Seed bank Cannings Graphs: How dormancy smoothes random genetic drift

TL;DR

This paper introduces a novel graph model for seed bank effects in Cannings populations, enabling duality, embedding, and limit theorems that reveal how seed banks influence genetic drift and genealogies.

Contribution

It presents a new graphical framework for analyzing seed bank models, extending classical results and providing insights into their genealogical structures.

Findings

Establishes a sampling duality for seed bank models.

Derives limit theorems generalizing M"ohle's results.

Shows how seed banks affect genealogical trees.

Abstract

In this article, we introduce a random (directed) graph model for the simultaneous forwards and backwards description of a rather broad class of Cannings models with a seed bank mechanism. This provides a simple tool to establish a sampling duality in the finite population size, and obtain a path-wise embedding of the forward frequency process and the backward ancestral process. Further, it allows the derivation of limit theorems that generalize celebrated results by M\"ohle to models with seed banks, and where it can be seen how the effect of seed banks affects the genealogies. The explicit graphical construction is a new tool to understand the subtle interplay of seed banks, reproduction and genetic drift in population genetics.