On the problems of the evolutionary optimization of life history. I. Markov model of Leslie life cycle 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 modelled 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 characteristics 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 linear Leslie 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 are determined both by multiple 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 R _L maximum and optimal distribution of fertility belongs to the field of linear programming.