ecological modelling 206 ( 2 0 0 7 ) 400–406 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/ecolmodel Equivalence of throughflow- and storage-based environs Seth A. Bata a,* , Stuart R. Borrett b , Bernard C. Patten c , Stuart J. Whipple c , John R. Schramski c , David K. Gattie d a Industrial Engineering and Management Systems, University of Central Florida, Orlando, FL 32816, USA b Computational Learning Laboratory, CSLI, Stanford University, Stanford, CA 94305, USA c Institute of Ecology, University of Georgia, Athens, GA 30602, USA d University of Georgia, Driftmier Engineering Center, Department of Biological & Agricultural Engineering, Faculty of Engineering, Athens, GA 30602, USA article info Article history: Received 6 October 2006 Received in revised form 24 March 2007 Accepted 3 April 2007 Published on line 23 May 2007 Keywords: Throughflow environ Storage environ Ecosystem Network Ecological network analysis Holism abstract An environ is a within-system partition of the environment associated with each ecosystem component. The methodologies for calculating throughflow-based and storage-based envi- rons have heretofore been considered quantitatively and qualitatively different. Below, we show, from the fundamental environ equations, that these two approaches are mathemat- ically equivalent by proving the throughflow-storage-equivalence relationship, T E = S E. This implies that ecosystem flows of energy or matter to storage and throughflow are one and the same, differing only in storage delays (flow impedances) along the way in the storage case. © 2007 Elsevier B.V. All rights reserved. 1. Introduction 1.1. Review of the development of ecological input–output analysis Lotka (1925) and Lindeman (1942) were among the first to rec- ognize the usefulness of analyzing flows of energy and matter in an ecosystem. Systems ecologists have since developed several approaches which can be traced back to earlier devel- opments in economic input–output analysis. The common objective of these approaches was to analyze the properties derivable from the system, represented as a network of flows. Leontief (1941) first proposed a demand-driven (or time- backward) approach in modeling currency flow in economic ∗ Corresponding author. Tel.: +1 706 614 0439. E-mail address: sbata@aol.com (S.A. Bata). systems. An approach that addressed the supply-driven (or time-forward) case was subsequently put forth by Ghosh (1958) and later by Augustinovics (1970). The concepts asso- ciated with input–output theory were soon applied to other systems. Hannon (1973) was the first to bring this insight into the realm of ecosystem study. A handful of major lines of thought has since devel- oped somewhat independently of one another in ecological input–output analysis. Costanza (1980) and Hannon focused on applications to ecological economics. Christensen and Pauly (1992) developed algorithms that balance ecosystem models, which have since found application through imple- mentation of the software ECOPATH. Ulanowicz (1986, 1997) examined the goal orientation of ecosystems. Through his 0304-3800/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2007.04.005