On the competition among discrete-structured populations: a matrix model for population dynamics of woodreed and birch growing together
1 Dept. of Geobotany, Biological Faculty, Moscow Lomonosov State University
e-mail: nulanova@mail.ru
2 Laboratory of Mathematical Ecology, Institute of Atmospheric Physics, Russian Academy of Sciences,
Pyzhevskiy per., 3, Moscow, 119017
e-mail: iyabelova@mail.ru; daniLaL@postman.ru
Presented is a synthesis of field, theoretical and modelling studies on joint dynamics of two species - common birch (Betula pendula Roth) and wood small reed (Calamagrostis epigeios (L.) Roth) - overgrowing a spruce forest clear-cut. A nonlinear matrix model for population dynamics of two species, which both possess non-trivial population structures and compete for a resource in common was developed as an expansion of the linear models for single-species, age-stage-structured population dynamics. Constant values of the age-stage-specific survival and reproduction rates have been modified with some decreasing functions of the (competitive group) abundances in the competitor species or/and the species itself. Special aggregation of the age-stage structure for each of the competitor species has reduced the dimension of the nonlinear matrix operator down to the level that admits accurate calibration of the model parameters on the observation data, as well as the search for an equilibrium and its stability analysis. When calibrated, the nonlinear model exhibits convergence to the steady equilibrium - a state of the phytocoenosis that is interpreted as young, closed-canopy, birch forest with suppressed woodreed population. The model illustrates the observed course of forest renewal: the appearance of birch germs and the growth of birch population overpass the woodreed competitive resistance and result in formation of young birch forest, where the birch exerts a strong suppressive impact on both the woodreed growth and the own young growth. Remarked is a potential of the model as an object of more general mathematical study and a tool to predict the course of forest renewal.
