On estimating (co)variance components in animal models with competition effects

There is an increased interest in estimating the (co)variance components of additive animal models with direct and competition effects (AMC). However, all attempts to estimate the dispersion parameters in different animal species faced problems of convergence and highly variable estimates. The trouble is related with the lack of asymptotic identifiability in certain AMC. This property is observed when calculating the 4 × 4 information matrix (I(θ)) for the AMC REML likelihood, and its smallest eigenvalue goes to zero. The singularity of I(θ) is due to confounding between the fixed pen (contemporary group) effect and the additive competition effects. The incidence matrix of additive competition effects (Zc) can be written as a function of the “intensity of competition” (IC) among animals in a contemporary group. The IC values can be interpreted as weighting factors expressing how intense pairs of animals compete in relation to all other animals. The sum of squares of the IC values in any row of Zc should add up to 1 (standardization) in order for the phenotypic variance of any given observation not to be affected by the number of competitors. Moreover, data sets to estimate the (co)variance components in the AMC should be obtained with some sort of design in order for the (co)variance components to be asymptotically identifiable. Examples are presented in which the IC’s are related to either time or number of competitors in the pen.