The use of multi-criteria assessment in developing a process model

Ecological data frequently contain multiple patterns. A process model of the system producing the data should be able to recreate those patterns. We describe a method and associated software where components of the pattern are used as multiple criteria to assess a model during its construction. Successive improvements are made to the model so that it describes more components of the pattern effectively. The software, Pareto-Evolve is an evolutionary algorithm. Initially it creates many individual sets of model parameters, each is used in the model to produce results that are then compared to patterns in a data set. Different individuals may achieve different components of the pattern and Pareto-Evolve calculates those that are most effective and uses them to produce new individuals. This is done by changing parameter values of individuals, called mutation, or exchanging parameter values between individuals, called crossover. This process is repeated over many generations so that a most effective parameterization evolves. We illustrate this method with a model for hourly increments of extension of the leading shoot of a conifer tree. The particular task here is to model water uptake by the plant in response to water loss due to transpiration, calculate a water deficit between uptake and loss, and calculate contraction and re-expansion of shoot tissue due to diurnal changes in tissue water deficit. We choose criteria corresponding to different phases in the diurnal pattern of expansion and model for up to six consecutive days. A value is set marking the limit within which the model must achieve the criteria for it to be judged as success. This value is called a binary discrepancy measure. Pareto-Evolve is used to make multiple searches with successively smaller binary discrepancy measures until all criteria are no longer achieved. At this point different parameter sets achieve different groups of criteria and we use these as indicators of how the structure of the model must be improved to achieve an overall better fit. In our example we find that contraction is more rapid than re-expansion, which is a hysteresis effect, and that re-expansion of tissue continues after water deficit within the tissue is estimated to have been removed. We discuss how this method can be used in model development and particularly how multiple criteria assessment can be used in model development. (c) 2006 Elsevier B.V. All rights reserved.