Demographic inference for spatially heterogeneous populations using long shared haplotypes

TL;DR

This paper develops a mathematical model and statistical method to infer dispersal and population density parameters in spatially heterogeneous populations using shared haplotype data, validated through simulations.

Contribution

It introduces a modified spatial Lambda-Fleming-Viot process and derives an analytical formula for shared haplotypes, enabling parameter inference in populations with spatial discontinuities.

Findings

Analytical formula for shared haplotypes depending on location

Effective inference of dispersal and density parameters

Validated method on simulated datasets

Abstract

We introduce a modified spatial $\Lambda$-Fleming-Viot process to model the ancestry of individuals in a population occupying a continuous spatial habitat divided into two areas by a sharp discontinuity of the dispersal rate and effective population density. We derive an analytical formula for the expected number of shared haplotype segments between two individuals depending on their sampling locations. This formula involves the transition density of a skew diffusion which appears as a scaling limit of the ancestral lineages of individuals in this model. We then show that this formula can be used to infer the dispersal parameters and the effective population density of both regions, using a composite likelihood approach, and we demonstrate the efficiency of this method on a range of simulated data sets.