title: The selection limit due to the conflict between truncation and stabilizing selection with mutation.
abstract: Long-term selection response could slow down from a decline in genetic variance or in selection differential or both. A model of conflict between truncation and stabilizing selection in infinite population size is analysed in terms of the reduction in selection differential. Under the assumption of a normal phenotypic distribution, the limit to selection is found to be a function of kappa, the intensity of truncation selection, omega 2, a measure of the intensity of stabilizing selection, and sigma 2, the phenotypic variance of the character. The maintenance of genetic variation at this limit is also analyzed in terms of mutation-selection balance by the use of the "House-of-cards" approximation. It is found that truncation selection can substantially reduce the equilibrium genetic variance below that when only stabilizing selection is acting, and the proportional reduction in variance is greatest when the selection is very weak. When truncation selection is strong, any further increase in the strength of selection has little further influence on the variance. It appears that this mutation-selection balance is insufficient to account for the high levels of genetic variation observed in many long-term selection experiments.
mesh_terms: D000483:Alleles; D014644:Genetic Variation; D008433:Mathematics; D008957:Models, Genetic; D009154:Mutation; D010641:Phenotype; D012641:Selection, Genetic