Succession in mixed boreal forest of Russia: Markov models and non-Markov effects

An aggregated scheme is presented for the ideal course of the post-tillage succession (natural overgrowing) among 15 forest types in a mixed (coniferous-broad-leaved) forest in Central Russia. A first, traditional Markov chain model describes the course of succession leading eventually to the climax state, which is recognised to be a polydominant spruce-broad-leaved forest. The model predicts the average times it would take to reach the climax from any other stage of succession, while the current state of the forest is estimated by means of a GIS technology. Present geobotanic knowledge, however, assures that the climax state cannot be reached in mixed forest under the current ecological pressures in general and the lack of sufficient biodiversity in particular. The succession rather terminates at the stage of subdominant diasporic subclimax—a phenomenon which traditional Markov chain models are unable to reproduce. We suggest a formalisation of the logic why the subclimax-to-climax transition does not occur under the above conditions, and this results in a non-Markov version of the traditional model. We show, by solving a non-linear eigenvalue problem and studying the asymptotic behaviour, that the limit vector of state probabilities depends non-trivially on the initial conditions. Convergence to the climax state takes place only for a restricted set of initial vectors representing a sufficient level of biodiversity, while the non-Markov chain absorbs at a subclimax state for other initial conditions.