The mean function provides robustness to linear inverse modelling flow estimation in food webs: A comparison of functions derived from statistics and ecological theories

Quantitative estimates of carbon flows within food webs are increasingly viewed as essential to progress on a number of questions in basic and applied ecosystem science. Inverse modelling has been used for more than 20 years to estimate flow values for incomplete data sets. Monte Carlo Markov Chain linear inverse modelling calculates a probability density function for each flow. Among this distribution of possible values for each flow, the mean is generally chosen when a single solution is needed. The objective of the present study is to compare the robustness of the result when using the mean function, compared with 2 other statistical functions and 7 ecological functions derived from ecological theories on ecosystem maturity. The performance of the various functions was tested by comparing their accuracy in reconstructing a complete data set, the marine food web of Sylt–Rømø Bight, with known flows systematically removed. This was carried out on seven habitats and for 4 levels of degradation of the information. The robustness of each function was measured by comparing the estimated values of flows from inverse modelling after degradation with values from the original, complete data set. The analysis of results shows that the error of the estimated flows increases with the degradation of information, independent of the considered function. Two functions, the mean and the system omnivory index, provide more precise results than the others independent of the level of degradation of the information considered. The mean had the least impact on the reconstruction of food web flow values and on their organization described by ecological network analysis indices.