Multitype $\Lambda$-coalescents and continuous state branching processes

Abstract

We provide new connections between multitype $\Lambda$-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 $\Lambda$-type reproduction. It provides some insight on different approaches to generalise $\Lambda$-coalescents to the multitype setup.