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A new understanding of the consequences of how ecosystem elements areinterconnected is emerging from the development and application of EcologicalNetwork Analysis. The relative importance of indirect effects is central tothis understanding, and the ratio of indirect flow to direct flow (I/D) is oneindicator of their importance. Two methods have been proposed for calculatingthis indicator. The unit approach shows what would happen if each system memberhad a unit input or output, while the realized technique determines the ratiousing the observed system inputs or outputs. When using the unit method, theinput oriented and output oriented ratios can be different, potentially leadingto conflicting results. However, we show that the input and output oriented I/Dratios are identical using the realized method when the system is at steadystate. This work is a step in the maturation of Ecological Network Analysisthat will let it be more readily testable empirically and ultimately moreuseful for environmental assessment and management.

Equivalence of the realized input and output oriented indirect effects metrics in ecological network analysis