RESEARCH AND ANALYSIS Modeling Metal Flow Systems Agents vs. Equations L. Andrew Bollinger, Chris Davis, Igor Nikoli´ c and Gerard P.J. Dijkema Keywords: agent-based modeling (ABM) closed loop industrial ecology mobile phones substance flow analysis (SFA) system dynamics Supporting information is available on the JIE Web site Summary Substance flow analysis (SFA) is a frequently used industrial ecology technique for studying societal metal flows, but it is limited in its ability to inform us about future developments in metal flow patterns and how we can affect them. Equation-based simulation modeling techniques, such as dynamic SFA and system dynamics, can usefully complement static SFA studies in this respect, but they are also restricted in several ways. The objective of this article is to demonstrate the ability of agent-based modeling to overcome these limitations and its usefulness as a tool for studying societal metal flow systems. The body of the article summarizes the parallel implementation of two models—an agent-based model and a system dynamics model—both addressing the following research question: What conditions foster the development of a closed-loop flow network for metals in mobile phones? The results from in silico experimentation with these models highlight three important differences between agent-based modeling (ABM) and equation-based modeling (EBM) techniques. An analysis of how these differences affected the insights that could be extracted from the constructed models points to several key advantages of ABM in the study of metal flow systems. In particular, this analysis suggests that a key advantage of the ABM technique is its flexibility to enable the representation of societal metal flow systems in a more native manner. This added flexibility endows modelers with enhanced leverage to identify options for steering metal flows and opens new opportunities for using the metaphor of an ecosystem to understand metal flow systems more fully. Introduction The study of the socioeconomic metabolism (Fischer- Kowalski and Huettler 1998) is a central task of the industrial ecology community, with substance flow analysis (SFA)—also referred to as material flow analysis (MFA)—having emerged as the dominant technique for investigating the physical flows of industrial economies. SFA has been used to quantify the partitioning of anthropogenic flows of substances such as chlo- rine (Kleijn et al. 1997), phosphorus (Matsubae-Yokoyama et al. 2009), and various metals (Gordon et al. 2004; John- son et al. 2005; Lifset et al. 2002). By providing a system-level Address correspondence to: L. Andrew Bollinger, Jaffalaan 5, 2628 BX Delft, The Netherlands. Email: l.a.bollinger@tudelft.nl c  2011 by Yale University DOI: 10.1111/j.1530-9290.2011.00413.x Volume 00, Number 00 view of material flow patterns, studies such as these have en- abled the identification of material flows and accumulations and the diagnosing of trends. They contribute to industrial ecology in its descriptive mode by characterizing human–environment interactions. However, SFA studies are essentially static snapshots of his- torical patterns and, as such, are limited in the degree to which they can inform us about future developments. They can tell us, for instance, about the global distribution of copper use in 2010 compared with 2000, but little about what this distribution might look like in 2020 or how our efforts to affect it might play out. Insofar as industrial ecology seeks to actively “influence the www.wileyonlinelibrary.com/journal/jie Journal of Industrial Ecology 1