The k‐systems glitch: granulation of predictor variables

Abstract

Ecosystem behavior is complex and may be controlled by many factors that change in space and time. Consequently, when exploring system functions such as ecosystem “health”, scientists often measure dozens of variables and attempt to model the behavior of interest using combinations of variables and their potential interactions. This methodology, using parametric or nonparametric models, is often flawed because ecosystems are controlled by events, not variables, and events are comprised of (often tiny) pieces of variable combinations (states and substates). Most events are controlled by relatively few variables (≤4) that may be modulated by several others, thereby creating event distributions rather than point estimates. These event distributions may be thought of as comprising a set of fuzzy rules that could be used to drive simulation models. The problem with traditional approaches to modeling is that predictor variables are dealt with in total, except for interactions, which themselves must be static. In reality, the “low” piece of one variable may influence a particular event differently than another, depending on how pieces of other variables are shaping the event, as demonstrated by the k‐systems state model of algal productivity. A swamp restoration example is used to demonstrate the changing faces of predictor variables with respect to influence on the system function, depending on particular states. The k‐systems analysis can be useful in finding potent events, even when region size is very small. However, small region sizes are the result of using many variables and/or many states and substates, which creates a high probability of extracting falsely‐potent events by chance alone. Furthermore, current methods of granulating predictor variables are inappropriate because the information in the predictor variables rather than that of the system function is used to form clusters. What is needed is an iterative algorithm that granulates the predictor variables based on the information in the system function. In most ecological scenarios, few predictor variables could be granulated to two or three categories with little loss of predictive potential.

Citation

Hoeppner, S.S. and Shaffer, G.P. (2004), "The k‐systems glitch: granulation of predictor variables", Kybernetes, Vol. 33 No. 5/6, pp. 962-972. https://doi.org/10.1108/03684920410534001