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

TL;DR

This paper demonstrates that in ecological network analysis, the realized input and output oriented indirect effects metrics are equivalent at steady state, enhancing the method's empirical testability and practical utility.

Contribution

It proves the equivalence of input and output oriented I/D ratios using the realized method at steady state, clarifying their relationship in ecological network analysis.

Findings

Input and output I/D ratios are identical at steady state using the realized method.

The result simplifies ecological network analysis and improves its empirical applicability.

This work supports better environmental assessment and management through clearer metrics.

Abstract

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