Model for fitting longitudinal traits subject to threshold response applied to genetic evaluation for heat tolerance

Reaction norm models have been proposed as an alternative for fitting Genotype by Environment interactions (GxE) in evolutionary biology and animal breeding [1]. In reaction norm models, the environment is often described by a continuous variable, and the phenotypes are partially explained by the regression of the genotypic values on the environmental values. When an environmental variable is observed on a continuous scale (i.e., temperature), it is expected to have a direct one-to-one relationship between the environmental scale and values. Consequently, the reaction norm model can be fitted by regressing the genotypic values on the observed environmental scale [2,3]. When the observed environmental scale is not continuous (i.e., herd classes), the genotypic values can be regressed on the effect of the categorical variable defining the different environments using, for example, least squared means of the class effects [4] or inferring the environmental values jointly with the remaining set of parameters in the model [5].In animal breeding applications of reaction norm models, it was assumed that both the mean and the variances are either continuous, monotone functions of the environmental values [4,6] or that they are such only when the environmental values exceed a certain threshold [2,7,3]. In past studies involving thresholds, the same threshold was assumed for all animals, and it was estimated based on the quality of the fit of the average performances as a function of environmental values.The objective of this study was to present a Bayesian hierarchical model for fitting a longitudinal trait showing an abrupt linear change at some value of the independent variable. Simulations were inspired by reaction norm models, and the procedure postulates that the effect of the environmental variable is not existent until it exceeds a certain unknown value particular for each individual with data. Furthermore, the model allows for partitioning individual variability on t