Abstract

Prediction of ecological phenomenon needs three components: a theoretical (or numerical) model based on the natural laws (physical, chemical, or biological), a sampling set of the reality, and a tolerance level. Comparison between the predicted and sampled values leads to the estimation of model error. In the error phase space, the prediction error is treated as a point; and the tolerance level (a prediction parameter) determines a tolerance ellipsoid. The prediction continues until the time when the error first exceeding the tolerance level (i.e., the error point first crossing the tolerance-ellipsoid). This time is called the first-passage time. Well-established theoretical framework such as the backward Fokker-Planck equation can be used to estimate the first-passage time-an up-time limit for any model prediction. A population dynamical system is used as an example to illustrate the concept and methodology and the dependence of the first-passage time on the model and prediction parameters.

Keywords: First passage time; Ecological model predictability; Tolerance level; Stochastic forcing; Backward fokker planck equations