Mathematical Models

Mathematical models can be extremely valuable representations of the real world. Given a reasonable level of accuracy, such models can help us understand the composition, functioning, and development of vegetation on the landscape over time. By doing so, humans can predict the consequences of treatment activities, estimate current and future forest resource quality/quantity, and plan for economic and social impacts resulting from those changes. The latter are often realized in far-reaching national/international policies or legislative mandates.

The southern Appalachian landscape consists of approximately 26 million acres of forest land which corresponds to 70% of the land area in the region (SAMAB 1996). There are pure deciduous forests such as oak, pure coniferous forests such as southern yellow pine, and mixed deciduous-coniferous forests such as mixed pine-hardwoods. Predicting the dynamic changes in these forests over time is the domain of vegetation simulation science. Vegetation simulation can be subdivided into four categories:

1. Gap phase forest succession models such as JABOWA (Botkin 1992)
2. Forestry growth and yield models for established stands such as FVS (Teck et al. 1996)
3. Understory and regeneration vegetation dynamics models such as REGEN (Loftis 1990)
4. Coarse woody debris models describing the dynamics of both standing and down woody material

This section will concentrate only on category 2 and 3 models. The gap phase models, category 1, applicable to the southern Appalachians are not yet covered in this encyclopedia. Such successional models have been used for multi-century simulations to examine species compositional changes. However, they do not provide the stand-level accuracy needed for silvicultural decision making (Waldrop et al., 1986). Growth and yield models for established stands, category 2, possess acceptable accuracy but typically do not consider regeneration. There are no existing forestry growth and yield models that consider understory dynamics and natural regeneration upon disturbance for use in the southern Appalachian region. No category 4 models applicable to the southern Appalachians are known to exist.