Genealogical processes of sequential Monte Carlo methods and other non-neutral population models under rapid mutation

TL;DR

This paper demonstrates that genealogical trees from various non-neutral population models, including SMC methods, converge to the Kingman coalescent under specific rescaling, impacting understanding of genetic algorithms and coalescent theory.

Contribution

It extends convergence results to non-neutral models and SMC methods, simplifies proofs, and corrects previous errors in coalescent convergence analysis.

Findings

Genealogies from non-neutral models converge to Kingman coalescent

Rescaling time affects SMC algorithm performance

Simplifies and corrects earlier convergence proofs

Abstract

We show that genealogical trees arising from a broad class of non-neutral models of population evolution converge to the Kingman coalescent under a suitable rescaling of time. As well as non-neutral biological evolution, our results apply to genetic algorithms encompassing the prominent class of sequential Monte Carlo (SMC) methods. The time rescaling we need differs slightly from that used in classical results for convergence to the Kingman coalescent, which has implications for the performance of different resampling schemes in SMC algorithms. In addition, our work substantially simplifies earlier proofs of convergence to the Kingman coalescent, and corrects an error common to several earlier results.