Stochastic neutral fractions and the effective population size

TL;DR

This paper develops a stochastic differential equation framework to analyze structured populations, introducing the concept of stochastic neutral fractions and deriving a general formula for effective population size in the presence of demographic noise.

Contribution

It introduces a novel SDE-based model for structured populations with infinite decomposability and provides a general formula for effective population size under small demographic noise.

Findings

Derived a general formula for effective population size

Revisited classical examples like expansion fronts

Provided a new framework for structured population dynamics

Abstract

The dynamics of a general structured population is modelled using a general stochastic differential equation (SDE) with an infinite decomposability property. This property allows the population to be divided into an arbitrary number of allelic components, also known as stochastic neutral fractions. When demographic noise is small, a fast-slow principle provides a general formula for the effective population size in structured populations. To illustrate this approach, we revisit several examples from the literature, including expansion fronts.