Mixed Models for Genetic analysis

Mixed Models for Genetic AnalysisSingle Trait Animal ModelThe simple mixed model used in animal breeding is a single trait animal model. It is an'animal' model because we fit a breeding value for each animal. ‘Single trait’ refers to thefact that animals have only observations on one character (trait) and there are only fixedeffects and additive genetic effects, and no other random effects such as maternal ordominance. It is important to understand the principles of the simplest model. Less simplemodels are based on the same principles, and therefore not really much more difficult tounderstand. Like in any other statistical model building more complicated models largelyrequires more knowledge of the data, and imagination of effects that could possibly becausing differences.More detailIn the single trait animal model with breeding value as the only random effect, we assume often that thematrix R is s equal to Iσ 2 e and the matrix G is equal to Aσ 2 a. The simple equations were therefore obtainedby multiplying the equations with the factor σ 2 e.⎛X'X⎜⎝ Z' XZ' ZX' Z+ λA−1⎞⎟⎠⎛⎜⎝b^u^⎞⎟⎠⎛X'Y⎞= ⎜ ⎟⎝ Z' Y ⎠2 2where λ = σ .e / σIN ASREML:Analysis of some kindanim !P The variable ‘anim’ is related to a pedigree filedage 10 !Art 6wwtgrp 322 !Aexample.pedexample.datwwt ~ mu rt dage !r anim !f grp#model definitionThere is no need to define variance structures more specifically, as there is only one extrarandom effect (besides residual) so one component of variance. One could put a scalrbehind the anim variable in the model statement to indicate a starting value (optional).i.e.bwt ~ mu bt dage !r anim 0.5 !f grpa#model definition50