### Abstract

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 language | English |
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Pages (from-to) | 465-479 |

Number of pages | 15 |

Journal | Journal of Theoretical Biology |

Volume | 195 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 21 1998 |

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### 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

### Cite this

*Journal of Theoretical Biology*,

*195*(4), 465-479. https://doi.org/10.1006/jtbi.1998.0807