Modelling of forest stand dynamics using Markov chains

Individual-Based Models and Scaling Methods for Ecological Forestry: Implications of Tree Phenotypic Plasticity

“…In this chapter, we consider a special case of equation (4), where the forest patches are fixed in size, so the rate of patch growth is zero g(t, a, ξ)=0. Variable a is considered as a successional stage of forest stand, and is discussed in another paper (Strigul et al, 2012). This formulation of the Matreshka model (equations 1-4) is analytically tractable in special cases, though the general analysis is a significant challenge.…”

“…The Matreshka model can be presented as a continuous or a discrete model, where partial differential and integral equations and Markov chains are employed, . A broad discussion of the model assumptions can be found in a recent paper (Strigul et al, 2012) focusing on the dynamics of forest stands (level 3 on Fig. 7).…”

“…This section introduces a modeling framework, called Matreshka (after the Russian nesting doll), for the scaling of vegetation dynamics from the individual level to the landscape level through the ecosystem hierarchical structure (Figure 7, see also Strigul et al (2012)). The Matreshka model is a particular realization of the hierarchical patch dynamics concept (Levin & Paine, 1974;Wu & Loucks, 1996) in application to forested ecosystems.…”

“…To describe the patch dynamics at the next hierarchal level, i.e., the forest stand mosaic, we employ the patch-mosaic modeling framework (Strigul et al, 2012). The Markov chain model for the mosaic of forest stands in the Lake states (MI, Wi, and MN) has been recently parameterized using the FIA data (Strigul et al, 2012). The Matreshka model unites already known models and uses the notion of ecological hierarchy that has been widely employed in landscape ecology (Bragg et al, 2004;Clark, 1991;Wu & Loucks, 1996).…”

“…The model, called Matreshka (after the Russian nesting doll) employs the PPA model as an intermediate step of scaling from the individual level to the forest stand level (or patch level). To describe the patch dynamics at the next hierarchal level, i.e., the forest stand mosaic, we employ the patch-mosaic modeling framework (Strigul et al, 2012). The Markov chain model for the mosaic of forest stands in the Lake states (MI, Wi, and MN) has been recently parameterized using the FIA data (Strigul et al, 2012).…”