Noise-induced regularity of spatial wave patterns in subalpine Abies forests

In subalpine forests dominated by Abies species in Japan and northeastern U nited States, trees show traveling wave of regeneration with many striped z ones of tree dieback, moving downwind at a constant rate. Previous theoreti cal studies have demonstrated that a very simple model can generate wave-li ke spatio-temporal patterns of tree regeneration in a lattice-structured ha bitat with each site occupied by a cohort of trees. A cohort taller than th e average height of its windward neighbor experiences stand-level dieback i n the next time step and the height becomes zero. Otherwise the cohort incr eases its height at a constant rate. Starting from a random initial pattern , this simple deterministic model can generate a saw-toothed pattern that m oves downwind at a constant rate, but the distance between adjacent dieback zones has a large variance. In this paper, we study the effects of "noises " in tree dieback rules in two forms which help to generate more regular pa tterns: (1) additional random disturbances at a low rate, which change the size of "clusters" (defined as a group of cohorts between adjacent dieback zones) by splitting a large cluster into two or by merging a small one with a neighbor, and (2) the stochastic rule of tree dieback, represented by th e probability of dieback in unit time being a sigmoidal function of the dif ference in the tree height between the site and the windward neighbors. The se noises are effective both for one-dimensional and two-dimensional models , but spatial patterns are much more regular in the two-dimensional model t han in the one-dimensional model. (C) 1998 Academic Press.