Economic weights for restriction of selection index as optimal strategy for combining multiple traits

Presently, selection indices combine EBV belonging to many phenotypes accounting for production and functional traits. In this situation, ensuring positive genetic trends becomes difficult, especially when an antagonistic genetic relationship between traits exists. For this reason, guaranteeing zero genetic progress for some traits could be advantageous, as it would allow maximization of the productive characteristics while maintaining steady other antagonistic traits. This approach can also be useful for traits with an intermediate optimum, such as type traits, or for phenotypes for which it is difficult to quantify a specific economic weight. On this point, deriving the economic weight for a restricted selected index can be an optimal strategy. In this article, we provide a brief demonstration of how to derive economic weights by the restriction of some antagonistic traits. This procedure is then validated in a real-life situation using a dual-purpose cattle breed, due to the presence of more than one antagonistic trait with respect to milk yield. The R code is also provided to apply this procedure. The practical application to an actual situation demonstrates that the method produces feasible solutions in situations where more antagonistic traits are considered for selection, and prevents the detriment of some functional traits. Finally, we demonstrated how to obtain the desired restricted genetic progress when heterogeneous sources of information are present and its influence on selection response.