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Based on the time-discrete model, we study the effect of selective proportional harvesting on the population dynamics with age and sex structure. When constructing the model, we assume that the population birth rate depends on the ratio of the sexes and the number of formed pairs. The regulation of population growth is carried out by limiting the juvenile’s survival when the survival of immature individuals decreases with an increase in the numbers of sex and age classes. We consider cases where the harvest is carried out only from a younger age class or from a group of mature females or males. We find that the harvesting of males or females at the optimal level is responsible for changing the ratio of females to males (taking into account the average size of the harem). We show that the maximum number of harvested males is achieved either at such a harvest rate when their excess number is withdrawn and the balance of sexes is established or at such an optimal catch quota at which the sex ratio is shifted towards breeding females. Optimal female harvesting, in which the highest number of them are taken, either maintains a preexisting shortage of adult males or leads to an excess of males or the fixing of a sex balance. We find that, depending on the population parameters for all considered harvesting strategies, the hydra effect can observe, i. e., the equilibrium size of the exploited sex and age-specific group (after reproduction) can increase with the growth of harvesting intensity. The selective harvesting, due to which the hydra effect occurs, simultaneously leads to an increase remaining population size and the number of harvested individuals. At the same time, the size of the exploited group after reproduction can become even more than without exploitation. Equilibrium harvesting with the optimal harvest rate that maximizes yield leads to a population size decrease. The effect of hydra is at lower values of the catch quota than the optimal harvest rate. At the same time, the consequence of the hydra effect may be a higher abundance of the age-sex group under optimal exploitation compared to the level observed in the absence of harvesting.

This study proposes and analyzes a discrete-time mathematical model of population dynamics with seasonal reproduction, taking into account the density-dependent regulation and sex structure. In the model, population birth rate depends on the number of females, while density is regulated through juvenile survival, which decreases exponentially with increasing total population size. Analytical and numerical investigations of the model demonstrate that when more than half of both females and males survive, the population exhibits stable dynamics even at relatively high birth rates. Oscillations arise when the limitation of female survival exceeds that of male survival. Increasing the intensity of male survival limitation can stabilize population dynamics, an effect particularly evident when the proportion of female offspring is low. Depending on parameter values, the model exhibits stable, periodic, or irregular dynamics, including multistability, where changes in current population size driven by external factors can shift the system between coexisting dynamic modes. To apply the model to real populations, we propose an approach for estimating demographic parameters based on total abundance data. The key idea is to reduce the two-component discrete model with sex structure to a delay equation dependent only on total population size. In this formulation, the initial sex structure is expressed through total abundance and depends on demographic parameters. The resulting one-dimensional equation was applied to describe and estimate demographic characteristics of ungulate populations in the Jewish Autonomous Region. The delay equation provides a good fit to the observed dynamics of ungulate populations, capturing long-term trends in abundance. Point estimates of parameters fall within biologically meaningful ranges and produce population dynamics consistent with field observations. For moose, roe deer, and musk deer, the model suggests predominantly stable dynamics, while annual fluctuations are primarily driven by external factors and represent deviations from equilibrium. Overall, these estimates enable the analysis of structured population dynamics alongside short-term forecasting based on total abundance data.