Mathematics of the Lefkovitch model: the reproductive potential and asymptotic cycles

A discrete-time model of discrete-stage-structured population dynamics is studied which generalises the classic Leslie model. The notion of reproductive potential is defined via the characteristic polynomial of the matrix of demographic parameters (Lefkovitch matrix), and the reproductive potential theorem is proved. A model where the demographic parameters are season-specific is proved to have no cycles in its annual dynamics, and we have found an inter-seasonal cycle resulting in the equilibrium population structure at the annual time scale. The seasonal model is calibrated on observation data for a population of Aporrectodea caliginosa worms under conditions of rlfear-Moscow localities. We have substituted certain assumptions for uncertainty in the data, and validity of the assumptions can thereafter be judged from the model results amenable to empiric tests.