Ecological Modelling 123 (1999) 193 – 205 Quantifying resource homogenization using network flow analysis Brian D. Fath a, *, Bernard C. Patten b a Warnell School of Forest Resources, Uniersity of Georgia, Athens, GA 30602, USA b Institute of Ecology, Uniersity of Georgia, Athens, GA 30602, USA Accepted 1 June 1999 Abstract This paper formally introduces the rheomode orientation to network flow analysis and provides a quantitative test for the ecological property of network homogenization. Using network flow analysis, it is possible to identify and quantify the direct, indirect, and integral contributions of flow between any two components in a reticulated system. Inspection of the integral (direct plus indirect) flow matrix reveals many interesting properties not obvious from an empirical investigation of proximate transactions. Using network flow analysis, we observe that the composition of direct flows is comprised of a fairly uniform mixture of resources from all the system components. We call this evening out of flow network homogenization (Patten, B.C., Higashi, M., Burns, T.P., 1990. Ecol. Model. 51, 1 – 28). Here we introduce a standard statistical technique to provide a quantitative test for network homogenization. This property is the direct result of a flow oriented analysis of ecological systems. This has broader implications for the standard trophic dynamics paradigm currently dominating ecological research. The central results from this approach indicate that networks are holistic entities which must be analyzed as such. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Homogenization; Indirect effects; Network flow analysis; Statistical ecology www.elsevier.com/locate/ecolmodel Movement gives shape to all forms. Structure gives order to movement. — Leonardo da Vinci (paraphrased in Bohm, 1976) 1. Introduction to network flow analysis Network flow analysis as used herein started as an environmental application of input – output analysis. Input – output analysis was developed by Leontief (1936, 1951, 1966) to analyze the interde- pendence of industries in an economy (Miller and Blair, 1985). As a branch of mathematical biol- ogy, it is relatively small with four somewhat independent lines of research. Hannon (1973) first used input – output analysis to investigate the in- * Corresponding author. Tel.: +1-706-5420350; fax: +1- 706-5420857. E-mail address: bfath@smokey.forestry.uga.edu (B.D. Fath) 0304-3800/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII:S0304-3800(99)00130-1