Is offspring-midparent regression affected by assortative mating of parents?
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Analysis of Variance↗
Biomedical subjects
A Gimelfarb
Publications and source records attributed to A Gimelfarb.
Additive variation maintained under stabilizing selection: a two-locus model of pleiotropy for two quantitative characters.
A model with two diallelic loci controlling two additive quantitative characters is suggested. One of the loci has a similar effect on both characters, whereas the second locus has an antagonistic effect on two characters. Both characters experience direct stabilizing selection. The model yields a stable polymorphic state, with both characters maintaining genetic variation. The genetic correlation between the characters at the equilibrium is zero, in spite of the pleiotropic effects of the loci controlling them.
Alleles↗
Multiplicative genotype-environment interaction as a cause of reversed response to directional selection.
In experiments with directional selection on a quantitative character a "reversed response" to selection is occasionally observed, when selection of individuals for a higher (lower) value of the character results in a lower (higher) value of the character among their offspring. A sudden change in environments or random drift is often assumed to be responsible for this. It is demonstrated in this paper that these two causes cannot account for the reversed response at least in some of the experiments. Multiplicative genotype-environment interaction is discussed as a possible cause of a reversed response to directional selection. Such interaction entails either disruptive or stabilizing genotypic selection, even when the phenotypic selection is directional.
Animals↗
Offspring-parent genotypic regression: how linear is it?
Linearity of offspring-parent regression is investigated for quantitative characters with dominance. This is done by fitting a second-order regression equation in orthogonal bivariate polynomials to the offspring's genotypic value and evaluating the significance of nonlinear terms in the equation. Three genetic models are considered.
Animals↗
The significance of specific distributions and functions in models of quantitative inheritance.
The main purpose of this paper is to attract attention to the fact that a mathematical model of quantitative inheritance can lead to qualitatively different results, if distributions and functions which in the model represent biological processes are assumed to take analytically different (even though qualitatively similar) forms. A simple model of the effect of environmental variation on the post-selection genotypic variance in a population under phenotypic stabilizing selection is considered. It is demonstrated that this model leads to qualitatively different conclusions depending on whether the phenotypic fitness function is assumed in a Gaussian or in a quadratic form.
Genetics, Population↗
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.
Alleles↗
On the within-sibship variance.
An approximate formula for the expected within-sibship genotypic variance of a polygenic, diallelic, additive character is obtained for arbitrary recombination between the loci affecting the character. The formula is exact, when there is no recombination, or when the recombination is free. It is also shown that, if the value of 1/2Vk (one-half of the parental genotypic variance) is assigned to the within-sibship genotypic variance, as in the model of Cavalli-Sforza and Feldman (1976, Proc. Natl. Acad. Sci. USA 73, 1689-1692), it implies the assumptions of random mating and of the perfect linkage. If, on the other hand, the value of 1/2Vo (one-half of the linkage equilibrium genotypic variance) is assigned to the within-sibship variance, as in the model of Rice, Cloninger, and Reich (1978, Amer. J. Hum. Genet. 30, 618-643), it implies the assumptions of random mating and either of the free recombination, or of the linkage equilibrium, if the recombination is not free.
Animals↗