A multi-species, density-dependent matrix growth model to predict tree diversity and income in northern hardwood stands

A density-dependent matrix model of stand growth is presented. The model was calibrated with re-measured plots in the northern hardwood forests in Wisconsin. Trees were divided into shade-tolerant, intermediate, and shade-intolerant species in twelve diameter classes. Model predictions were tested against post-sample observations for short-term (15-year) and long-term (steady-state) accuracy. This growth model was then applied to study stand growth dynamics with and without management. Starting with the current average stand state, the predicted stand basal area of an unmanaged stand rose steadily to a maximum, dropped gradually, and finally reached a steady state. The time paths of basal area and tree size diversity were highly and positively correlated. Instead, tree species diversity decreased when size diversity and basal area increased, and vice-versa. When harvesting was introduced, it was found that more intensive harvest increased the diversity of tree species, while decreasing the diversity of tree size. A 20-year cutting cycle could produce higher economic returns than a 10-year cutting cycle, with similar size and species diversity. Harvesting most of the saw timbers every 20 years could be a good compromise between economics and tree diversity, at the stand level.