  The food web is a directed graph in which nodes label species and directed
links represent the predation between species. The cascade model generates
random food webs. The continuum cascade model is a Poisson approximation of the
cascade model. The recursion to obtain the probability distribution of the
longest chain length generated by the continuum cascade model has the solution
with traveling wave. We consider a branching random walk to study the
asymptotic probability on the position of wave front.
