A GALTON-WATSON BRANCHING PROCESS IN VARYING ENVIRONMENTS WITH ESSENTIALLY CONSTANT OFFSPRING MEANS AND TWO RATES OF GROWTH1

Summary A Galton-Watson process in varying environments (Zn), with essentially constant offspring means, i.e. E(Zn)/mnα∈(0, ∞), and exactly two rates of growth is constructed. The underlying sample space Ω can be decomposed into parts A and B such that (Zn)n grows like 2non A and like mnon B (m > 4).