Definition and calculation of uncertainty in ecological process models

We present a method of multi-criteria assessment for the analysis of process model uncertainty that combines analysis of model structure, parameters and data requirements. There are three components in calculation and definition of uncertainty. (1) Assessment criteria: Uncertainty in a process model is reduced as the model can simultaneously simulate an increased number of assessment criteria selected to test specific aspects of the theory being investigated, and within acceptable limits set for those criteria. This reduces incomplete specification of the model-the characteristic that a model may explain some, but not all, of the observed features of a phenomenon. The calculation required is computation of the Pareto set which provides the list of simultaneously achieved criteria within specified ranges. (2) Parameter values: Uncertainty in a process model is reduced as the distribution of values for parameters simulating multiple assessment criteria within their acceptable limits becomes unimodal and with reduced range. This reduces non-uniqueness in the model-the characteristic that there may be alternative representations and no a priori way of deciding between them. The calculation required is analysis of parameter values within each group of the Pareto set, for their distributions and possible correlations which contributes to a definition of non-uniqueness in terms of whether multiple modes in parameter values are equally plausible. (3) Data and information: Uncertainty in a process model is reduced as the acceptable limits for assessment criteria are defined with increasing precision. The calculations required are to define acceptability ranges for the assessment criteria either through empirical investigations or through inference from related theories. This provides a definition of the relationship of the model to empirical and theoretical construction thought to be important. Three types of criteria should be used in assessment of uncertainty: (i) Tests of the quantitative domains of the model outputs. (ii) Examination of features explicitly predicted by the theory that the model describes. (iii) Tests between alternative structures in model formulation. The ability of a model to satisfy these criteria simultaneously is calculated using evolutionary computation and results are presented as a Pareto optimal set. Deficiencies in the model are revealed by manipulating acceptable limits around the assessment criteria, inclusion and exclusion of different criteria, and examining the distribution of model parameter values as non-dominated groups achieving different combinations of assessment criteria form in the Pareto optimal set. We illustrate this procedure through application to a simple model of competition between plants in single species even-aged populations. We use six assessment criteria and test an alternative to the model. (C) 2009 Elsevier B.V. All rights reserved.