Institute for Complex Analysis of Regional Problems Far-Eastern Branch Russian Academy of Science, Birobidzhan, Russia
Institute of Automation and Control Processes Far-Eastern Branch Russian Academy of Science, Vladivostok, Russia

Abstract. This article develops and investigates a simple mathematical model that simultaneously studies influence of age and sex structure formation and sex ratio on demographic and evolutionary processes. We assume fertility depends on the population sex ratio and is described by the modified harmonic mating function with switching. The population size is regulated by limiting the juvenile survival rate when immature individual survival decreases with growth of sex-age class sizes. We received the conditions for sustainable development of the population in the parametric space of the model. The relationships between the group sizes of newborns and mature females and males are analyzed. The growth of the harem size is shown to result in higher the newborn group size in case of female numerical dominance. The offspring number demonstrates the same tendency as the sex group with the smallest number in the cases of higher female survival rate and higher newborn female proportion, and lower male survival rate. Excessive asymmetry of the sexes is shown to lead to a decrease in reproduction of polygamous species. Complex scenarios of population dynamics are studied. Transitions between different dynamic modes are caused by changes in both population parameters determining birth, survival and self-regulation rates, and the formation process of the mating pairs. The model parametric space is shown to have multistability areas in which the initial condition variation can lead to the realization of one dynamic mode or the other. The multistability is the result of both the system nonlinearity and the complex bifurcation mechanisms, and the changing pair formation principle. Consequently, even a small variation of the current population size changing the sex ratio complicates the population behavior and can give significant change in the dynamic mode observed.

Key words: mathematical modeling, population dynamics, age and sex structures, self-regulation, dynamic modes, multistability.