# The seed bank coalescent with simultaneous switching

## TL;DR

This paper introduces a novel seed bank model with simultaneous switching, leading to a new jump-diffusion limit and a unique coalescent process with multiple activation and deactivation events, extending classical population genetics models.

## Contribution

It presents a new Wright-Fisher type model incorporating simultaneous switching and establishes a novel coalescent structure with multiple activation/deactivation events.

## Key findings

- Derivation of a new jump-diffusion limit for the scaled frequency processes.
- Development of a new coalescent process with multiple activation/deactivation events.
- Conditions for coming down from infinity for these coalescents.

## Abstract

We introduce a new Wright-Fisher type model for seed banks incorporating "simultaneous switching", which is motivated by recent work on microbial dormancy. We show that the simultaneous switching mechanism leads to a new jump-diffusion limit for the scaled frequency processes, extending the classical Wright-Fisher and seed bank diffusion limits. We further establish a new dual coalescent structure with multiple activation and deactivation events of lineages. While this seems reminiscent of multiple merger events in general exchangeable coalescents, it actually leads to an entirely new class of coalescent processes with unique qualitative and quantitative behaviour. To illustrate this, we provide a novel kind of condition for coming down from infinity for these coalescents using recent results of Griffiths.