Influence of Harvest on the Dynamics of Populations with Age and Sex Structures

Abstract

The paper investigates influence of sex- and age-specific harvest on the dynamics of structured populations based on the mathematical model with discrete time. We assume birth rate depends on the population sex ratio and is described by the modified harmonic mating function with switching. The population size is regulated by decreasing juvenile survival rate with growth of sex-age class sizes. The aim is to study the mechanisms of formation and evolution of dynamic modes for the exploited structured population models due to harvesting intensity. Conditions for sustainable development of the exploited population are received. Dynamic modes of the population models are studied. Influence of birth, survival, and self-regulation rates, the formation process of the mating pairs, and sex- and age-specific harvest on transitions between different dynamic modes are investigated. Sex-specific harvest of mature females or males will change the pair formation if the sex class, whose number of individuals is more, is exploited. Depending on values of the population parameters, the sex- and age-specific harvest (juveniles, mature females or males) can result in both damping of the oscillations, which stabilizes population dynamics, and the oscillation appearance, including two-year or quasiperiodic population fluctuations. The model of exploited population reveals the phenomenon of multistability, which is typical for a population without harvesting. The multistability is the result of complex bifurcations occurring due to both the system nonlinearity and the changing pair formation principle.

Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part I

“…However, this approach makes it possible to study and take into account the possibility of changing the dynamic mode in an exploited population. In particular, it was shown that, for an exploited two-age population (both with and without sex structure), it remains possible to implement various dynamic modes at the same population parameter values depending on the initial abundance, which is characteristic of a freely developing population (Neverova et al, , 2017(Neverova et al, , 2018Revutskaya et al, 2018). Therefore, to stabilize the dynamics, the current population size should be "retained" in the basin of attraction of the mode of interest (for example, by reducing the abundance of one of the age and sex classes).…”

Dynamic Modes of Structured Population under Sex- and Age- Specific Harvest

“…f < hm) увеличение доли изъятия самок и самцов не приведет к изменению соотношения полов. Такое поведение системы типично и для случая, когда промыслу подвергались только самки репродуктивного возраста [17].…”

“…Данная работа развивает предшествующие авторские исследования [17] и посвящена изучению влияния избирательного промысла самок и самцов репродуктивного возраста на динамику численности популяции с половой и возрастной структурами методами математического моделирования. Предполагается, что при промысле добываются самки и самцы репродуктивного возраста с одинаковой интенсивностью.…”

Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect

“…For example, the commercial value of sturgeon, whitefish, and salmon varies depending on their age [1]. Note that the consequences of age-specific or stage-specific harvesting have been extensively investigated [2][3][4][5][6][7][8][9][10][11][12], while the impact of harvesting individuals of different sexes on population dynamics has been less studied [13][14][15][16][17][18][19].…”