Abstract
A discrete-time model of a structured population dynamics considering both density-dependent regulation and natural selection is studied. In the model, the dynamics of two population groups corresponding to different development stages is described, and birth rate limitation is considered. Fertility is assumed to change during microevolution. The stability loss of nontrivial fixed points was shown to realise according to the Neimark–Sacker scenario and the Feigenbaum one. Bifurcations, dynamic modes and possible shifting for the proposed model are explored. Bistability and multistability are also revealed. The phase space structure of bistability and multistability areas in which a variation in population sizes or population genotype compositions can lead to shift in the dynamic modes is examined using attraction basins. The multistability of genetic structure dynamics is also investigated. The presence of multistability fundamentally increases the quantity and variety of possible evolutionary scenarios and makes them dependent on both parameter values and initial conditions. In particular, shifting dynamic mode in a population can occur because of an increase in an individual’s reproductive potential during natural evolution.
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