Case Of Single Locus Research Articles

Modelling of selection acting upon the pleioptropic locus in a population with two age classes

We created and examined a mathematical model describing the size and genetic composition dynamics in a population with two age classes, where the survival of both zygotes and adult individuals is determined by one pleioptropic locus. Even under present limitations, as the outside effects of a complex multigenic system are reduced to the case of single locus, our model demonstrates a wide range of different evolutionary scenarios for possible changes in the population dynamics. An increase in the reproductive potential and survival is accompanied by a transition from stable to oscillating population numbers. However, the evolutionary growth of these parameters may be nonmonotonic and may fluctuate significantly. In the case of antagonistic pleioptropy, an increase in one of these parameters usually leads to a predictable decrease in the other. This, in turn, may even stabilize the numbers and genetic compositions of the age groups. We demonstrated that selection acting on later stages of the life cycle is accompanied by violation of the Hardy-Weinberg equilibriums that link allele and genotype frequencies. We obtained a balance ratio, which allowed us to compare the combined fitness of the genotypes and to demonstrate that selection leads to the exclusion of the least adapted genotypes. Initial conditions may in some cases determine the genetic composition and pattern of population size dynamics.

One- and Two-Locus Population Models With Differential Viability Between Sexes: Parallels Between Haploid Parental Selection and Genomic Imprinting

A model of genomic imprinting with complete inactivation of the imprinted allele is shown to be formally equivalent to the haploid model of parental selection. When single-locus dynamics are considered, an internal equilibrium is possible only if selection acts in the opposite directions in males and females. I study a two-locus version of the latter model, in which maternal and paternal effects are attributed to the single alleles at two different loci. A necessary condition for the allele frequency equilibria to remain on the linkage equilibrium surface is the multiplicative interaction between maternal and paternal fitness parameters. In this case the equilibrium dynamics are independent at both loci and results from the single-locus model apply. When fitness parameters are additive, analytic treatment was not possible but numerical simulations revealed that stable polymorphism characterized by association between loci is possible only in several special cases in which maternal and paternal fitness contributions are precisely balanced. As in the single-locus case, antagonistic selection in males and females is a necessary condition for the maintenance of polymorphism. I also show that the above two-locus results of the parental selection model are very sensitive to the inclusion of weak directional selection on the individual's own genotypes.

The donation game with roles played between relatives

We consider a social game with two choices, played between two relatives, where roles are assigned to individuals so that the interaction is asymmetric. Behaviour in each of the two roles is determined by a separate genetic locus. Such asymmetric interactions between relatives, in which individuals occupy different behavioural contexts, may occur in nature, for example between adult parents and juvenile offspring. The social game considered is known to be equivalent to a donation game with non-additive payoffs, and has previously been analysed for the single locus case, both for discrete and continuous strategy traits. We present an inclusive fitness analysis of the discrete trait game with roles and recover equilibrium conditions including fixation of selfish or altruistic behaviour under both behavioural contexts, or fixation of selfish behaviour under one context and altruistic behaviour under the other context. These equilibrium solutions assume that the payoff matrices under each behavioural context are identical. The equilibria possible do depend crucially, however, on the deviation from payoff additivity that occurs when both interacting individuals act altruistically.

Multilocus autosomal sex determination

The two basic one locus sex determination models, diploid individual sex determination and parental sex determination, are generalized to the multilocus framework. As in the single locus case, it is established that there are two classes of polymorphic equilibria, equilibria with even sex ratio and equilibria with equal allele frequencies in the two sexes. The condition for external stability of this second class equilibria to invasion by a "new" mutant allele is that a "new" appropriately averaged sex ratio near the equilibrium be moved closer to the even sex ratio. However, stable polymorphisms with noneven sex ratio are not those that have a sex ratio as close as possible to 1/2, in contrast to the single locus case.

The resolution of genotype x environment interaction in segregation analysis of nuclear families.

A model is presented for the effects of one or two loci, a measured index of the environment and genotype x environment (G x E) interaction of risk for a discontinuous trait. Initial properties of the model are explored for the single locus case, with and without the effects of environment and G x E interaction. Seven data sets were simulated, each comprising 500 nuclear families on whom an environmental index has been measured. Maximum-likelihood estimation procedures were used to obtain parameter estimates under seven models for each data set. Likelihood ratio tests were constructed, and in all cases it was possible to identify the "correct" model for the simulated data. The matrices of information realized showed that the parameters could be estimated with acceptable precision and that the effects of genes, environment, and G x E interaction could be resolved in the simulated populations. The effects on conventional segregation analysis of ignoring the environment and G x E are considered.

Competition between phenotypes.

We present two models for phenotypic-dependent interspecific competition. In both cases the survivorship of individuals of one population depends on the entire phenotypic distribution of the other species. The first model considers a continuously varying metric trait, with assortative or random mating; the second model examines a character controlled by two alleles at a single locus. Pursuing the notion that each population maximizes its mean fitness we define a vector-optimum strategy using the concepts of cooperative and competitive optima. It is found that the dynamical constraints placed on the equations of motion by Mendelian genetics often prevent a population from evolving to a strategic optimum. However, for the single locus case with complete dominance, the competitive optimum always coincides with some dynamical equilibrium on the Hardy-Weinberg manifold.

THE PROBABILITY OF FIXATION OF A MUTANT: THE TWO-LOCUS CASE.

The quantitative investigation of problems in population genetics has mainly been concerned, until recently, with the analysis of gene frequencies at a single locus. Such an approach is natural as a first step, but necessarily requires assumptions about the interaction effects of other loci to be meaningful. Despite the latter restriction a number of important results have been obtained from this approach, to a large extent by the researches of R. A. Fisher and Sewall Wright. Latterly interest has moved to multilocus behavior, and as a first step in this direction the two-locus case has received increasing attention (see, for example, Kimura (1956), Lewontin and Kojima (1960), Bodmer and Parsons (1962), Moran (1964)). Although such an extension from the single locus case still requires assumptions about the interactions of the loci considered with the remaining loci, it is at least possible to treat, for example, the effect of linkage between loci, which would be impossible in a single locus analysis (see in particular Kimura (1956) and Bodmer and Parsons (1962)). In another direction, Moran (1964) has shown that the analogues of several single locus theorems (including Fisher's fundamental theorem of natural selection) are no longer always true in the two locus case. All the investigations referred to above consider deterministic models, a stochastic treatment not having been attempted so far. A notable feature of the deterministic analyses is that close linkage between the loci appears, in all cases considered, to be desirable. An example of this, considered