Modeling of wave regeneration in subalpine Abies forests: population dynamics with spatial structure

The wave regeneration of forest trees is studied theoretically in model populations with a lattice structure, in which each lattice point corresponds to a stand containing a cohort of trees. Tree height at each site is assumed to increase at a constant rate, and trees die in unit time if they are taller than their windward neighbors, with the height difference greater than a critical value. Starting from a random initial distribution, the spatial pattern becomes a saw-toothed shape, and moves at a constant rate downwind without changing its shape. Four other models are also examined in which both the absolute height (or age) and the height difference between neighbors affect the tree mortality. Two rules (AND and OR rules) produce very irregular final patterns that are not saw toothed, but the other two (SUM and PRODUCT rules) often generate patterns that are close to saw toothed and more regular than those produced by the basic model. Both periodic boundary conditions and fixed height boundary conditions are examined. Two-dimensional models tend to produce more regular wave regenerating patterns than one-dimensional models. -Authors