Sustainable levels of biodiversity are thought to be tightly linked to food-web architecture. Theoretical arguments suggest existence of a numerically small upper limit to the average number of trophic links per species, thus limiting species richness for a given probability of linking consumer-resources pairs. However, since link-strength distributions are empirically dominated by weak links, the concepts of link presence and absence are ill defined. This and other conceptual difficulties left empirical tests of the theory ambiguous. Our approach to test the theory relies on carefully analyzing the diets of sub-samples of the community, rather than trying to sample a complete community and its food web. To obtain an upper bound for the number of links per species, we concentrated on high-level predators, which rather tend to be generalists, and measured the number of links per predator, which is always larger than the number of links per species.

Results/Conclusions

For fish and squid in six large ocean communities, we determined diet partitioning functions (DPF) [Rossberg et al., J. Theor. Biol., 243(2), 261–272, 2006], i.e., the average number of species contributing more than a threshold fraction to a consumer's diet as a function of this threshold. We find that these empirical DPFs can be described by a universal functional form related to a power law. For a 1% threshold, the number of links per consumer is small (~ 8) even though the communities are large, thus confirming the theory. We argue that inconsistencies in link-thresholding and species resolution had led to earlier results to the contrary.  The power-law forms of the DPFs, but not their (very similar) exponents, are explained by a simple statistical theory.