Available online at www.sciencedirect.com Mathematics and Computers in Simulation 79 (2008) 368–378 A method for aggregating state variables in large ecosystem models Jock Lawrie ∗ , John Hearne School of Mathematical and Geospatial Sciences, RMIT University, 368-374 Swanston Street, Melbourne, Australia Received 18 November 2006; received in revised form 2 November 2007; accepted 8 January 2008 Available online 17 January 2008 Abstract Simplifying large ecosystem models is essential if we are to understand the underlying causes of observed behaviours. However, such understanding is often employed to achieve simplification. This paper introduces a method for model simplification that can be applied without requiring intimate prior knowledge of the system. Its utility is measured by the resulting values of given model diagnostics relative to those of the original model. The method uses a least-squares criterion to identify sets of state variables that can be aggregated, and then generates a modified model structure and accompanying parameters that enable these variables to be replaced with the aggregates. The method is applied to a model of the nitrogen cycle in Port Phillip Bay, Victoria, Australia. Aside from reducing the model’s order, the method enables the reduced model to retain an ecological interpretation, and reveals insights into the system’s structure. © 2008 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Large ecosystem models; Aggregation; Partial proper orthogonal decomposition 1. Introduction In recent decades, several large ecosystem models have been developed and widely used. Common examples include Ecopath with Ecosim [7] in aquatic settings, and the model JABOWA [4] in forestry. Despite their utility, many problems are associated with such models [32,28]. For example, large models can be difficult to calibrate and validate [17,30], and their data requirements may be impractical [19]. Also, an observed behaviour may have many possible underlying causes, making it difficult to gain insights into the system and draw reliable conclusions. One way of avoiding these issues is to develop smaller models that serve the same purpose as the large models. Although several examples of this strategy have been documented [10–13], there are no definitive rules for determining the appropriate model size and complexity for a given modelling objective. Indeed, if a model is too simple it may misrepresent the dynamics associated with an observed output, or not be capable of producing the output at all [12,32]. Consequently, some authors have concluded that moderately complex models are the most instructive when investigating ecosystem dynamics [9,32,35]. To this end, this paper discusses a method for reducing the complexity of large ecological models without sacrificing the behaviours that are relevant to the specified modelling objective. The method involves aggregating state variables, thereby reducing the order of the system. ∗ Corresponding author. E-mail addresses: jock.lawrie@gmail.com, maths@rmit.edu.au (J. Lawrie). 0378-4754/$32.00 © 2008 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.matcom.2008.01.001