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Background  Modern dairy cattle breeding goals include several production and more and more functional traits. Estimated breeding values (EBV) that are combined in the total merit index usually come from single-trait models or from multivariate models for groups of traits. In most cases, a multivariate animal model based on phenotypic data for all traits is not feasible and approximate methods based on selection index theory are applied to derive the total merit index. Therefore, the objective of this study was to compare a full multitrait animal model with two approximate multitrait models and a selection index approach based on simulated data.    Methods  Three production and two functional traits were simulated to mimic the national Austrian Brown Swiss population. The reference method for derivation of the total merit index was a multitrait evaluation based on all phenotypic data. Two of the approximate methods were variations of an approximate multitrait model that used either yield deviations or de-regressed breeding values. The final method was an adaptation of the selection index method that is used in routine evaluations in Austria and Germany. Three scenarios with respect to residual covariances were set up: residual covariances were equal to zero, or half of or equal to the genetic covariances.    Results  Results of both approximate multitrait models were very close to those of the reference method, with rank correlations of 1. Both methods were nearly unbiased. Rank correlations for the selection index method showed good results when residual covariances were zero but correlations with the reference method decreased when residual covariances were large. Furthermore, EBV were biased when residual covariances were high.    Conclusions  We applied an approximate multitrait two-step procedure to yield deviations and de-regressed breeding values, which led to nearly unbiased results. De-regressed breeding values gave even slightly better results. Our results confirmed that ignoring residual covariances when a selection index approach is applied leads to remarkable bias. This could be relevant in terms of selection accuracy. Our findings suggest that the approximate multitrait approach applied to de-regressed breeding values can be used in routine genetic evaluation.

A comparison of methods to calculate a total merit index using stochastic simulation