 
Summary: 1
On the GaltonWatson predatorprey process
Gerold Alsmeyer
Mathematisches Seminar
Universit¨at Kiel
LudewigMeynStraße 4
D24098 Kiel
We consider a probabilistic, discretetime predatorprey model of the fol
lowing kind: There is a population of predators and a second one of prey.
The predator population evolves according to an ordinary supercritical
GaltonWatson process. Each prey is either killed by a predator in which
case it cannot reproduce, or it survives and reproduces independently of
all other population members and according to the same offspring dis
tribution with mean > 1. The resulting process (Xn, Yn)n0, where
Xn and Yn, resp., denote the number of predators and prey of the nth
generation, is called a GaltonWatson predatorprey process. The two
questions of almost certain extinction of the prey process (Yn)n0 given
Xn , and of the right normalizing constants dn, n 1 such that
Yn/dn has a positive limit on the set of nonextinction are completely
answered. Proofs are based on an reformulation of the model as a certain
