Identifiability of a Coalescent-based Population Tree Model

TL;DR

This paper proves that a coalescent-based population tree model is identifiable, meaning its parameters can be uniquely determined from data, which is crucial for accurate evolutionary inference.

Contribution

We demonstrate the identifiability of the coalescent-based population tree model, enabling reliable parameter estimation and advancing the theoretical foundation of population genetics models.

Findings

Model parameters can be expressed as functions of subsample probability distributions

Proves the model's identifiability, supporting maximum likelihood estimation consistency

Provides a theoretical basis for future empirical applications

Abstract

Identifiability of evolutionary tree models has been a recent topic of discussion and some models have been shown to be non-identifiable. A coalescent-based rooted population tree model, originally proposed by Nielsen et al. 1998 [2], has been used by many authors in the last few years and is a simple tool to accurately model the changes in allele frequencies in the tree. However, the identifiability of this model has never been proven. Here we prove this model to be identifiable by showing that the model parameters can be expressed as functions of the probability distributions of subsamples. This a step toward proving the consistency of the maximum likelihood estimator of the population tree based on this model.