Genealogy of flows of continuous-state branching processes via flows of   partitions and the Eve property
  We encode the genealogy of a continuous-state branching process associated with a branching mechanism $\Psi$ - or $\Psi$-CSBP in short - using a stochastic flow of partitions. This encoding holds for all branching mechanisms and appears as a very tractable object to deal with asymptotic behaviours and convergences. In particular we study the so-called Eve property - the existence of an ancestor from which the entire population descends asymptotically - and give a necessary and sufficient condition on the $\Psi$-CSBP for this property to hold. Finally, we show that the flow of partitions unifies the lookdown representation and the flow of subordinators when the Eve property holds. 
Cyril Labb\'e
math.PR