Aggregation error in nonlinear ecological models

Conditions are presented for accurately representing the dynamics of several components of a nonlinear ecological system by a single state variable. For mass-balance ecosystem models, only two conditions exist that permit such aggregation without introducing error into the model. Under the first condition, components can be lumped if their environmental losses (e.g. respiration or migration) are characterized by identical linear functions. Under the second condition, the components must maintain constant proportionality throughout their transient behavior. If these conditions are violated, it is not possible to aggregate without error. However, it is shown that aggregation error can still be minimized. The theorems developed here extend related results derived for the general theory of systems and have the advantage of generality, being applicable to nonlinear models of considerable complexity.