[Svirezhev's substitution principle and matrix models for dynamics of populations with complex structures]

Matrix models of discrete-structured population dynamics became a traditional tool in plant and animal demography, aided with developments in the proper mathematics and wide spread of software products, which greatly facilitate creating models in the man-machine dialogue mode, but leave behind the scenes the issue of whether the methods applied are adequate to the problem posed. A principal discrepancy of this kind does appear in a problem to calibrate the projection matrix on observation data of the "identified individuals with uncertain parents" type: simplifying recipes from an ecological software package contradict the idea of polyvariant ontogeny as an adaptation mechanism. The problem becomes solvable if we substitute an extremal adaptation principle for the uncertainty in data as follows: the unknown reproduction rates are assumed to distribute among the reproductive groups in such a way that maximizes the potential growth rate of the model population under the current conditions. In combination with findings from mathematical analysis of a wide class of matrix models, this principle turns the model into a reliable tool to test research hypotheses. Considered as an example is a matrix model (published elsewhere) for the population dynamics of Calamagrostis canescens woodreed, a perennial clonal plant species with a complex, age-stage-based population structure.