Contents

We define a multi-type coalescent point process of a general branching process with finitely many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population, providing types along ancestral lineages of all individuals in the standing population. We show that this point-process is a functional of a certain Markov chain defined by the planar embedding of the branching process. This Markov chain is further used to determine statistical properties of the ancestral tree, such as the time to the most recent common ancestor (MRCA) of two consecutive individu-als in the standing population, as well as of two individuals of the same type. These formulae are particularly simple for branching processes with a multi-type linear-fractional (LF) off-spring distribution. We illustrate their use by showing how an (a)symmetrical offspring distribution affects features of the ancestral tree in a two-type LF branching processes. Running head. The multi-type coalescent point process. MSC Subject Classification (2000). Key words and phrases. genealogical tree – coalescent point process – multi-type branchin