Fluctuations in real population sizes: Mathematical modeling and estimation of demographic parameters

This study proposes an approach for estimating the demographic parameters of stage structure of real populations on the basis of their total population size, providing a useful tool for managing species abundance dynamics. To estimate the parameters, we use a transformation from discrete-time two-component models of structured populations to delay-difference equations that depend on the total population size. The two-component model assumes that at the beginning of each breeding season, the population comprises two cohorts: a younger group of juveniles and an older group of mature individuals. Population growth is regulated either by constraining fertility or by limiting the juvenile survival. The proposed approach was tested using available data on the population dynamics of fur-bearing animals in the Jewish Autonomous Region of the Russian Far East. The analyzed species include the squirrel, mountain hare, Manchurian hare, raccoon dog, and Siberian weasel. Their offspring reach reproductive maturity by the next breeding season. The estimates obtained via the proposed approach generally fall within biologically meaningful parameter ranges and reflect population dynamics similar to those observed in nature. In summary, this approach enables the analysis and modeling of population stage structure, as well as the estimation of demographic coefficients using the total size data of the population.