The site frequency spectrum for coalescing Brownian motion
Yubo Shuai
TL;DR
This paper studies the genetic diversity in an expanding population using coalescing Brownian motion models, establishing a law of large numbers for the site frequency spectrum in both circular and linear geometries.
Contribution
It introduces a novel application of coalescing Brownian motion to model genealogies in expanding populations and proves a weak law of large numbers for the site frequency spectrum.
Findings
Law of large numbers established for the site frequency spectrum
Results hold for both circular and linear population models
Provides a mathematical framework for genetic diversity analysis in expanding populations
Abstract
We consider an expanding population on the plane. The genealogy of a sample from the population is modelled by coalescing Brownian motion on the circle. We establish a weak law of large numbers for the site frequency spectrum in this model. A parallel result holds for a localized version where the genealogy is modelled by coalescing Brownian motion on the line.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Nonlinear Dynamics and Pattern Formation · Theoretical and Computational Physics