First passage flows in ecological networks: measurement by input-output flow analysis

This paper explains the rationale behind measuring first passage flows of conservative substances in ecological networks by a simple modification of input-output flow analysis (Higashi et al., 1993a, Ecol. Model., 66: 1–42). Pilette and Kincaid (1992, Ecol. Model., 64: 1–10) posed this “first flow-through” problem and described a different method to solve it. This method, however, does not account for their intended “all non-duplicated routes and transfers” from one compartment to another, and consequently underestimates indirect transfers. In addition, it incorrectly treats storages as equivalent to flows. We correct their version, according to the discrete time input-output flow-storage analysis of Higashi et al. (1993b, Ecol. Model., 66: 43–64), and derive a correct evaluation of direct transfers. This, however, turns out to be equivalent to simple flow ratios obtained from standard, continuous time input-output flow analysis.