The evolution of a quantitative trait subject to stabilizing selection and immigration, with the
immigrants deviating from the local optimum, is considered under a number of different models of
the underlying genetic basis of the trait. By comparing exact predictions under the infinitesimal
model obtained using numerical methods with predictions of a simplified approximate model based
on ignoring linkage disequilibrium, the increase in the expressed genetic variance as a result of
linkage disequilibrium generated by migration is shown to be relatively small and negligible,
provided that the genetic variance relative to the squared deviation of immigrants from the local
optimum is sufficiently large or selection and migration is sufficiently weak. Deviation from
normality is shown to be less important by comparing predictions of the infinitesimal model with a
model presupposing normality. For a more realistic symmetric model, involving a finite number of
loci only, no linkage and equal effects and frequencies across loci, additional changes in the genetic
variance arise as a result of changes in underlying allele frequencies. Again, provided that the
genetic variance relative to the squared deviation of the immigrants from the local optimum is
small, the difference between the predictions of infinitesimal and the symmetric model are small
unless the number of loci is very small. However, if the genetic variance relative to the squared
deviation of the immigrants from the local optimum is large, or if selection and migration are
strong, both linkage disequilibrium and changes in the genetic variance as a result of changes in
underlying allele frequencies become important.