An R package for nonparametric inference on dynamic populations with infinitely many types

TL;DR

This paper introduces an R package that enables nonparametric Bayesian inference for Fleming-Viot diffusions, allowing analysis of population dynamics with infinitely many types from discrete samples over time.

Contribution

The authors develop software for nonparametric inference on Fleming-Viot diffusions, addressing computational challenges and extending existing tools beyond finite-dimensional Wright-Fisher models.

Findings

Efficient approximation of filtering and smoothing distributions for Fleming-Viot diffusions.

Implementation of Monte Carlo methods to reduce computational costs.

Software availability for complex population genetic models.

Abstract

Fleming-Viot diffusions are widely used stochastic models for population dynamics which extend the celebrated Wright-Fisher diffusions. They describe the temporal evolution of the relative frequencies of the allelic types in an ideally infinite panmictic population, whose individuals undergo random genetic drift and at birth can mutate to a new allelic type drawn from a possibly infinite potential pool, independently of their parent. Recently, Bayesian nonparametric inference has been considered for this model when a finite sample of individuals is drawn from the population at several discrete time points. Previous works have fully described the relevant estimators for this problem, but current software is available only for the Wright-Fisher finite-dimensional case. Here we provide software for the general case, overcoming some non trivial computational challenges posed by this setting. The R package FVDDPpkg efficiently approximates the filtering and smoothing distribution for Fleming-Viot diffusions, given finite samples of individuals collected at different times. A suitable Monte Carlo approximation is also introduced in order to reduce the computational cost.