“Sweet FA”: Scope for a factor-analytic model for genotype

8 A review of the literature is presented, showing that the mixed model 9 analogues of models employed in the analysis of multi-environment trials in 10 plant breeding are directly applicable to genotype × environment and related 11 problems in animal breeding. In particular, the so-called ’additive main effect, 12 multiplicative interaction’ or ’bi-linear’ models accommodate heterogeneity 13 of variance and are characterised by a factor-analytic covariance structure. 14 While this can be implemented by imposing such structure on the genetic 15 covariance matrix in a multi-trait model, an equivalent model is to fit the ge16 netic common factors and specific effects separately. This increases the total 17 number of equations in the model. However, as both common factors and 18 specific effects for an individual are uncorrelated, the coefficient matrix in 19 the pertaining mixed model equations is sparse, with dramatically reduced 20 non-zero off-diagonal elements. Using international genetic evaluation as an 21 example, it is shown that such ‘extended’ factor analytic model can substan22 tially reduce computational requirements of genetic evaluation schemes, in 23 addition to providing a parameterisation which is of interest in its own right. 24 Cases investigated include simulated data for a trait recorded in 8, 12 or 16 25 countries, and data on weaning weight in beef cattle, including those from 26 a current feasibility study for a world-wide genetic evaluation in Hereford. 27 Results suggest that with judicious implementation, reductions in computing 28 time of 50% or more are feasible. 29 factor analysis / genotype x environment interaction / genetic evaluation / 30 mixed model /multivariate 31