Dynamic modeling of wave regeneration (Shimagare) in subalpine Abies forests

In a previous paper, we studied the wave regeneration of forest trees in model populations with one-dimensional lattice structures, by assuming that the tree height increases at a constant rate and that a tree dies in unit time if it is sufficiently taller than its windward neighbor. Starting from random initial distribution, the spatial pattern becomes of a saw-toothed shape, moving at a constant rate. In this paper, the model is extended in several directions: first, as the range of wind-shielding effect of trees increases, the speed of the final wave regenerating pattern increases. Second, a two-dimensional model is demonstrated to generate the patterns with dieback zones spaced more regularly than in those generated by a one-dimensional model. The effect of habitat heterogeneity is also studied. Third, the effect of disturbance in the form of additional stochastic mortality is studied. Finally the biological implication of these results to wave regeneration in forests is discussed.