A class of models with only a few easily identifiable parameters are introduced to allow the long-term consequences of disturbances in a natural forest to be qualitatively described. Formulated in terms of the von-Foerster partial differential equation, these models can be reduced to an integro-differential equation for the seedlings' density as a function of time. This seedlings equation contains a small parameter, the ratio of seedlings' re-establishment time and the average life span of a tree. The re-establishment time, typically 2-5 years, measures the time for the number of seedlings to adapt to a change in available resources.

The problem is solved using numerical and asymptotic methods. By means of Banach's fixed point theorem in a suitable function space, it can be shown that these methods converge even when the number of seedlings intermittently vanishes and the solution is not continuously differentiable. In this case, for a certain range of parameters, periodic solutions occur.