A study of equal node models for food webs

It is argued to study better non-binary (weighted) food webs where links are measured quantitatively, instead of binary (unweighted) food webs where links are just present or absent. Binary webs can simply be deduced from the more general non-binary ones: if a flux is larger than a critical flux value (below denoted by “cut”) a link is drawn, otherwise it is not. However, the amount of a flux between two nodes critically depends on the biomass of these nodes. Unfortunately, a clear definition of what to subsume into one node is missing up to now. The simplest (and probably most important) statistical description of non-binary food webs is given by the flux distribution function. However, this function may strongly be changed by just merging two nodes into one (as we have shown). In order to solve this decisive problem we propose to setup food webs with all nodes containing the same amount of biomass: equal-node-webs. A simple merging of just two nodes is forbidden here, because such a merged node would contain more biomass. The best basis for such a new food web theory would be provided by empirical equal-node-webs, established by field ecologists. However, such data has not been available up to now. Nevertheless, we demonstrate some advantages of studying equal-node-webs. For that purpose, first we show—by means of two example food webs—how equal-node-webs can be deduced from already published non-binary webs. Second, we describe the deduced equal-node-webs by their flux distribution functions as well as by different statistical measures. It is shown that equal-node-webs are more scale invariant than common non-binary food webs. Therefore, equal-node-webs provide a crucial, trustworthy basis for sound statistical descriptions and comparative analyses of food webs. er, the article contains a new detailed comparison between a highly productive lake and a low productive one. It is shown that the food web of the latter has a higher complexity than that of the former.