Stéphane Guindon

Accurate estimation of the dispersal velocity or speed of evolving organisms is no mean feat. In fact, existing probabilistic models in phylogeography or spatial population genetics generally do not provide an adequate framework to define velocity in a relevant manner. For instance, the very concept of instantaneous speed simply does not exist under one of the most popular approaches that models the evolution of spatial coordinates as Brownian trajectories running along a phylogeny (Lemey et al ., 2010). Here, we introduce a new family of models – the so-called “Phylogenetic Integrated Velocity” (PIV) models – that use Gaussian processes to explicitly model the velocity of evolving lineages instead of focusing on the fluctuation of spatial coordinates over time. We describe the properties of these models and show an increased accuracy of velocity estimates compared to previous approaches. Analyses of West Nile virus data in the U.S.A. indicate that PIV models provide sensible predictions of the dispersal of evolving pathogens at a one-year time horizon. These results demonstrate the feasibility and relevance of predictive phylogeography in monitoring epidemics in time and space.

The introduction of the spatial Lambda-Fleming-Viot model (LV) in population genetics was mainly driven by the pioneering work of Alison Etheridge, in collaboration with Nick Barton and Amandine Véber about ten years ago (1,2). The LV model provides a sound mathematical framework for describing the evolution of a population of related individuals along a spatial continuum. It alleviates the "pain in the torus" issue with Wright and Malécot's isolation by distance model and is sampling consistent, making it a tool of choice for statistical inference. Yet, little is known about the potential connections between the LV and other stochastic processes generating trees and the spatial coordinates along the corresponding lineages. This work focuses on a version of the LV whereby lineages move infinitely rapidly over infinitely small distances. Using simulations, we show that the induced LV tree-generating process is well approximated by a birth-death model. Our results also indicate that Brownian motions modelling the movements of lineages along birth-death trees do not generally provide a good approximation of the LV due to habitat boundaries effects that play an increasingly important role in the long run. Finally, we describe efficient algorithms for fast simulation of the backward and forward in time versions of the LV model.

Significance: Statistical phylogeography has led to substantial progress in our understanding of the pace and means by which organisms colonize their habitats. Yet, inference from these models often relies on implicit assumptions pertaining to spatial sampling design, potentially leading to biased estimation of key biological parameters. While sampled locations sometimes convey signal about the processes that shape spatial biodiversity, they do not always do so. We present a statistical approach that permits accurate estimation of dispersal rates, even in cases where spatial sampling is driven by practical motivations unrelated to the outcome of the evolutionary process. The proposed framework paves the way to further developments in phylogeography with key applications, including the efficient monitoring of pandemics and invasive species during the course of their evolution.

I present here an in-depth, although non-exhaustive, review of two topics in molecular dating. Clock models, which describe the evolution of the rate of evolution, are considered first. Some of the shortcomings of popular approaches -- uncorrelated clock models in particular -- are presented and discussed. Autocorrelated models are shown to be more reasonable from a biological perspective. Some of the most recent autocorrelated models also rely on a coherent treatment of instantaneous and average substitution rates while previous models are based on implicit approximations. Second, I provide a brief overview of the processes involved in collecting and preparing fossil data. I then review the main techniques that use this data for calibrating the molecular clock. I argue that, in its current form, the fossilized birth-death process relies on assumptions about the mechanisms underlying fossilization and the data collection process that may negatively impact the date estimates. Node-dating approaches make better use of the data available, even though they rest on paleontologists' intervention to prepare raw fossil data. Altogether, this study provides indications that may help practitioners in selecting appropriate methods for molecular dating. It will also hopefully participate in defining the contour of future methodological developments in the field.

The reconstruction of ancestral genetic sequences from the analysis of contemporaneous data is a powerful tool to improve our understanding of molecular evolution. Various statistical criteria defined in a phylogenetic framework can be used to infer nucleotide, aminoa-cid or codon states at internal nodes of the tree, for every position along the sequence. These criteria generally select the state that maximises (or minimises) a given criterion. Although it is perfectly sensible from a statistical perspective, that strategy fails to convey useful information about the level of uncertainty associated to the inference. The present study introduces a new criterion for ancestral nucleotide reconstruction that selects a single state whenever the signal conveyed by the data is strong, and a combination of multiple states otherwise. Simulations demonstrate the benefit of this approach with a substantial increase in the accuracy of ancestral sequence reconstruction without significantly compromising on the precision of the solutions returned.

This study introduces a new Bayesian technique for molecular dating that explicitly accommodates for uncertainty in the phylogenetic position of calibrated nodes derived from the analysis of fossil data. The proposed approach thus defines an adequate framework for incorporating expert knowledge and/or prior information about the way fossils were collected in the inference of node ages. Although it belongs to the class of “node-dating” methods, this method shares interesting properties with “tip-dating” techniques. Yet, it alleviates some of the computational and modeling difficulties that hamper tip-dating approaches. The influence of fossil data on the probabilistic distribution of trees is the crux of the matter considered here. More specifically, among all the phylogenies that a tree model (e.g., the birth death process) generates, only a fraction of them “agree” with the fossil data. Bayesian inference under the new model requires taking this fraction into account. However, evaluating this quantity is difficult in practice. A generic solution to this issue is presented here. The proposed approach relies on a recent statistical technique, the so-called exchange algorithm, dedicated to drawing samples from “doubly intractable” distributions. A small example illustrates the problem of interest and the impact of uncertainty in the placement of calibration constraints in the phylogeny given fossil data. An analysis of land plant sequences and multiple fossils further highlights the pertinence of the proposed approach.

1 This study focuses on a conceptual issue with Bayesian inference of divergence times using Markov chain Monte Carlo. The influence of fossil data on the probabilistic distribution of trees is the crux of the matter considered here. More specifically, among all the phylogenies that a tree model (e.g., the birth-death process) generates, only a fraction of them “agree” with the fossil data at hands. Bayesian inference of divergence times using Markov Chain Monte Carlo requires taking this fraction into account. Yet, doing so is challenging and most Bayesian samplers have simply overlooked this hurdle so far, thereby providing approximate estimates of divergence times and tree process parameters. A generic solution to this issue is presented here. This solution relies on an original technique, the so-called exchange algorithm, dedicated to drawing samples from “doubly intractable” distributions. A small example illustrates the problem of interest and the impact of the approximation aforementioned on tree parameter estimates. The analysis of land plant sequences and multiple fossils further illustrates the importance of proper mathematical handling of calibration data in order to derive accurate estimates of node age.