Modelling of forest stand dynamics using Markov chains

Understanding forest complexity and self-organization across multiple scales is essential for both ecology and natural resource management. In this paper, we develop a Markov chain approach for the modelling of forest stand dynamics. The aim of this work is to generalize the recently developed Perfect Plasticity Approximation (PPA) model for scaling of vegetation dynamics from individual level to the landscape level through the ecosystem hierarchical structure. Our basic assumption is that the forested ecosystem and disturbance regimes can be modelled on 3 hierarchical scales (levels): individual trees, forest stand (or patch, defined as a spatial unit about 0.5–1 ha of the same forest at one successional stage.) and landscape (collection of forest patches of different forest/soil types at different successional stages) levels. In our modelling approach the PPA model is an intermediate step for scaling from the individual level to the forest stand level (or patch level). In this paper we develop a Markov chain model for stage-structured dynamics of forest stands (patches). In order to determine the structure of the Markov chain model and estimate parameters, we analyze the patch-mosaic patterns of forest stands of the Lake States (MI, WI, and MN) recorded in the USDA FIA database as well as data for other US states and Canada. The distribution of macroscopic characteristics of a large collection of forest patches is considered as an estimate of the stationary distribution of the underlying Markov chain. The data demonstrates that this distribution is unimodal and skewed to the right. We identify the simplest Markov chain that produces such a distribution and estimate the upper bound of the probability of disaster for this Markov chain.