A multi-epoch model for the number of species within genera.

An early question in evolutionary theory asked why frequency distributions of taxonomic group sizes exhibit "hollow curves" so frequently. An answer to this question was provided by G. Udny Yule's seminal contribution introducing a discrete model for those distributions. But Yule observed that the fit of his model to observed distributions was sometimes imperfect, in particular for the class of reptiles. The present study introduces a multi-epoch extension of the discrete Yule model that accounts for unobserved extinction of ancient lineages. The multi-epoch model is described as a Pòlya urn embedded in a continuous-time branching process with an harmonic sequence of diversification rates. The main results include equivalent descriptions of multi-epoch models, their probability distributions, expected values, tail behavior and a self-similarity property. As an illustration of the theory, the multi-epoch model is applied to study the taxonomic diversity of reptile species, and provides a much better fit to the observed distribution of species than the original discrete Yule model.

Inferring gene duplications, transfers and losses can be done in a discrete framework.

In the field of phylogenetics, the evolutionary history of a set of organisms is commonly depicted by a species tree-whose internal nodes represent speciation events-while the evolutionary history of a gene family is depicted by a gene tree-whose internal nodes can also represent macro-evolutionary events such as gene duplications and transfers. As speciation events are only part of the events shaping a gene history, the topology of a gene tree can show incongruences with that of the corresponding species tree. These incongruences can be used to infer the macro-evolutionary events undergone by the gene family. This is done by embedding the gene tree inside the species tree and hence providing a reconciliation of those trees. In the past decade, several parsimony-based methods have been developed to infer such reconciliations, accounting for gene duplications ([Formula: see text]), transfers ([Formula: see text]) and losses ([Formula: see text]). The main contribution of this paper is to formally prove an important assumption implicitly made by previous works on these reconciliations, namely that solving the (maximum) parsimony [Formula: see text] reconciliation problem in the discrete framework is equivalent to finding a most parsimonious [Formula: see text] scenario in the continuous framework. In the process, we also prove several intermediate results that are useful on their own and constitute a theoretical toolbox that will likely facilitate future theoretical contributions in the field.

Learning Hyperbolic Embedding for Phylogenetic Tree Placement and Updates.

Phylogenetic placement, used widely in ecological analyses, seeks to add a new species to an existing tree. A deep learning approach was previously proposed to estimate the distance between query and backbone species by building a map from gene sequences to a high-dimensional space that preserves species tree distances. They then use a distance-based placement method to place the queries on that species tree. In this paper, we examine the appropriate geometry for faithfully representing tree distances while embedding gene sequences. Theory predicts that hyperbolic spaces should provide a drastic reduction in distance distortion compared to the conventional Euclidean space. Nevertheless, hyperbolic embedding imposes its own unique challenges related to arithmetic operations, exponentially-growing functions, and limited bit precision, and we address these challenges. Our results confirm that hyperbolic embeddings have substantially lower distance errors than Euclidean space. However, these better-estimated distances do not always lead to better phylogenetic placement. We then show that the deep learning framework can be used not just to place on a backbone tree but to update it to obtain a fully resolved tree. With our hyperbolic embedding framework, species trees can be updated remarkably accurately with only a handful of genes.