The superposition method for the reconstruction of food webs

Understanding trophic positions is essential for analysing complex food webs. While calculating these positions can be straightforward when feeding relationships and their proportions are known, determining diet coefficients traditionally requires substantial time and effort. Modern analytical techniques, such as stable isotope analysis, provide an efficient alternative for estimating trophic positions. Stable isotope analysis provides trophic position estimates, but this information alone does not reveal prey–predator relationships. To help reconstruct food webs, a method is needed to convert trophic positions into diet coefficients. Our method employs a superposition of potential prey pairs, with weighting coefficients given by probabilities computed using Bayesian statistics. We present a mathematical inverse analysis approach to estimate diet coefficients using a minimal dataset consisting only of trophic positions. This approach provides a robust and parsimonious framework for reconstructing potential feeding networks from minimal data, offering a quantitative bridge between, but not limited to, stable isotope measurements and ecological network structure.