How what you don’t know affects what you do know: Exploring an application of a linear inverse modeling uncertainty analysis on network models

Background/Question/Methods

Ecosystem Network Analysis (ENA) is a useful technique to quantify the movement of energy and matter through ecosystems.  Ecosystem networks consist of compartments and weighted, directed edges that represent the storage and movement, respectively, of energy or matter. The magnitudes of these network components can be assigned using empirical measurements, literature values, or plausible estimation.  While the literature often reports these parameters as a single value, they must contain varying degrees of uncertainty that propagates through the analysis.  This ambiguity is problematic for statistical inference.  A recent comparative study of two networks in the Cape Fear River Estuary (CFRE), NC, applied linear inverse modeling combined with a Monte Carlo approach to address this challenge, but how this technique affects broader ENA results is unclear. Here, we used the enaR package for R to investigate how ten different degrees of uniform uncertainty affected ENA results in the CFRE networks.  We also assessed the sensitivity of ENA result variability to uncertainty in each edge using a sensitivity statistic.  We hypothesized that the 1) variability in ENA results would increase linearly with increasing uniform uncertainty, and 2) sensitivity of ENA results would be greatest to uncertainty in edges with greater flows.

Results/Conclusions

The results of this work supported the hypothesis that variability in ENA results would increase linearly with uniform uncertainty.  A linear regression revealed a strong positive relationship between uniform uncertainty and variability of three common network-level statistics: Total System Throughflow (TST), Finn’s Cycling Index (FCI), and the ratio of Indirect-to-Direct flows (I/D) for both of the CFRE models (r²>0.99, p<0.001 in all cases).  However, the sensitivity analysis conducted in this study did not support the second hypothesis that ENA results would most sensitive to uncertainty in edges with greater flows.  No relationship was observed between flow magnitude and sensitivity for TST, FCI, or I/D in either of the CFRE networks.  This finding suggests that uncertainty in some fluxes may be more critical for the precision of model results than uncertainty in others. The fact that uncertainty analysis from the original CFRE comparative study, which was not applied uniformly, does not fall on the line predicted by a uniform increases in uncertainty further suggests that model structure may play a key role in determining how influential each edge can be.  Future work will focus on identifying which factors make ENA results more sensitive to uncertainty in some edges than others.