A question central to food-web research concerns the dimensionality of trophic niche space, that is, the number and nature of independent traits relevant for determining consumer-resource interactions. Food-web topologies can often be interpreted by assuming resource traits to be specified by points along a line and each consumer's diet to be given by resources contained in an interval along this line.  This phenomenon, called intervality, is now known for over 30 years and is widely acknowledged to indicate that niche space is close to one-dimensional.  Accordingly, much current food-web theory builds on the paradigm of a low-dimensional niche space.
Several recent observations suggest, however, that phylogenetic correlations in food webs offer an alternative explanation of intervality, leaving the role of niche-space dimensionality unclear.  To illuminate the interplay of these two mechanisms for intervality, we determined the quantitative dependence of intervality (in terms of various measures previously adopted in the literature) on niche-space dimensionality and phylogenetic correlations in model food webs.

Results/Conclusions

Our results show that degrees of intervality observed in nature can be reproduced in arbitrary-dimensional trophic niche spaces when phylogenetic correlations between resource traits are taken into account.  Intervals then correspond to segments in phylogenetically ordered resource lists.  We also show that, contrary to expectations, higher-dimensional niche spaces enhance intervality.  Analytic arguments show that this relationship will hold for a large class of models.  
We conclude that trophic niche-space dimensions should be identified and counted by means other than topological network analysis; some promising alternatives are shortly discussed.  By lifting the constraint of low niche-space dimensionality and highlighting the impact of evolutionary dynamics, the phylogenetic interpretation of intervality encourages novel theoretical and empirical approaches to food webs.
This work was supported by an Irish Beaufort Marine Research Award (A.G.R.), the European Marie Curie Research Training Network FishACE (Å.B., U.D.),  the European Science Foundation, the Austrian Science Fund, and the Vienna Science and Technology Fund (U.D.).