BIC.
The models that were used to estimate G*E interactions were animal models with pedigree information over three generations, in contrast with other studies that used simpler models such as sire models
[13, 16] or sire-maternal grand sire models
. Two types of models were tested: multiple-trait and reaction norm models. A drawback of multiple-trait models is that they require classification of environments, which cannot represent the full diversity of environments. Moreover, in this study, the multiple-trait model was applied to the “paragon” dataset, in which extreme environments were not represented, which led to a reduction in environmental variance. Despite this reduced diversity of environments, a clear heterogeneity of heritabilities among the three herd clusters was identified. In contrast, reaction norms model an “infinite” number of environments, which more precisely depicts the existing continuum of the environment. Generally, the parameter that describes the environment in reaction norm models is a single measure such as age at calving, herd size
, or herd-year averages of protein yield
. This environment parameter can also be a synthetic variable that summarizes information of several environmental variables. In
, 65 environmental variables were reduced into four PC by a factor analysis and were used separately. Hence, one major improvement in the current study was that several PC were used simultaneously to describe the environment. The number of parameters to estimate in the model was limited by using linear reaction norms rather than more sophisticated functions such as polynomials. The next step will be to study the possibility to simultaneously account for a larger number of PC to describe the environment. In particular, a reduced rank genetic matrix could be used to summarize the effect of several PC on the genetic effect. Reaction norm models applied to the diversity dataset allowed the investigation of extreme environments (for one or two PC). Here, an average residual variance which did not depend on the environment was used to estimate heritabilities with the reaction norm model. Consequently, differences of heritabilities across environments were only due to differences in genetic variances, which may have exacerbated differences in heritabilities between environments. These differences of heritabilities across environments might be exacerbated by the use of linear reaction norms and of an average residual variance. Thus, the reaction norm model could be improved by allowing different residual variances across environments.
No reranking of animals was shown for production traits. These traits have been selected for a long time, and thus, animals may be well adapted to all herd managements that currently exist in France. Nevertheless, within the context of the development of a sustainable agriculture, new ecological constraints appear such as controlling the use of phytosanitary products or protecting some agricultural areas. Also, new economical constraints due to reorganization of agricultural areas, with a decrease in the number of farmers or the end of quotas and liberalisation of milk production could raise new types of herd managements. Depending on how breeders react to these constraints, the range of environments could get larger. Thus, G*E interaction studies will have to be updated in order to assess whether animals remain well adapted to all herd environments.
Greater G*E interactions might exist for more recently selected traits. For these traits, the processes may not have already removed the animals’ capacity to be specifically adapted to a particular environment. Thus, on a follow-up study, we will investigate G*E interactions on functional traits.