The cascade model generates a food web at random. In it the species are
labeled from 0 to m, and arcs are given at random between pairs of the
species. For an arc with endpoints i and j (i<j), the species i is
eaten by the species labeled j. The chain length (height), generated at
random, models the length of food chain in ecological data. The aim of this
note is to introduce the random sequential generation of intervals as a Poisson
model which gives naturally an analogous behavior to the cascade model