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.