arXiv subjects

Remco Bouckaert

Publications and source records attributed to Remco Bouckaert.

5 recordsLinked to original sources

arXiv2021

Combinatorial perspectives on Dollo-$k$ characters in phylogenetics

Recently, the perfect phylogeny model with persistent characters has attracted great attention in the literature. It is based on the assumption that complex traits or characters can only be gained once and lost once in the course of evolution. Here, we consider a generalization of this model, namely Dollo parsimony, that allows for multiple character losses. More precisely, we take a combinatorial perspective on the notion of Dollo-$k$ characters, i.e. traits that are gained at most once and lost precisely $k$ times throughout evolution. We first introduce an algorithm based on the notion of spanning subtrees for finding a Dollo-$k$ labeling for a given character and a given tree in linear time. We then compare persistent characters (consisting of the union of Dollo-0 and Dollo-1 characters) and general Dollo-$k$ characters. While it is known that there is a strong connection between Fitch parsimony and persistent characters, we show that Dollo parsimony and Fitch parsimony are in general very different. Moreover, while it is known that there is a direct relationship between the number of persistent characters and the Sackin index of a tree, a popular index of tree balance, we show that this relationship does not generalize to Dollo-$k$ characters. In fact, determining the number of Dollo-$k$ characters for a given tree is much more involved than counting persistent characters, and we end this manuscript by introducing a recursive approach for the former. This approach leads to a polynomial time algorithm for counting the number of Dollo-$k$ characters, and both this algorithm as well as the algorithm for computing Dollo-$k$ labelings are publicly available in the Babel package for BEAST 2.

math.CO↗

arXiv2019

Bayesian inference of species trees using diffusion models

We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with a new algorithm for numerically computing likelihoods of quantitative traits. The diffusion approach allows for analysis of datasets containing hundreds or thousands of individuals. The method, which we call \snapper, has been implemented as part of the Beast2 package. We introduce the models, the efficient algorithms, and report performance of \snapper on simulated data sets and on SNP data from rattlesnakes and freshwater turtles.

q-bio.PE↗

arXiv2018

Model selection and parameter inference in phylogenetics using Nested Sampling

Bayesian inference methods rely on numerical algorithms for both model selection and parameter inference. In general, these algorithms require a high computational effort to yield reliable estimates. One of the major challenges in phylogenetics is the estimation of the marginal likelihood. This quantity is commonly used for comparing different evolutionary models, but its calculation, even for simple models, incurs high computational cost. Another interesting challenge relates to the estimation of the posterior distribution. Often, long Markov chains are required to get sufficient samples to carry out parameter inference, especially for tree distributions. In general, these problems are addressed separately by using different procedures. Nested sampling (NS) is a Bayesian computation algorithm which provides the means to estimate marginal likelihoods together with their uncertainties, and to sample from the posterior distribution at no extra cost. The methods currently used in phylogenetics for marginal likelihood estimation lack in practicality due to their dependence on many tuning parameters and the inability of most implementations to provide a direct way to calculate the uncertainties associated with the estimates. To address these issues, we introduce NS to phylogenetics. Its performance is assessed under different scenarios and compared to established methods. We conclude that NS is a competitive and attractive algorithm for phylogenetic inference. An implementation is available as a package for BEAST 2 under the LGPL licence, accessible at https://github.com/BEAST2-Dev/nested-sampling.

q-bio.QM↗

arXiv2011

Exact coalescent likelihoods for unlinked markers in finite-sites mutation models

We derive exact formulae for the allele frequency spectrum under the coalescent with mutation, conditioned on allele counts at some fixed time in the past. We consider unlinked biallelic markers mutating according to a finite sites, or infinite sites, model. This work extends the coalescent theory of unlinked biallelic markers, enabling fast computations of allele frequency spectra in multiple populations. Our results have applications to demographic inference, species tree inference, and the analysis of genetic variation in closely related species more generally.

q-bio.PE↗

arXiv2011

Inferring Species Trees Directly from Biallelic Genetic Markers: Bypassing Gene Trees in a Full Coalescent Analysis

The multi-species coalescent provides an elegant theoretical framework for estimating species trees and species demographics from genetic markers. Practical applications of the multi-species coalescent model are, however, limited by the need to integrate or sample over all gene trees possible for each genetic marker. Here we describe a polynomial-time algorithm that computes the likelihood of a species tree directly from the markers under a finite-sites model of mutation, effectively integrating over all possible gene trees. The method applies to independent (unlinked) biallelic markers such as well-spaced single nucleotide polymorphisms (SNPs), and we have implemented it in SNAPP, a Markov chain Monte-Carlo sampler for inferring species trees, divergence dates, and population sizes. We report results from simulation experiments and from an analysis of 1997 amplified fragment length polymorphism (AFLP) loci in 69 individuals sampled from six species of {\em Ourisia} (New Zealand native foxglove).

q-bio.PE↗