The effects of aggregation on the performance of the inverse method and indicators of network analysis

Food webs are usually aggregated into a manageable size for their interpretation and analysis. The aggregation of food web components in trophic or other guilds is often at the choice of the modeler as there is little guidance in the literature as to what biases might be introduced by aggregation decisions. We examined the impacts of the choice of the a priori model on the subsequent estimation of missing flows using the inverse method and on the indices derived from ecological network analysis of both inverse method-derived flows and on the actual values of flows, using the fully determined Sylt-Rømø Bight food web model. We used the inverse method, with the least squares minimization goal function, to estimate 'missing' values in the food web flows on 14 aggregation schemes varying in number of compartments and in methods of aggregation. The resultant flows were compared to known values; the performance of the inverse method improved with increasing number of compartments and with aggregation based on both habitat and feeding habits rather than diet similarity. Comparison of network analysis indices of inverse method-derived flows with that of actual flows and the original value for the unaggregated food web showed that the use of both the inverse method and the aggregation scheme affected indices derived from ecological network analysis. The inverse method tended to underestimate the size and complexity of food webs, while an aggregation scheme explained as much variability in some network indices as the difference between inverse-derived and actual flows. However, topological network indices tended to be most robust to both the method of determining flows and to the inverse method. These results suggest that a goal function other than minimization of flows should be used when applying the inverse method to food web models. Comparison of food web models should be done with extreme care when different methodologies are used to estimate unknown flows and to aggregate system components. However, we propose that indices such as relative ascendency and relative redundancy are most valuable for comparing ecosystem models constructed using different methodologies for determining missing flows or for aggregating system components.