A central limit theorem concerning uncertainty in estimates of individual admixture

TL;DR

This paper establishes a central limit theorem for estimating individual admixture proportions, accounting for finite reference database size and marker number, with implications for forensic genetics.

Contribution

It introduces a new central limit theorem for admixture estimates considering finite reference data, enhancing understanding of uncertainty in genetic analysis.

Findings

Central limit theorem for finite reference database size

Simulation results demonstrating uncertainty effects

Application insights for forensic genetics

Abstract

The concept of individual admixture (IA) assumes that the genome of individuals is composed of alleles inherited from $K$ ancestral populations. Each copy of each allele has the same chance $q_k$ to originate from population $k$, and together with the allele frequencies $p$ in all populations at all $M$ markers, comprises the admixture model. Here, we assume a supervised scheme, i.e.\ allele frequencies $p$ are given through a reference database of size $N$, and $q$ is estimated via maximum likelihood for a single sample. We study laws of large numbers and central limit theorems describing effects of finiteness of both, $M$ and $N$, on the estimate of $q$. We recall results for the effect of finite $M$, and provide a central limit theorem for the effect of finite $N$, introduce a new way to express the uncertainty in estimates in standard barplots, give simulation results, and discuss applications in forensic genetics.