Genetic variation maintained in multilocus models of additive quantitative traits under stabilizing selection

Stabilizing selection for an intermediate optimum is generally considered to deplete genetic variation in quantitative traits. However, conflicting results from various types of models have been obtained. While classical analyses assuming a large number of independent additive loci with individually small effects indicated that no genetic variation is preserved under stabilizing selection, several analyses of two-locus models showed the contrary. We perform a complete analysis of a generalization of Wright's two-locus quadratic-optimum model and investigate numerically the ability of quadratic stabilizing selection to maintain genetic variation in additive quantitative traits controlled by up to five loci. A statistical approach is employed by choosing randomly 4000 parameter sets (allelic effects, recombination rates, and strength of selection) for a given number of loci. For each parameter set we iterate the recursion equations that describe the dynamics of gamete frequencies starting from 20 randomly chosen initial conditions until an equilibrium is reached, record the quantities of interest, and calculate their corresponding mean values. As the number of loci increases from two to five, the fraction of the genome expected to be polymorphic declines surprisingly rapidly, and the loci that are polymorphic increasingly are those with small effects on the trait. As a result, the genetic variance expected to be maintained under stabilizing selection decreases very rapidly with increased number of loci. The equilibrium structure expected under stabilizing selection on an additive trait differs markedly from that expected under selection with no constraints on genotypic fitness values. The expected genetic variance, the expected polymorphic fraction of the genome, as well as other quantities of interest, are only weakly dependent on the selection intensity and the level of recombination

Fluctuating Environments and the Role of Mutation in Maintaining Quantitative Genetic Variation

We study a class of genetic models in which a quantitative trait determined by several loci is subject to temporally fluctuating selection. Selection on the trait is assumed to be stabilizing, but with an optimum that varies periodically and may be perturbed stochastically. The population mates at random, is infinitely large, and has discrete generations. We pursue a statistical and numerical approach, covering a wide range of ecological and genetic parameters, to determine the potential of fluctuating environments in maintaining quantitative-genetic variation. Whereas, in contrast to some recent claims, this potential seems to be rather limited in the absence of recurrent mutation, in combination with it fluctuating environments may frequently generate high levels of additive genetic variation. It is investigated how the genetic variation maintained depends on the ecological parameters and on the underlying genetics

Age differences between distributions of genotypes among pregnant women: evidence of fertility selection.

SummaryThe number of children produced by a modern woman is usually below her total reproductive capacity and is determined by circumstances other than natural selection. It is, therefore, practically impossible to detect differences in natural fertilities associated with different types (e.g. phenotypes, genotypes) of women. This does not mean, however, that natural selection at the reproductive level cannot at all be detected today. If women of a particular type have high natural fertility, this usually means that they reproduce (become pregnant) at a higher rate than women of a type with lower natural fertility. Hence, when there is a limit on the number of children, women of the first type will reach the limit at an earlier age than women of the second type. As a result, types that have a higher natural fertility should be overrepresented among pregnant women of younger ages and, consequently, underrepresented among older ones, as compared to types with a lower natural fertility. Based on this notion, a model of age-related differences between distributions of types among pregnant women is suggested. The model is applied to data on MNSs-blood group and PGM1 (phosphoglucomutase) types in a sample of pregnant women and an evidence of natural selection at the reproduction level associated with these genetic markers is obtained

Quantitative character dynamics: Gametic model

A gametic model of quantitative character dynamics is introduced that fills the gap between the two existing models: genic and zygotic/phenotypic. In this model, a gamete is treated as the elementary unit of evolution, all biological processes at the levels below gametic remain unspecified, and a gamete is characterized by its effect on the quantitative character rather than by the genotype. The hereditary and developmental processes are accounted for in a generalized form by gametogenetic and developmental functions defined for a pair of gametic effects representing an individual. A parameterization of these functions is suggested that imposes constraints on the heredity of quantitative characters similar to the constraints imposed by traditional genic models. It is shown that this parameterization can be derived for some polygenic additive models. General expressions for the dynamics of the mean and variance of additive quantitative characters are obtained, and the dynamics under random mating for sex-independent, sex-controlled, and sex-linked characters are considered. Comparisons with the dynamics predicted by genic models are made.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23784/1/0000022.pd

Analysis of “nontraditional” relationships under assortative mating

The set of conditions on the genetical and developmental mechanisms of quantitative characters as well as on selection and mating system presented in (Gimelfarb, 1981) is expanded, thus enabling one to obtain the genotypic covariances between relatives for a larger variety of relationships. It is also demonstrated that the frequency of a relationship in a population under assortative mating may in general be different from the frequency of this relationship in the population under random mating. A subpopulation of relatives is not necessarily a representative sample of the whole population with respect to the quantitative character distribution. However, for any relationship which is a combination of descendant-ancestor, full sib, Type 1 and Nth uncle-niece relationships, its frequency in a population under assortative mating is the same as in the population under random mating, and the subpopulation of such relatives is a representative sample of the whole population.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46942/1/285_2004_Article_BF00275216.pd

A general linear model for the genotypic covariance between relatives under assortative mating

A linear model for the genotypic covariance between relatives under assortative mating comprising the “classical linear model” and the model of “selective assortative mating” is proposed. The general conditions on the genetical and developmental mechanisms of quantitative characters, as well as on selection and the mating system, on which the model is based, are explicitly stated and discussed. A classification of different relationships is presented and it is shown that these conditions are sufficient to obtain the genotypic covariance between relatives only if the relationship is a combination of descendant-ancestor, full sib, Type 1 and N th uncle-niece relationships. All the “traditional” relationships, i.e., those for which the covariances of the relatives have been obtained in the literature, fall into this category. These conditions also ensure that the regression of the individual's genotypic value on the genotypic value or phenotype of any of its ancestors is always linear.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46941/1/285_2004_Article_BF00275215.pd

Phosphotyrosine-protein-phosphatases and human reproduction: an association between low molecular weight acid phosphatase (ACP1) and spontaneous abortion.

ACP1 (low molecular weight acid phosphatase) genetic polymorphism has been studied in 173 women with a history of two or more consecutive spontaneous abortions and in 1508 control subjects, including 482 normal pregnant women. The proportion of carriers of ACP1 *C allele (* A/ *C, *B/*C) in women with a history of repeated spontaneous abortion is lower than in normal pregnant women and other control groups, Women with repeated spontaneous abortion show a specific decrease of ACPI S isoform concentration as compared to normal pregnant women, The other component of ACP I activity, the F isoform, does not show a significant difference between the two groups. The data suggest that women with ACP1 genotypes showing a high concentration of S isoform are relatively 'protected' against spontaneous abortion, Preliminary analysis of a sample of 352 normal puerperae along with their newborn babies supports this hypothesis

Le Chatelier principle in replicator dynamics

The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has deep roots, e.g., in thermodynamics it is closely related to the second law and the positivity of the entropy production. Here we study the applicability of the Le Chatelier principle to evolutionary game theory, i.e., to perturbations of a Nash equilibrium within the replicator dynamics. We show that the principle can be reformulated as a majorization relation. This defines a stability notion that generalizes the concept of evolutionary stability. We determine criteria for a Nash equilibrium to satisfy the Le Chatelier principle and relate them to mutualistic interactions (game-theoretical anticoordination) showing in which sense mutualistic replicators can be more stable than (say) competing ones. There are globally stable Nash equilibria, where the Le Chatelier principle is violated even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium can amplify small perturbations, though both this type of equilibria satisfy the detailed balance condition.Comment: 12 pages, 3 figure

Dynamical Models in Quantitative Genetics

In this paper the author investigates models in quantitative genetics and shows that under quite reasonable assumptions the dynamics can display rather counter-intuitive behavior. This research was conducted as part of the Dynamics of Macrosystems Feasibility Study in the System and Decision Sciences Program

Understanding and using quantitative genetic variation

Quantitative genetics, or the genetics of complex traits, is the study of those characters which are not affected by the action of just a few major genes. Its basis is in statistical models and methodology, albeit based on many strong assumptions. While these are formally unrealistic, methods work. Analyses using dense molecular markers are greatly increasing information about the architecture of these traits, but while some genes of large effect are found, even many dozens of genes do not explain all the variation. Hence, new methods of prediction of merit in breeding programmes are again based on essentially numerical methods, but incorporating genomic information. Long-term selection responses are revealed in laboratory selection experiments, and prospects for continued genetic improvement are high. There is extensive genetic variation in natural populations, but better estimates of covariances among multiple traits and their relation to fitness are needed. Methods based on summary statistics and predictions rather than at the individual gene level seem likely to prevail for some time yet