Speaker
Eric Foxall
(University of British Columbia)
Description
We give conditions for an exchangeable genealogy model, with an arbitrary sequence of population and litter sizes, to have either a unique infinite path, or a unique lineage whose descendants eventually dominate the population. Conditions relate naturally to the coalescent time scale: the second property holds iff infinite time passes on this scale, while the first property holds if a truncated version of this time scale diverges. We make use of the well-known lookdown representation, also giving a more intuitive derivation of the lookdown via the complementary notions of forward and backward neutrality. We also discuss connections of the first property to the question of identifiability of the lookdown labelling from the unlabelled tree.
Author
Eric Foxall
(University of British Columbia)
