Parameter Identifiability of a Multitype Pure-Birth Model of Speciation

TL;DR

This paper proves that parameters of a multitype pure-birth speciation model are identifiable from large evolutionary trees without observing internal or leaf types, ensuring reliable inference.

Contribution

It establishes the first formal proof of parameter identifiability for a multitype pure-birth model in phylogenetics.

Findings

Parameters are identifiable up to label swapping.

Identifiability holds from asymptotic distributions of large trees.

No internal or leaf type observations are required.

Abstract

Diversification models describe the random growth of evolutionary trees, modeling the historical relationships of species through speciation and extinction events. One class of such models allows for independently changing traits, or types, of the species within the tree, upon which speciation and extinction rates depend. Although identifiability of parameters is necessary to justify parameter estimation with a model, it has not been formally established for these models, despite their adoption for inference. This work establishes generic identifiability up to label swapping for the parameters of one of the simpler forms of such a model, a multitype pure birth model of speciation, from an asymptotic distribution derived from a single tree observation as its depth goes to infinity. Crucially for applications to available data, no observation of types is needed at any internal points in the tree, nor even at the leaves.