Quantitative characters under assortative mating: gametic model

The gametic model introduced by Gimelfarb (1982, Theor. Pop. Biol. 22, 324-366) is applied to investigating the dynamics, represented in the model by a second-order recurrence equation, the the variance of sex-independent and sex-controlled characters under assortative mating. It is shown that, for any additive character, there always exists a unique equilibrium for the variance, which is stable. Dynamical properties of the variance under positive and negative matings are considered, and numerical evaluations of the equilibrium values as well as of the dynamical changes of the variance are presented. Comparisons with results from a biological experiment are made.