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

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