Technical note: An approach to derive breeding goals from the preferences of decision makers

This paper deals with the use of the Choquet integral to identify breeding objectives and construct an aggregate genotype. The Choquet integral can be interpreted as an extension of the aggregate genotype based on profit equations, substituting the vector of economic weights by a monotone function, called capacity, which allows the aggregation of traits based, for instance, on the preferences of decision makers. It allows the aggregation of traits with or without economic value, taking into account not only the importance of the breeding value of each trait but also the interaction among them. Two examples have been worked out for pig and dairy cattle breeding scenarios to illustrate its application. It is shown that the expression of stakeholders' or decision makers' preferences, as a single ranking of animals or groups of animals, could be sufficient to extract information to derive breeding objectives. It is also shown that coalitions among traits can be identified to evaluate whether a linear additive function, equivalent of the Hazel aggregate genotype where economic values are replaced by Shapley values, could be adequate to define the net merit of breeding animals.