On the Genealogical Structure of Critical Branching Processes in a Varying Environment

Abstract

Critical branching processes in a varying environment behave much the same as critical Galton-Watson processes. In this note we like to confirm this finding with regard to the underlying genealogical structures. In particular, we consider the most recent common ancestor given survival and the corresponding reduced branching processes, in the spirit of Zubkov (1975) and Fleischmann and Siegmund-Schultze (1977).