Small Networks but not Small Worlds: Unique Aspects of Food Web Structure

Contrary to prior reports, we find that a set of 16 food webs, with 25 to 172 nodes, from a variety of aquatic and terrestrial ecosystems, generally display neither Òsmall-worldÓ nor Òscale-freeÓ topological properties. The food webs do display relatively short characteristic path lengths consistent with small-world topology. However, most food webs display less clustering than that expected in small-world networks, which appears related to the small size of food webs. The ratio of observed to random clustering coefficients across biological and non-biological networks increases linearly with network size over 7 orders of magnitude (r = 0.90). A 1:1 clustering ratio occurs in networks with ~40 nodes. Most food webs display single-scale exponential or uniform degree distributions rather than the scale-free, power-law distributions previously reported for food webs and many other networks. Uniform degree distributions have not been reported previously for real-world networks. The failure to observe scale-free topology in most food webs appears related to the relatively small size, high connectance, and differences in the assembly of food webs compared to other real-world networks.