Spatial Structure in SORTIE

The Role of Spatial Interactions

Local interaction among trees strongly influence the emergent community structure in forests. Several different approaches have been advanced for incorporating this spatial structure into forest models ranging from simple patch models to explicitly spatial, individual-based simulations (Botkin et al. 1972; Shugart 1984; Horn et al. 1989; Urban et al. 1991; Shugart and Prentice 1992; Shugart and Smith 1992; Pacala et al. 1993). Increasingly complex treatments of space carry more potential to include a diversity of spatial interactions, but model predictions also become more difficult to understand (Urban et al. 1991; Pacala and Hurtt 1993). Embracing a detailed description of space requires more empirical data leading to a narrow focus on specific questions in a single ecosystem. No single approach to capturing spatially structured interactions is likely to be adequate for all ecological systems, but determining the appropriate level of detail is an important step in understanding the influence of spatial interactions on emergent community structure (Levin 1992; Levin et al. 1997; Bolker et al. 1997).

Local light availability

Light availability at the forest floor. Local light availability on a 5-m grid is shown next to the forest. Notice that beech and hemlock cast much deeper shadows than yellow birch.

Patch formation resulting from localized dispersal. The same forest landscape is broken into panels to visualize single-species patterns. Notice that yellow birch is the only species to disperse seedlings away from patches of adults.

Understanding the role of spatial interactions in controlling landscape dynamics is vital (Wiens and Milne 1989; Durrett and Levin 1994; Lubchenco 1995; Levin et al. 1997). SORTIE provides a natural framework to investigate the role of spatial processes in forest dynamics, because the model is both spatially explicit and empirically based. These detailed simulations provide the reference set of simulations based on the detailed tracking of spatial interactions. Assessment of the role of spatial interactions is made by removing this spatial coupling.

In mean-field (spaceless) models, individuals are assumed to be well mixed, indicating that all possible tree interactions are equally important. This assumption implies that all trees experience shade as if they lived in the average tree neighborhood and that all seeds disperse globally. Simulating mean-field SORTIE was achieved with two changes in the SORTIE program. In order to remove the spatial structure from light competition, a fine grid was imposed on the forest, and statistics on the local neighborhood were measured in each grid cell. These measures of local tree density were averaged, and the light was then estimated under this average neighborhood. Dispersal was simply made random across the entire landscape so that recruits from all trees were equally likely to disperse to any point. These changes were superimposed on the simulation and removed all horizontal spatial information from SORTIE (Pacala and Deutschman 1995). Simulations of this spaceless version of the model was then compared to the base-line simulations both with and without disturbance.