¹Far Eastern Federal University, Vladivostok, Russia
²Institute of Automation and Control Processes Far Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia
³Institute for Complex Analysis of Regional Problems, FEB RAS, Birobidzhan, Russia

Abstract. Understanding the mechanisms that determine population dynamics and structure is essential for assessing the long-term persistence of species and communities under changing environmental conditions, as well as for developing optimal strategies for natural resource management. This paper proposes a population model consisting of four age–sex groups. An additional equation describes a situation typical of harvested species (e.g., pinnipeds and ungulates): males that have reached sexual maturity do not breed for several seasons because they cannot compete for females with older, larger reproductive males. Introducing this group allows, first, a more detailed description of the life cycle – specifically, accounting for reduced survival upon entering the reproductive stage due to competitive struggle for harems. Second, this model is convenient for studying selective harvesting, where non-breeding individuals are removed – a practice often used to preserve the reproductive potential of a population.
We perform an analytical and numerical study of the proposed four-component model with seasonal breeding and birth rate dependent on the sex ratio. Additionally, we analyze the influence of within‑population parameters on the average harem size and its productivity. We show that the loss of stability of the nontrivial equilibrium in the biologically meaningful parameter range occurs only via a Neimark–Sacker bifurcation, leading to quasiperiodic oscillations. Fluctuations in population size arise at high values of the birth rate coefficient, which is typical for species with multiple offspring per pregnancy (e.g., wild boar). In species with single offspring per pregnancy and one breeding season per year (e.g., northern fur seal and most pinnipeds), the birth rate coefficient does not exceed unity; therefore, the nontrivial equilibrium is stable, and observed population fluctuations may be attributed to external factors – changes in environmental conditions, food availability, or harvesting.