A DETERMINISTIC MULTI-TIER MODEL OF ASSORTATIVE MATING FOLLOWING SELECTION

A deterministic model is presented of assortative mating following sel ection on either phenotype or best linear unbiased prediction (BLUP) e stimates of breeding values (ebv) in an infinite population. The model is based on modified theory for multitier open nucleus breeding schem es. It is shown that the percentage increase in genetic gain of assort ative mating over random mating is greatly increased at low to moderat e heritability when BLUP rather than mass selection is used. The perce ntage increase in genetic gain at equilibrium of assortative mating ov er random mating is independent of initial heritability and family str ucture when selection is on BLUP ebv. The same is true in the early ge nerations if there is ample pedigree history available before selectio n commences. The deterministic prediction of the percentage increase i n genetic gain at equilibrium of assortative mating over random mating is 11, 24 and 66% when 10, 50 and 90% of progeny are selected on BLUP ebv. Stochastic simulation is used to evaluate the accuracy of the de terministic model. Both deterministic and stochastic results for assor tative mating indicate a considerably increased value over random mati ng in certain situations than has previously been reported.