Direction of regeneration waves in grid-based models for forest dynamics

Progressing waves of regeneration are observed in forest ecosystems such as Shimagare fir forests. The patterns generated by lattice models for forest dynamics often show similar waves of disturbance and recovery. This paper introduces a method to detect and quantify the directional movement of these waves. The method is based only on the disturbance times of the sites and allows to distinguish three types of wave patterns: patterns with global direction, patterns with local direction, and patterns without direction. We apply this to several grid-based models for forest dynamics which are evaluated analytically or by simulation. The results reveal a clear distinction of the models which earlier studies were not able to detect.