HOW MUCH HERITABLE VARIATION CAN BE MAINTAINED IN FINITE POPULATIONS BY MUTATION-SELECTION BALANCE?

The joint effects of stabilizing selection, mutation, recombination, and random drift on the genetic variability of a polygenic character in a finite population are investigated. A simulation study is performed to test the validity of various analytical predictions on the equilibrium genetic variance. A new formula for the expected equilibrium variance is derived that approximates the observed equilibrium variance very closely for all parameter combinations we have tested. The computer model simulates the continuum-of-alleles model of Crow and Kimura. However, it is completely stochastic in the sense that it models evolution as a Markov process and does not use any deterministic evolution equations. The theoretical results are compared with heritability estimates from laboratory and natural populations. Heritabilities ranging from 20% to 50%, as observed even in lab populations under a constant environment, can only be explained by a mutation-selection balance if the phenotypic character is neutral or the number of genes contributing to the trait is sufficiently high, typically several hundred, or if there are a few highly variable loci that influence quantitative traits.