[On the problems of the evolutionary optimization of life history. I. A Markov model of the Leslie life history and optimization of fertility].

The paper considers the properties of individual life history corresponding to the Leslie model of age-structured population. The life history is simulated as a finite Markov chain with absorption at a death state of individual. In this model, individual longevity, average number of offspring R(L) (produced by an individual over the entire life), and some other known parameters of the life history have been derived using simple probability methods that do not involve matrix calculus and their individual components have been interpreted. In the Leslie linear population model (derived by simple modification of a Markov chain), R(L) determines the growth or decline of a population. Individuals with higher R(L) values have evolutionary advantages in the population due to accelerated growth in their number The selection of fertility as a factor of the increase in R(L) is considered. In the Leslie model, fertility is a set of correlated quantitative traits, where the age-specific fertility components determined both by multipl loci and the environment. According to the genetic theory of quantitative trait selection, they evolve towards an increase in R(L). Taking into account the limited resources for reproduction, selection optimizes the fertility distribution according to age. Optimal distribution corresponds to the attainment of the maximum R(L). This complies with the maximization of the rate of population growth (r-selection), which is characteristic of linear population models. The search for the RL maximum and optimal distribution of fertility belongs to the field of linear programming.

[On the problems of the evolutionary optimization of life history. II. To justification of optimization criterion for nonlinear Leslie model].

The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism's traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of success of an individual's life history. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environmental conditions (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R(L), as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R(L). In terms of adaptive dynamics, the maximum R(L) corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.

[Oxidative stress, rRNA genes, and antioxidant enzymes in pathogenesis of schizophrenia and autism: modeling and clinical advices].

Ribosomal genes (RG), or genes for rRNA, are represented by multiple tandem repeats in eukaryotic genomes, and just a part of them is transcriptionally active. The quantity of active copies is a stable genome feature which determines the cell's capability for rapid synthesis of proteins, necessary to cope with stress conditions. Low number of active RG copies leads to reduced stress resistance and elevated risk of multifactorial disorders (MFD). Oxidative stress (OS) in the brain cells is believed to be involved in the pathogenesis of infantile autism (IA) and schizophrenia, i.e., MFDs with a manifested genetic predisposition. With autism, OS markers are found almost in every research, whilst with schizophrenia, the OS data are contradictory. Earlier, in a sample of patients with schizophrenia, we have found significantly higher quantity of active RG copies than at the average in healthy population. Here we have estimated the number of active RG copies in a sample of patients with IA (n = 51) and revealed significantly lower mean value than in healthy population. A novel mathematical model of the dynamic pattern of OS has been proposed. The model is realized as an ordinary differential equation system, supposing induction of antioxidant protection enzymes being mediated by reactive oxygen species (ROS), with the subsequent decrease of ROS content in a cell. The rate of synthesis of antioxidant protection enzymes is limited by the ribosome synthesis rate which depends on the number of active RG copies. Analysis of the model showed that the system always approaches a single stable equilibrium point along a damped oscillation trajectory, which in some degree resembles the dynamics of 'predator-prey' interaction in Lotka-Volterra model. The stationary ROS level inversely depends on the number of active RG copies. Our study explains the inconsistency of clinical data of OS in schizophrenia and suggests a novel criterion for discriminative cytogenetic diagnostics of schizophrenia and IA, as well as allows to assume that antioxidant therapy should be effective only for children with low number of active RG copies.

[Population variability and biometric models of organism trait coordination].

Natural variability of individuals in a population can be considered as a result of experiments set up by nature. The coordinated (coadapted) changes of traits among individuals are consequences of the influence of causal factors in common. With a unique common cause, the coordination law can be expressed by means of the trajectory for joint trait changes due to causal influence. In the case of several variable common factors and fixed specific ones, the coordination law can be expressed by means of a surface in the trait space, the surface corresponds all possible values of the common factors. Considered in this paper, is a principle possibility to estimate the regularities of individual trait coordination (due to the common factors of individual variability) by biometric methods. Application of regression analysis for assessing the coordination does not correspond to the sense of the problem: under regression the joint trait changes are caused not only by the common coordinating factors, but also by the specific ones. The multivariate biometric models of trait variability determination by latent fundamental factors have no direct relation to the causal determination of traits. Under the same causal dependences, trait correlations and statistical factors can strongly vary. Without additional information (that is not contained in random sample), biometric methods do not allow to estimate the causal regularities hidden under uncontrolled intrapopulation variability.

[Analysis of genealogical structure of populations. I. A method of collecting genealogical data in numerical form]. / Analiz genealogicheskoi struktury populiatsii. I. K metodike sbora genealogicheskikh dannykh v chislennom vide.

A method for collecting genealogical data with respect to an individual, a family, and members of the whole population is suggested. The essence of vertical pedigree construction consists of the same type of steps for filling in data (in the fixed order which excludes skips in the enumeration of lines of descent) about the father and the mother of the next ancestor. Each number in the received ordered list of ancestors uniquely determines a path (line of descent) to the given pedigree member. The path is explicitly described by a sequence of digits 0 and 1 (that corresponds to the sequence of fathers and mothers in the line of descent) at binary notation of this number. As a result, a pedigree is presented as a set of numbered rows that contain information, which uniquely identifies direct ancestors as individual persons. Results of joining separate pedigrees are recorded as a family list that contains lists of children for each parental pair. A pair of parents (more exactly, pointers of their families in the previous generation and numbers of pair members in their families) plays the role of the family "heading." Such a family list permits one to trace lines of descent and relationships for any population members presented in the list. It contains all genealogical information within the bounds of the study in a compact form. Here the process of collection requires considerably less time than traditional graphic representation of pedigrees. In addition, due to repeated checks of data during accumulation of material, error is minimized. Using pedigrees that have been collected, it is possible to calculate the coefficient of inbreeding manually. In connection with the wide prevalence of personal computers at present, it is also important that the data received are in fact ready to direct input to a computer for further automated data processing.

[Analysis of genealogical structure of populations. II. The use od numerical pedigrees for calculation of inbreeding coefficient]. / Analiz genealogicheskoi struktury populiatsii. II. Ob ispol'zovanii chislennykh rodoslovnykh dlia rascheta koéffitsienta inbridinga.

A method for calculation of inbreeding coefficient F in a numerical pedigree with no reference to its graphic representation is suggested. For calculation of F, a formula that does not take into account inbreeding coefficients of common ancestors and admits intersections in a loop is used. An advantage of this method is that it automatically finds all loops formed by paths to common ancestors. Detecting these loops via their tracing in a graphic pedigree with intersecting lines of descent creates a possibility of errors. A criterion of existence of at least one common link for two numerical paths is presented. It enables one to exclude pairs of paths to common ancestors that do not form loops. The methods considered for computing F in a given pedigree give exact values of the inbreeding coefficient for autosomal and sex-linked loci and generalize the known approximate approaches. The methods are illustrated by examples.

[Demographic genetic approach in anthropologic research. II. A method for calculating the coefficient of consanguinity in a complex nongraphic pedigree]. / Genetiko-demograficheskii podkhod v antropologicheskikh issledovaniiakh. II. Sposob vychisleniia koéffitsienta inbridinga v slozhnoi negraficheskoi rodoslovnoi.

A simplified method of manual calculation for inbreeding coefficient (and/or relationship) from complicated pedigree tables presented in a nongraphic mode is offered. The method is based on the use of positional dual codes of ancestors in which all genealogical links of the proband are reflected.

[Population genetics of the inhabitants of Northern European USSR. I. Data on the structure of 6 villages in Archangel Oblast]. / K populiatsionnoi genetike naseleniia Evropeiskogo Severa SSSR. Soobshchenie I. Kannye po strukture shesti dereven' Arkhangel'skoi oblasti

The paper deals with two demographic characteristics of 6 villages in the Archangelsk Region of the RSFSR (river Peosa region) significant from the genetical standpoint. These data were obtained by means of the examination of 843 persons (75,07% of the total number of inhabitants) and of the analysis of complete list of inhabitants permanently living in the villages studied. The proportion of the reproductivity age class was 28.94%, the numbers of men and woman among them being about equal. The average number of children per family in families that have already completed their reproductive period was 3.87, the variance being 4.51 (the data obtained on the basis of examination of over 90 families). The average age of marriage was established to be about 24 years, the duration of each generation being about 32 years. The average index of endogamy per village was observed to be 58.40%, the contribution of the gametes of the preceding generation per village being 72.86%. The migrational influx of gametes from other localities per total of 6 villages was 2.52%. It was shown by the comparison of the character of migrations with mathematical models that the matrix migrational model is the most adequate one.

[Population genetics of the inhabitants of Northern European USSR. II. Blood group distribution and antropogenetic characteristics in 6 villages in Archangel Oblast]. / K populiatsionnoi genetike naseleniia Evropeiskogo Severa SSR. Soobshchenie II. Dannye po raspredeleniiam nekotornykh grupp krovi i antropogeneticheskikh priznakov v shesti derevniakh Arkhangel'skoi oblasti

The paper deals with the distribution of genetic markers (systems ABO, MN, Rh (D), Hp, PTC) and a number of demographic (folding of arms, hand clasping, tongue rolling, right- and left-handedness, of the type of ear lobe, of the types of dermatoglyphic patterns) in the inhabitants of 6 villages in the Mezen District of the Archangelsk Region of the RSFSR (river Peosa basin). The data presented in this work were obtained in the course of examination of over 800 persons. Differences in the interpretation of the results of generally adopted methods of statistical analysis of samples from small populations are discussed. Among the systems analysed in one third of all the cases there was a statistically significant deviation from Hardy-Weinberg's ratios. For the MN blood groups and haptoglobins this was caused by the excess of heterozygotes. The test of Hardy--Weinberg's ratios at the level of two-loci phenotypes revealed no statistically significant deviations either in separate villages or in all the villages taken together. The analysis of heterogeneity with respect to markers inherited according to Mendel's law revealed statistically significant differences between villages in all the systems except haptoglobins. A considerable heterogeneity in the distribution of family names, the frequencies of some of them varying from village to village from 0 to 90%. Statistically significant differences between villages were shown for all the anthropogenetic characters except arm folding, hand clasping and right-left-handedness. Considering the uniformity of the environmental pressure in the region examined, the heterogeneity of the population studied is apparently associated with a random genetic differentiation (genetic drift) and, possibly, with the effect of the progenitor.