Scaling fine-scale processes to large-scale patterns using models derived from models: meta-models

Ecologists and natural resource managers face a common scaling dilemma in many applications. Our conventional knowledge base is rather fine-scale, but many of the issues that now face us are of much larger extent, often played out at landscape to regional scales. As an extreme example, consider the potential effects of anthropogenic climatic change on forests. Our best mechanistic understanding of the effects of temperature, moisture, and CO2 on tree growth is at the level of plant ecophysiology (i.e., leaves, seedlings, and perhaps single trees; see Stran and Cure, 1985; Bazzaz, 1990), while assessments of these effects are typically addressed at regional or even global scales (e.g., Smith and Tirpak, 1989; IPCC, 1996; Walker and Steffen, 1996). other applications, while less extreme, do not escape this fundamental scaling mismatch. For example, forest managers now integrate their activities at the level of ecosystems and at scales of entire forests (i.e., landscapes), yet we still work most comfortabIy at the scales we know best; that is, stand-level prescriptions carried out on individual trees.

Ecologists are increasingly savvy about scale (Delcourt et al. 1983; Wiens, 1989; Levin, 1992). The basic scaling rule that trades off spatial resolution and detail for spatial extent is appreciated: detailed fine-scale studies are carried out on small study areas, while studies of much broader extent necessarily sacrifice details to emphasize coarser-resolution patterns. This trade-off comes at some expense; applications at disparate scales are divorced from one another empirically and some-times conceptually. For example, many models that address forest dynamics at the scale of the stand (ca. 1-10 ha) simulate the behavior of individual trees (Botkin etal., 1972a,b; Shugart, 1984; DeAngelis and Gross, 1992) or are based on field measurements of individual trees (e.g., FVS: Wykoff et al., 1982; Dixon, 1994).At intermediate scales, point models are often implemented to represent "averagestands" (e.g., PnET: Aber and Federer, 1992; Century: Parton et al., 1987). Thesepoint models are in fact scale-indeterminate, but arc typically interpreted as if they represent homogeneous stands (a few m2 for grasslands, lOs to 100s m2 for forests).At a still larger extent, global vegetation simulation models used in climate-change research simulate plant functional types, cover types, or other abstractions of forests,and include dynamics that are analogies for plant demography (e.g., VEMAP,1995). These differences in state variables and dynamics are appropriate as a strict scaling rule, yet as a result these classes of models do not share a common empirical basis; nor, in some cases, do they even share a common conceptual model of how vegetation responds to environmental forcings.

Our goal is to devise a modeling approach that can bridge disparate scales while preserving a common empirical and conceptual basis across scales. Our approach begins with a fine-scale model (in this case, a gap model), and then uses it to derivenew models as statistical abstractions of the fine-scale model. The derived models operate at coarser resolution and hence over larger spatial extent, but they retain those finer-scale details needed for larger-scale applications. Because the derived models are statistically derived from the gap model, they are in a sense models of the fine-scale model: meta-models.

In the following sections an overview is provided of the general approach toscaling a gap model up to landscapes, and then three models are presented as illustrations of the meta-modeling approach. Some of the methodological issues of parameterizing and testing-such models are discussed, and the chapter closes with a prospectus of where this approach seems to be leading.