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

Area of Science:

• Ecology
• Mathematical Biology
• Forest Science

Background:

• Subalpine forests dominated by Abies species exhibit traveling wave regeneration with distinct zones of tree dieback moving downwind.
• A simple deterministic model can generate these wave-like patterns but with high variance in dieback zone spacing.

Purpose of the Study:

• To investigate how introducing "noises" into tree dieback rules can lead to more regular spatial patterns in forest regeneration.
• To analyze the effects of random disturbances and stochastic dieback probabilities on wave patterns.

Main Methods:

• A theoretical model simulating forest regeneration on a lattice structure was used.
• Two types of noise were introduced: random disturbances affecting cluster sizes and a stochastic dieback rule based on height differences.
• The model was applied to both one-dimensional and two-dimensional scenarios.

Main Results:

• Both introduced noise forms were effective in generating more regular spatial patterns.
• Random disturbances influenced cluster size by splitting large clusters or merging small ones.
• The stochastic dieback rule, modeled as a sigmoidal function, also contributed to pattern regularity.
• Two-dimensional models exhibited significantly more regular spatial patterns than one-dimensional models.

Conclusions:

• Introducing noise, specifically random disturbances and stochastic dieback probabilities, enhances the regularity of traveling wave patterns in forest regeneration models.
• The findings suggest that natural variations and probabilistic events play a crucial role in shaping observable patterns in Abies forests.
• Spatial patterns are more organized in two-dimensional environments compared to one-dimensional ones, highlighting the influence of dimensionality on pattern formation.