Alternative attractors in an ecological-genetic model of populations with non-overlapping generations

This study classifies and analyzes various bifurcations of fixed points of the simple model of population dynamics with its number described by Ricker's model and intrapopulation parameters determined by a single di-allelic locus. The model considered shows such nonlinear phenomena as multistability and coexistence of alternative attractors, which can violate the simple combination of the action of evolutionary-genetic and density-dependent ecological-dynamic processes, where gene elimination is determined by the genotypes' resource parameters and the population number stability depends on their Malthusian parameters. The most interesting pattern in this regard is existence of polymorphic attractors, when the resource parameter of heterozygotes is not maximal. It presents a clear violation of the principle of natural selection optimality, which is caused precisely by the multistable phenomena of nonlinear dynamics. By which of the alternative attractors the dynamics is characterized by depends sensitively on the initial conditions, even small external influences can became significant, as they can shift the system from one attraction basin to another, and thus fundamentally change the dynamic mode and nature of the evolutionary process. (C) 2017 Elsevier B.V. All rights reserved.