Population dynamics of the additive polygenic system under truncation selection]

Common features of the equations describing dynamics of the additive polygenic system under truncation selection are summarized. A combination of parameters playing the role of the effective selective pressure on the ith polygenic locus was revealed. The product of mean relative fitnesses of the individual polygenic loci, [formula: see text], was shown to play the role of relative mean fitness of the polygenic population. This value depends on the measurable parameters of the character distribution in the population: [formula: see text]. It was shown that under the constant population number during truncation selection, the characteristic of the best genotype increases, [formula: see text]; which is also a product of the frequencies of preferable genotypes at individual polygenic loci. This value plays the role of the proportion of the number of the best ("champion") genotype in the population. In fact, this is the champion genotype polygene consensus pattern frequency, which a priori indicates the possibility of the champion pattern fixation. The analogue of Haldane's dilemma for the polygenic system which restrict the number of polygenes simultaneously subjected to adaptive evolution [formula: see text] was obtained for the case of constant effective population number (Ne = const).     

The joint effects of selection and assortative mating on multiple polygenic characters

Communicated by A. Robertson     

The divergence of a polygenic system subject to stabilizing selection, mutation and drift

Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.     

Computer Simulation of Joint Selection Response of MGE Patterns and a Polygenic System

Using computer simulation, selection response of three genome patterns—polygenes, mobile genetic elements (MGEs), and labels of identity by origin (LIOs)—were studied. In each generation of selection, variability of each pattern type was described by an UPGMA tree. Stringent positive truncation (+) selection on an additive polygenic trait and recombination between segments of the genetic map were considered. MGEs were classified into three groups: modifiers (enhancers) of the polygenic expression, markers, and independent copies. It was shown that at generations 30 to 40, 95–96% and 70–80% of respectively enforced and non-enforced active polygenic alleles were fixed (2–3% and 16–17% lost). In all generations, H ⁿ _k max D ⁿ _kof the length of the maximal route along the tree. At the same time, modifier MGEs were fixed for 85–88% (lost for 11–12%); marker MGEs, for 60–70% (lost for 21–25%); and independent copies, for 30–40 (lost for 50–60%). The behavior of independent MGE copies was generally consistent with the predictions of the genetic drift theory, modifier MGEs behaved similarly to the modified polygenes, and marker MGEs exhibited intermediate properties. The LIO patterns showed rapid homozygotization: their variability dropped dramatically between generations 10 and 30. In F50, the final consensus pattern of polygenes included 16 out of 18 enforced and 18 out of 21 non-enforced polygenic alleles. The fixation/loss ratios were 16 : 3 for modifier MGEs, 15 : 6 for marker MGEs, and 25 : 28 (with 7 polymorphic) for independent copies. The LIO consensus pattern contained 13 out of 100 original markers, which formed 26 fragments of one to ten map segments in size; 21 fragments contained active polygenic alleles, and 14 of them had also modifier MGEs. Recombinational shuffling of patterns was not completed. In the course of selection, active polygenic alleles take along adjacent segments, including those containing modifier MGEs and markers. These constitute the conservative part of all consensus patterns while the remaining segments are random.     

Computer modeling of human movements]

A dynamic model for studying man's movements is proposed. Lagrange equations of the second order are used. Differential equations of the model are presented in the matrix form, and all the coefficients involved are calculated from recurrent formulae. The dynamic model described is easily algorythmized. Differentiating operations can be thus avoided which are realized on electron computers with difficulities.     

Analysis of MGE Dm412 localization pattern in Drosophila melanogaster lines undergoing long-term selection for a quantitative character]

The subpopulation composed of the mixture of Drosophila isogenic lines with interrupted wing radial vein (mutation radius incompletus, ri) was subjected to long-term selection in different directions for increase or decrease in expression of the ri gene. As a result, the lines with contrasting different values of mean character phenotype were developed. The isogenic lines of mean character phenotype were developed. The isogenic lines and F2 from their crosses with selected lines were analysed by the pattern of copia-like MGE DM412 localization. The isogenic lines were shown to have individual pattern, the selected lines differing strongly from them. Selection led to the loss of Dm412 localization sites during negative selection, while positive selection results both in loss and acquisition of sites. Correlation between the phenotype of the quantitative character and the pattern of MGE Dm412 was revealed.     

The effects of intraspecific competition and stabilizing selection on a polygenic trait

The equilibrium properties of an additive multilocus model of a quantitative trait under frequency- and density-dependent selection are investigated. Two opposing evolutionary forces are assumed to act: (i) stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and (ii) intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the equilibrium structure, in particular, number, degree of polymorphism, and genetic variance of stable equilibria, is affected by the strength of frequency dependence, and what role the number of loci, the amount of recombination, and the demographic parameters play. To this end, we employ a statistical and numerical approach, complemented by analytical results, and explore how the equilibrium properties averaged over a large number of genetic systems with a given number of loci and average amount of recombination depend on the ecological and demographic parameters. We identify two parameter regions with a transitory region in between, in which the equilibrium properties of genetic systems are distinctively different. These regions depend on the strength of frequency dependence relative to pure stabilizing selection and on the demographic parameters, but not on the number of loci or the amount of recombination. We further study the shape of the fitness function observed at equilibrium and the extent to which the dynamics in this model are adaptive, and we present examples of equilibrium distributions of genotypic values under strong frequency dependence. Consequences for the maintenance of genetic variation, the detection of disruptive selection, and models of sympatric speciation are discussed.     

Computer system for simulating population dynamic patterns of polygenes and mobile genetic elements upon truncation selection for a quantitative trait

A computer system was developed for simulation of population dynamics of interacting polygene patterns and mobile genetic elements (MGEs) under selection for a quantitative trait. The system is stochastic (Monte Carlo) and takes into account the main sources of random change in the patterns (recombinations, transpositions, excisions), genetic drift, and determined trends of selection and other genetic processes in a finite population. Using this model, it is possible to analyze the dynamics of many population parameters that cannot be experimentally estimated: frequencies of polygenic alleles, proportions of adaptive and random fixations, average heterozygosities of polygenes and MGEs, coefficient of inbreeding, heritability, etc. In addition, the model can be used to test various hypotheses on polygene-MGE interaction.     

Classification of large-time behaviors in a reaction-diffusion system modeling diallelic selection

We study a mathematical model from population genetics, describing a single-locus diallelic (A/a) selection-migration process. The model consists of a coupled system of three reaction-diffusion equations, one for the density of each genotype, posed in a bounded domain or in the whole space R(n). The genotype AA is advantageous, due to a smaller death rate, and the main concern is to determine whether or not the disadvantageous gene a is eliminated in the large time limit. This model was studied in the celebrated work of Aronson and Weinberger (1975,1977), where they derived a simplified scalar model as an approximation of the full system and studied the asymptotic behavior for the scalar model. In particular they showed that, in the fully recessive case (same death rate for the heterozygote and inferior homozygote), the behavior crucially depends on the space dimension. In a previous paper, we were able to prove that their results concerning the scalar model in the fully recessive case remain valid in a certain sense for the full system. In this paper, we reconsider the general case (all possible values of the death and birth rates). We succeed to give a complete picture of whether or not the disadvantageous gene a can survive as t→∞, according to the values of the death and birth rates and of the space dimension. We find distinctive behaviors according to whether the homozygote is superior, intermediate, or inferior and, in the latter case, to whether the common birth rate is smaller or higher than the difference of the death rates of the two heterozygotes. In cases when the disadvantageous gene disappears, the decay rate of its frequency is estimated as well.     

Comparative analysis of MGE 412 patterns in 18 isogenic lines of Drosophila melanogaster

Comparative analysis of patterns of mobile genetic element 412 was conducted in 18 isogenic lines of Drosophila melanogaster isolated in three isogenic experiments in 1987 through 1999. Twelve "extra-hot" isogenization sites (in 15-18 lines) and 23 "hot" isogenization sites (> or = 10 lines) were found; of these, 19 occurred in the original heterogeneous line. These sites virtually do not overlap with hot induction sites of transposition. Sites of the latter group generally retain their positions during isogenization. It was shown that no more than 20% of the new sites were brought from the balancer by double recombination, while inbreeding and outbreeding caused 80% of them. Different factors were shown to have different hot isogenization sites. A similarity tree was constructed for the patterns of 18 isogenic lines. The maximum peak of the tree was very low (< 0.25), i.e., the isogenic lines are more similar to than different from one another. The tree was subdivided into subtrees. The division was in good agreement with the isogenization groups corresponding to individual isogenization experiments. Significant correlation was found between the total fragment length and the number of new sites per lines.     

The joint effects of kin, multilevel selection and indirect genetic effects on response to genetic selection

Kin and levels-of-selection models are common approaches for modelling social evolution. Indirect genetic effect (IGE) models represent a different approach, specifying social effects on trait values rather than fitness. We investigate the joint effect of relatedness, multilevel selection and IGEs on response to selection. We present a measure for the degree of multilevel selection, which is the natural partner of relatedness in expressions for response. Response depends on both relatedness and the degree of multilevel selection, rather than only one or the other factor. Moreover, response is symmetric in relatedness and the degree of multilevel selection, indicating that both factors have exactly the same effect. Without IGEs, the key parameter is the product of relatedness and the degree of multilevel selection. With IGEs, however, multilevel selection without relatedness can explain evolution of social traits. Thus, next to relatedness and multilevel selection, IGEs are a key element in the genetical theory of social evolution.     

Epistasis in polygenic traits and the evolution of genetic architecture under stabilizing selection

We consider the effects of epistasis in a polygenic trait in the balance of mutation and stabilizing selection. The main issues are the genetic variation maintained in equilibrium and the evolution of the mutational effect distribution. The model assumes symmetric mutation and a continuum of alleles at all loci. Epistasis is modeled proportional to pairwise products of the single-locus effects. A general analytical formalism is developed. Assuming linkage equilibrium, we derive results for the equilibrium mutation load and the genetic and mutational variance in the house of cards and the Gaussian approximation. The additive genetic variation maintained in mutation-selection balance is reduced by any pattern of the epistatic interactions. The mutational variance, in contrast, is often increased. Large differences in mutational effects among loci emerge, and a negative correlation among (standard mean) locus mutation effects and mutation rates is predicted. Contrary to the common view since Waddington, we find that stabilizing selection in general does not lead to canalization of the trait. We propose that canalization as a target of selection instead occurs at the genic level. Here, primarily genes with a high mutation rate are buffered, often at the cost of decanalization of other genes. An intuitive interpretation of this view is given in the discussion.     

Negative priming in a joint selection task

Recent studies have suggested that the observation of another individual executing a movement activates representations of the observed movement in the observer. These representations are thought to be used by other systems to facilitate a variety of social cognitive processes, such as social searches. Previous research on social searches has primarily involved contexts where targets were presented in isolation. Typical environments, however, contain targets and non-targets and one must select the correct information for task completion. To gain insight into the processes underlying social searches, participants completed negative priming tasks alone and in pairs. Results indicated that there were no differences in the negative priming effects resulting from the participants observed or performed the preceding selection task. Further, the correlations between individual and joint negative priming suggest that similar processes were activated on these tasks. The findings support the co-representation hypothesis and provide insight into the processes underlying selection in individual and social settings.     

The polygenic system of cycloheximide inactivation inSchizophyllum commune

Resistant and sensitive strains ofSchizophyllum commune inactivate the fungicidal antibiotic cyeloheximide. This property is controlled by 3 – 4 genes. Intergenic interactions play an important role here. Heritability of the inactivation is high (0.8 – 0.9).     

Sympathico-adrenal system activity in a primary immune response]

Experiments were carried out on linear mice immunized with sheep erythrocytes; it was found that the primary immune respose developed against the background of significant changes in the state of the sympathico-adrenal system, whose activity was determined by the dynamics of catecholamines in the blood and in the tissues of a number of organs, including the thymus, the spleen and the lymph nodes. By comparing the value of specific and neurohumoral indices it was revealed that the neurohumoral shifts preceded the maximal development of the immune response. On the example of studying the catecholamine dynamics the opinion on a close association between the state of the regulatory mechanisms and the effector formations responsible for the formation of specific immunological reactions was confirmed. It is suggested that a full-value immunological response developed on condition of activation of the sympathico-adrenal system.