Parameter Identifiability of a Multitype Pure-Birth Model of Speciation

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.

Automated summary

Diversification models describe the random growth of evolutionary trees to model the historical relationships of species. This study establishes the identifiability of parameters for one form of such a model, a multitype pure birth model of speciation, based on an asymptotic distribution derived from a single tree observation. The key finding is that type observations are not needed at any internal points or leaves of the tree for practical applications.