Three approximations to the combined model likelihood (including varia
tion due to both polygenes and a major gene) used in segregation analy
sis were compared in their ability to estimate the parameters describi
ng the model. Paternal half-sib data simulated under four different co
mbined models were used. In general, when a combined model provides th
e best explanation of the data the parameter estimates from all three
approximations investigated are, on average, in good agreement with th
e values simulated. The use of Hermite integration to replace the inte
gration in the combined model likelihood provided the parameter estima
tes closest to those simulated. The other two approximations, based on
extensions of linear mixed-model theory, gave estimates further from
the expected values, however, these latter two methods can estimate tr
ansmitting abilities for the sires directly from the analyses. The thr
ee approximations are similar in their ability to genotype sires at th
e major locus. On average, with the models studied here, about 65 per
cent of sires can be successfully genotyped.