  We investigate numerically and analytically a recently proposed model for
food webs [Nature {\bf 404}, 180 (2000)] in the limit of large web sizes and
sparse interaction matrices. We obtain analytical expressions for several
quantities with ecological interest, in particular the probability
distributions for the number of prey and the number of predators. We find that
these distributions have fast-decaying exponential and Gaussian tails,
respectively. We also find that our analytical expressions are robust to
changes in the details of the model.
