Pleiotropy as a factor maintaining genetic variation in quantitative characters under stabilizing selection

A model of pleiotropy with N diallelic loci contributing additively to N quantitative traits and stabilizing selection acting on each of the traits is considered. Every locus has a major contribution to one trait and a minor contribution to the rest of them, while every trait is controlled by one major locus and N-1 minor loci. It is demonstrated that a stable equilibrium with the allelic frequency equal to 0.5 in all N loci can be maintained in such a model for a wide range of parameters. Such a 'totally polymorphic' equilibrium is maintained for practically any strength of selection and any recombination, if the relative contribution by a minor locus to a trait is less than 20% of the contribution by a major locus. The dynamic behaviour of the model is shown to be quite complex with a possibility under sufficiently strong selection of multiple stable equilibria and positive linkage disequilibria between loci. It is also suggested that pleiotropy among loci controlling traits experiencing direct selection can be responsible for apparent selection on neutral traits also controlled by these loci.