Considerations on measures of precision and connectedness in mixed linear models of genetic evaluation

Abstract

Three criteria for the quality of a genetic evaluation are compared: the prediction error variance (PEV); the loss of precision due to the estimation of the fixed effects (degree of connectedness) (IC); and a criterion related to the information brought by the evaluation in terms of generalized coefficient and determination (CD) (precision). These criteria are introduced through simple examples based on an animal model. The main differences between them are the choice of the matrix studied (CD vs PEV, IC), the method used to account for the relationships (CD vs PEV), the use of a reference matrix or model (PEV vs CD, IC), and the data design (IC vs PEV, CD). IC is shown to favor designs with limited information provided by the data and another index is suggested, which minimizes this drawback. The behavior of IC and CD is studied in a hypothetical 'herd + sire' model. The precision criteria set a balance between connectedness level and information provided by the data, whereas the connectedness criteria favor the model with minimum information and maximum connectedness level. Genetic relationships between animals decrease both PEV and genetic variability. PEV considers only the favorable effects on PEV; CD accounts for both effects. CD sets a balance between the design and the information brought by the data, the PEV and the genetic variability and is thus a method of choice for studying the quality of a genetic evaluation.