Recent Progress and Problems in Food Web Theory

In 1968 I proposed a way to set lower bounds on the dimensionality of trophic niche space by using data on food webs. In 19'78 I showed that, in community food webs in a single habitat, the data on trophic niche overlap were consistent with a onedimensional trophic niche space more often than might be expected from some simplified random models of food webs. This note has three parts. First, I will comment on some recent explanations and criticisms of my empirical finding of a high frequency of interval food webs (Sect. 2). Second, I will review some recent mathematical progress in the graph theory of food webs (Sect. 3). Third, I will s tate an outstanding theoretical question concerning the combinatorial structure of food webs (Sect. 4): to explain the observed distributions of the length of maximal food chains. I conclude with a list of open problems.