We review theoretical approaches to the understanding of food webs. After an
overview of the available food web data, we discuss three different classes of
models. The first class comprise static models, which assign links between
species according to some simple rule. The second class are dynamical models,
which include the population dynamics of several interacting species. We focus
on the question of the stability of such webs. The third class are species
assembly models and evolutionary models, which build webs starting from a few
species by adding new species through a process of "invasion" (assembly models)
or "speciation" (evolutionary models). Evolutionary models are found to be
capable of building large stable webs.Comment: 34 pages, 2 figures. To be published in "Handbook of graphs and
networks" S. Bornholdt and H. G. Schuster (eds) (Wiley-VCH, Berlin