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Properties of the continuum seed-bank coalescent

Likai Jiao

Abstract

We study properties of the \textit{continuum seed-bank coalescent} proposed by \cite{jiao2023wright} such as \textit{not coming down from infinity} and \textit{bounds on the expected time to the most recent common ancestor}. We also provide results on the limiting distributions and propose some interesting open problems.

Properties of the continuum seed-bank coalescent

Abstract

We study properties of the \textit{continuum seed-bank coalescent} proposed by \cite{jiao2023wright} such as \textit{not coming down from infinity} and \textit{bounds on the expected time to the most recent common ancestor}. We also provide results on the limiting distributions and propose some interesting open problems.
Paper Structure (11 sections, 10 theorems, 90 equations)

This paper contains 11 sections, 10 theorems, 90 equations.

Table of Contents

  1. Introduction
  2. Definition and basic properties
  3. Duality
  4. Exchangeability
  5. Limiting distribution of the ancestral line
  6. Comparisons of $E[T_{MRCA}]$
  7. Accelerated coalescent
  8. Not coming down from infinity
  9. Lower bound of $E[T_{MRCA}]$
  10. Decelerated coalescent
  11. Upper bound of $E[T_{MRCA}]$

Key Result

Proposition 2.5

The continuum seed-bank coalescent$\{\Pi^{\infty}_{t}\}_{t\geq 0}$ is exchangeable.

Theorems & Definitions (30)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Proposition 2.5
  • proof
  • Proposition 2.6
  • proof
  • Lemma 2.7
  • proof
  • ...and 20 more