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

Akiko Satake, Takuya Kubo, Yoh Iwasa

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


In subalpine forests dominated by Abies species in Japan and northeastern United States, trees show traveling wave of regeneration with many striped zones of tree dieback, moving downwind at a constant rate. Previous theoretical studies have demonstrated that a very simple model can generate wave-like spatio-temporal patterns of tree regeneration in a lattice-structured habitat with each site occupied by a cohort of trees. A cohort taller than the average height of its windward neighbor experiences stand-level dieback in the next time step and the height becomes zero. Otherwise the cohort increases its height at a constant rate. Starting from a random initial pattern, this simple deterministic model can generate a saw-toothed pattern that moves 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 patterns: (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 the probability of dieback in unit time being a sigmoidal function of the difference in the tree height between the site and the windward neighbors. These noises are effective both for one-dimensional and two-dimensional models, but spatial patterns are much more regular in the two-dimensional model than in the one-dimensional model.

Original languageEnglish
Pages (from-to)465-479
Number of pages15
JournalJournal of Theoretical Biology
Issue number4
Publication statusPublished - Dec 21 1998

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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