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In a striking result, Louca and Pennell [S. Louca, M. W. Pennell, Nature 580, 502–505 (2020)] recently proved that a large class of phylogenetic birth–death models is statistically unidentifiable from lineage-through-time (LTT) data: Any pair of sufficiently smooth birth and death rate functions is “congruent” to an infinite collection of other rate functions, all of which have the same likelihood for any LTT vector of any dimension. As Louca and Pennell argue, this fact has distressing implications for the thousands of studies that have utilized birth–death models to study evolution. In this paper, we qualify their finding by proving that an alternative and widely used class of birth–death models is indeed identifiable. Specifically, we show that piecewise constant birth–death models can, in principle, be consistently estimated and distinguished from one another, given a sufficiently large extant timetree and some knowledge of the present-day population. Subject to mild regularity conditions, we further show that any unidentifiable birth–death model class can be arbitrarily closely approximated by a class of identifiable models. The sampling requirements needed for our results to hold are explicit and are expected to be satisfied in many contexts such as the phylodynamic analysis of a global pandemic. 

Phylogenomics---the estimation of species trees from multi-locus datasets---is a common step in many biological studies. However, this estimation is challenged by the fact that genes can evolve under processes, including incomplete lineage sorting (ILS) and gene duplication and loss (GDL), that make their trees different from the species tree. In this paper, we address the challenge of estimating the species tree under GDL. We show that species trees are identifiable under a standard stochastic model for GDL, and that the polynomial-time algorithm ASTRAL-multi, a recent development in the ASTRAL suite of methods, is statistically consistent under this GDL model. We also provide a simulation study evaluating ASTRAL-multi for species tree estimation under GDL. All scripts and datasets used in this study are available on the Illinois Data Bank: https://doi.org/10.13012/B2IDB-2626814_V1.