Identifiability and inference of phylogenetic birth-death models.

Recent theoretical work on phylogenetic birth-death models offers differing viewpoints on whether they can be estimated using lineage-through-time data. Louca and Pennell (2020) showed that the class of models with continuously differentiable rate functions is nonidentifiable: any such model is consistent with an infinite collection of alternative models, which are statistically indistinguishable regardless of how much data are collected. Legried and Terhorst (2022) qualified this grave result by showing that identifiability is restored if only piecewise constant rate functions are considered.

Rates of convergence in the two-island and isolation-with-migration models.

A number of powerful demographic inference methods have been developed in recent years, with the goal of fitting rich evolutionary models to genetic data obtained from many populations. In this paper we investigate the statistical performance of these methods in the specific case where there is continuous migration between populations. Compared with earlier work, migration significantly complicates the theoretical analysis and requires new techniques.

A class of identifiable phylogenetic birth-death models.

In a striking result, Louca and Pennell [S. Louca, M. W.

Polynomial-Time Statistical Estimation of Species Trees Under Gene Duplication and Loss.

Phylogenomics-the estimation of species trees from multilocus data sets-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 article, we address the challenge of estimating the species tree under GDL.

Impossibility of Consistent Distance Estimation from Sequence Lengths Under the TKF91 Model.

We consider the problem of distance estimation under the TKF91 model of sequence evolution by insertions, deletions and substitutions on a phylogeny. In an asymptotic regime where the expected sequence lengths tend to infinity, we show that no consistent distance estimation is possible from sequence lengths alone. More formally, we establish that the distributions of pairs of sequence lengths at different distances cannot be distinguished with probability going to one.