Computing tree size under dynamical models of diversification

A phylogenetic tree has three types of attributes: size, shape (topology), and branch lengths. Phylodynamic studies are often motivated by questions regarding the size of clades, nevertheless, nearly all of the inference methods only make use of the other two attributes. In this paper, we ask whether there is additional information if we consider tree size more explicitly in phylodynamic inference methods. To address this question, we first needed to be able to compute the expected tree size distribution under a specified phylodynamic model; perhaps surprisingly, there is not a general method for doing so – it is known what this is under a Yule or constant rate birth-death model but not for the more complicated scenarios researchers are often interested in. We present three different solutions to this problem: using i) the deterministic limit; ii) master equations; and iii) an ensemble moment approximation. Using simulations, we evaluate the accuracy of these three approaches under a va..., , , # Data from: The Untapped Potential of Tree Size in Reconstructing Evolutionary and Epidemiological Dynamics [https://doi.org/10.5061/dryad.fn2z34v3w](https://doi.org/10.5061/dryad.fn2z34v3w) *Mathematica* notebooks for calculating the distribution of tree size across diversification models (SupMatA_DiversityDependence) and for comparing the distribution of tree sizes across congruent model scenarios (SupMatB_Congruence). Notebook files (.nb) files were written in written in **Wolfram Mathematica version 14.1.0.0**. A PDF printout of each file is also included for users without the proprietary software. In SupMatA we first provide code for simulating phylogenetic trees under a time-dependent and density-dependent diversification model. For each specific diversification model (Exponential, Logistic, and SIR) we then calculate the distribution of tree sizes using various approaches (e.g., deterministic approximation, master equations, or ensemble moment approximation) and compare the ...