On identifiability of (co)variance components in animal models with competition effects.

RODOLFO J. C. CANTET; CAPPA EDUARDO P.

JOURNAL OF ANIMAL BREEDING AND GENETICS-ZEITSCHRIFT FUR TIERZUCHTUNG UND ZUCHTUNGSBIOLOGIE

Wiley - Blackwell

Lugar: New York; Año: 2008 vol. 125 p. 371 - 381

0931-2668

There is an increased interest in estimating the (co)variance components of additive animal models with direct and competition effects (AMC). However, some attempts to estimate the dispersion parameters in different animal species faced problems of convergence or inaccurate estimates when pen effects entered the model. We argue that the problem relates to lack of identifiability of the (co)variance components in some AMC. The check for identifiability of the dispersion parameters in mixed models with linear (co)variance structure requires that all the eigenvalues of the REML information matrix (I(è)) be positive. We show, by way of simple numerical examples, that the singularity of I(è) is due to confounding between fixed pen effects and the additive competition effects (SBVs). It is also observed that setting pen effects as random does not always remedy the collinearity with SBVs. An alternative AMC is presented in which the incidence matrix of the SBVs can be written as a function of the “intensity of competition” (IC) among animals in the same pen. Examples are presented in which the IC’s are related to time. The distribution of families of full and half sibs across pens also plays a role in the identifiability and asymptotic variances of the (co)variance components.