Optimal control of a homogeneous population under natural selection

The study examines the impact of equilibrium harvesting with an optimal withdrawal rate on the dynamics and evolution of a population with non-overlapping generations, which is described by the Verhulst model with genetically determined parameters. It has been analytically shown that in a state providing the maximum level of seizure, the genetic composition value remains the same as in a population without withdrawal, while the equilibrium population size reduces by half. The type of genetic equilibrium may also shift.