Reduced subcritical Galton-Watson processes in a random environment

We study the structure of genealogical trees of reduced subcritical Galton- Watson processes in a random environment assuming that all (randomly varyin g in time) offspring generating functions are fractional linear We show tha t this structure may differ significantly from that of the 'classical' redu ced subcritical Galton-Watson processes. In particular, it may look like a complex 'hybrid' of classical reduced super and subcritical processes. Some relations with random walks in a random environment are discussed. AMS 199 1 Subject Classification: Primary 60J80, 60J15.