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The Feller diffusion as the limit of a coalescent point process
Conrad J Burden1, Robert C Griffiths2
1Mathematical Sciences Institute, Australian National University, Canberra, Australia.
Theoretical Population Biology
|July 14, 2026
Summary
This study explores the Feller diffusion as a limit of coalescent point processes. New methods are developed to analyze the coalescent properties of Poisson-sampled Feller diffusions, extending existing birth-death process analyses.
Area of Science:
- * Mathematical Biology
- * Probability Theory
- * Stochastic Processes
Background:
- * The Feller diffusion is a key model in population genetics and probability.
- * Recent advancements have focused on scaling limits of branching processes.
- * Existing methods often analyze Bernoulli sampling, limiting applicability to finite populations.
Purpose of the Study:
- * To unify recent results on scaling limits of branching processes.
- * To extend Bernoulli sampling to Poisson-sampled Feller diffusions.
- * To develop methods for analyzing k-sampled Feller diffusions.
Main Methods:
- * Analyzing the Feller diffusion as a limit of coalescent point processes.
- * Reinterpreting branching process results within the Feller diffusion framework.
- * Adapting methods from k-sampled birth-death processes.
Main Results:
- * The coalescent tree of a Poisson-sampled Feller diffusion mirrors a Bernoulli-sampled birth-death process.
- * A node height distribution with a specific algebraic form was identified.
- * New analytical methods for k-sampled Feller diffusions were established.
Conclusions:
- * The study provides a unified approach to understanding Feller diffusion properties.
- * Findings extend the analysis of population sampling in diffusion models.
- * The developed methods offer new tools for studying coalescent phenomena.
Keywords:
Branching processCoalescent point processDiffusion processFeller diffusionSampling distributionsMore Related Videos
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