Canopy stability and scaling of forested ecosystems from individuals to the stand level

One of challenging problems in ecology is to describe average dynamics of spatially distributed ecological systems by macroscopic equations. Recently we have developed a new scaling method for forested ecosystems, from individual trees to forest stands (Strigul et al., 2007), which we call the perfect plasticity approximation (PPA). The PPA is based on the assumption that individual trees have unlimited plasticity to fill available space in the competition for light. It follows that, at the individual level, the outcome of tree competition for light depends only on tree size and allometry, and is independent of the spatial location of the tree in the stand. Any two trees of the same species and size have the same growth and mortality likelihood. Using the PPA, we were able to derive macroscopic equations, based on the von Foerster equation, which adequately describe stand dynamics, tree density, size distributions, and succession. Here we demonstrate that the model produces unstable canopies and periodic regimes if the underlying assumptions at the individual tree level are not realistic. In several particular cases we were able to analytically investigate observed oscillations and we have demonstrated that in different situations different mechanisms of oscillations can be involved. In particular, we have discovered the Hopf bifurcations, homoclinic orbits, and structural instability of some tree crowns. Unstable canopies pointed to the shortcomings in biological assumptions concerning form and growth of individual trees. The introduction of more realistic individual tree patterns led to stable canopy structures.