Ecological Models

Analyzing Ecological Models

A central challenge in ecology is understanding the emergence of large-scale community and ecosystem properties as the result of interactions among individuals (Jarvis 1993; Bascompte and Sole 1995; Grimm 1995; Lubchenco 1995). This task involves identifying which interactions at the small scales contribute most to large-scale dynamics. No complete methodology exists for identifying which details in a complex system control particular aspects of the larger system (Jarvis 1993; Levin et al. 1997). Exploring the causal determinants of large-scale behavior in detailed simulation models provides an environment to explore questions of scaling and relevant detail (Huston et al. 1988; Cale 1995; Rastetter and Shaver 1995; Turner and O'Neill 1995).

Classical approaches to ecological dynamics are highly aggregated, ignoring environmental spatiotemporal heterogeneity in order to achieve simplicity of description. Ideally, this simplification leads to models that can be solved analytically or probed numerically in a complete and systematic fashion (Ludwig 1987; Gross et al. 1992). However, models built on phenomenologically derived macroscopic relationships have limited applicability beyond the conditions under which they were derived (Pacala and Hurtt 1993; Pastor and Post 1993). Alternatively, detailed mechanistic models allow the natural inclusion of more biological detail (Huston 1991; Uchmanski and Grimm 1996; Bolker et al. 1997). At first glance, incorporating all potentially important details in a simulation model might seem attractive, but the inclusion of too much detail obscures understanding and may increase sensitivity and error propagation in the simulation (Ludwig and Walters 1985; Levin 1991; Levin et al. 1997). Thus, identifying appropriate detail represents a fundamental step in the modeling process.

No complete methodology exists for identifying relevant detail in a complex system, although analytical methods, usually based on finding appropriate approximations, are starting to emerge (see Levin and Pacala 1997; Bolker et al., in press). In contrast, direct computational approaches to finding the determinants of model behavior can be pursued. This approach relies on a series of experiments in which key interactions among individuals are removed or approximated (Huston et al. 1988; Cale 1995; Rastetter and Shaver 1995; Turner and O'Neill 1995). Statistical analysis can provide clues to understanding why the aggregate formulation does or does not result in similar large-scale patterns (Huston 1991; Gross et al. 1992; Shugart and Smith 1992b). Additionally, analyses at smaller scales provide insight into the emergence of behavior as a consequence of coupled, localized interactions among individuals (Turner and O'Neill 1995).

Visualizing the complex interactions from these model experiments provides an excellent avenue for exploring these questions of relevant detail (Levin 1991; Huston et al. 1988; Cale 1995; Turner and O'Neill 1995). In statistics, the idea that visualizing data is a necessary part of the analysis is well established (see, for example, Anscombe's pivotal paper "Graphs in Statistical Analysis" (1973); Tukey 1977; Tufte 1983; Cleveland 1985).

Modern data graphics can do much more than simply substitute for small statistical tables. At their best, graphics are instruments for reasoning about quantitative information. Often the most effective way to describe, explore, and summarize a set of numbers -- even a very large set -- is to look at pictures of those numbers. Furthermore, of all methods for analyzing and communicating statistical information, well-designed graphics are usually the simplest and at the same time most powerful.
--- From the introduction to Tufte 1983

We rely on the visualizations to facilitate the process of discovery as well as to communicate the results. Here, we present our attempts to visualize the results of several experiments with SORTIE, a forest model (Pacala et al. 1993), in order to understand causality in this complex simulation.