Multitype $\hat{I}›$-coalescents and continuous state branching processes

Abstract

We provide new connections between multitype $\hat{I}›$-coalescents and multitype continuous state branching processes via duality and a homeomorphism on their parameter space. The approach is based on a sequential sampling procedure for the frequency process of independent CSBPs, and provides forward and backward processes for multitype population models under $\hat{I}›$-type reproduction. It provides some insight on different approaches to generalise $\hat{I}›$-coalescents to the multitype setup.