  We present a mathematical analysis of the speciation model for food-web
structure, which had in previous work been shown to yield a good description of
empirical data of food-web topology. The degree distributions of the network
are derived. Properties of the speciation model are compared to those of other
models that successfully describe empirical data. It is argued that the
speciation model unifies the underlying ideas of previous theories. In
particular, it offers a mechanistic explanation for the success of the niche
model of Williams and Martinez and the frequent observation of intervality in
empirical food webs.
