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

TL;DR

This paper establishes new links between multitype $ ext{Lambda}$-coalescents and multitype continuous state branching processes, enhancing understanding of multitype population models through duality and parameter space analysis.

Contribution

It introduces a novel approach using sequential sampling and duality to connect multitype $ ext{Lambda}$-coalescents with continuous state branching processes, expanding the theoretical framework.

Findings

Established duality between multitype $ ext{Lambda}$-coalescents and CSBPs.

Developed a homeomorphism on parameter space for these processes.

Provided insights into generalizing $ ext{Lambda}$-coalescents to multitype models.

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.