Box 1. The niche model by Williams & Martinez (2000)
The niche model requires the number of trophic species (the number of nodes, \(S_{0}\)) and connectance (the fraction of realized feeding interactions out of all potentially possible, \(C\)) as input parameters (Table 1). It hierarchically ranks species according to the “niche value,” \(n_{i}\), randomly drawn from a uniform distribution and assigns a feeding range to each species as follows. The range size,\(r_{i}\) (\(i\) is the index for taxa), is determined by first drawing a random variable, \(\eta_{i}\), from a beta distribution calibrated to obtain the desired connectance and then multiplying \(\eta_{i}\) by the niche value for \(i\ (r_{i}=\eta_{i}n_{i})\). The center of the feeding range, \(c_{i}\), is randomly chosen from a uniform distribution in \(\left[\frac{r_{i}}{2},n_{i}\right]\), and the range is then determined as\(\left[c_{i}-\frac{r_{i}}{2},c_{i}+\frac{r_{i}}{2}\right]\). Therefore, species with larger niche values tend to have larger feeding ranges. The ranges are set such that cannibalism is allowed (i.e.,\(n_{i}\) can fall in the range of \(i\)). All the taxa whose niche values fall in the feeding range of another are regarded as the prey of the latter. The taxa with no prey are identified as basal taxa (i.e., autotrophs). The taxon with the lowest niche values is designated as an autotroph. We discard disconnected webs, webs with connectance beyond a given tolerance level (\(C_{\text{error}}\)), and webs with taxa not connected to a basal taxon.