CENTRE ON THE PROBLEMS OF ECOLOGY AND PRODUCTIVITY OF FORESTS

RUSSIAN ACADEMY OF SCIENCES

Logofet D.O. Markov Chains as Succession Models: New Perspectives of the Classic Paradigm // Forest Science (Lesovedenie). 2010. No 2. P. 46-59 (in Russian).

Markov chains as a simple kind of the discrete-state random processes serve as a pertinent tool to formally describe a course of succession when the chain states are identified with certain succession stages and a scheme of transitions between these stages is known. The data on the duration of stages and the likelihood of alternative transitions can be transformed to the estimation of the transition probability matrix. An immanent property of absorbing chains, such as the convergence to the final stable distribution of its states, corresponds to the classic paradigm of the succession theory: the regular successive movement from pioneer stages to the stable (poly) climax one. The Markov model enables certain estimates of climax attainability times for various initial states and the proper probability distribution in the case of several climax states. Modern views of the forest ecosystem steady-state as a dynamic mosaic of newly formed and permanently overgrowing gaps in the closed forest canopy with the full-term distributions by species and age composition well fit the formalism of nonabsorbing regular chains that suggests the estimation of the relative area under various stages via the model steady-state vector. A novel generation of Markov succession models – time-inhomogeneous Markov chains – introduces some causality features into the pure phenomenological description, which is typical of their homogeneous prototypes, thus responding a challenge to models of long-term forest dynamics under the climate change.

Succession scheme, Markov behavior, stage duration, probability of transition, transition matrix, absorbing state, fundamental matrix, attainability time, invariancy, ergodicity, non-Markov effects

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