Philosophical Transactions of the Royal Society B: Biological Sciences最新文献

In mathematical models of phylogenetic trees evolving in time, a labelled history for a rooted labelled bifurcating tree is a temporal sequence of the branchings that give rise to the tree. That is, given a leaf-labelled tree with [Formula: see text] leaves and [Formula: see text] internal nodes, a labelled history is an identification between the internal nodes and the set [Formula: see text], such that the label assigned to a given node is strictly greater than the labels assigned to its descendants. We generalize the concept of labelled histories to [Formula: see text]-furcating trees. Consider a rooted labelled tree in which each internal node has exactly [Formula: see text] children, [Formula: see text]. We first generalize the enumeration of labelled histories for a bifurcating tree ([Formula: see text]) to enumerate labelled histories for an [Formula: see text]-furcating tree with arbitrary [Formula: see text]. We formulate a conjecture for the rooted unlabelled [Formula: see text]-furcating tree shape on [Formula: see text] internal nodes whose labelled topologies have the most labelled histories. Finally, we enumerate labelled histories for [Formula: see text]-furcating trees in a setting that allows for simultaneous branchings. These results advance mathematical phylogenetic modelling by extending computations concerning fundamental features of bifurcating phylogenetic trees to a more general class of multifurcating trees.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

Good representations for phylogenetic trees and networks are important for enhancing storage efficiency and scalability for the inference and analysis of evolutionary trees for genes, genomes and species. We propose a new representation for rooted phylogenetic trees that encodes a tree on [Formula: see text] ordered taxa as a vector of length [Formula: see text] in which each taxon appears exactly twice. Using this new tree representation, we introduce a novel tree rearrangement operator, termed an HOP, that results in a tree space of linear diameter and quadratic neighbourhood size. We also introduce a novel metric, the HOP distance, which is the minimum number of HOPs to transform a tree into another tree. The HOP distance can be computed in near-linear time-a rare instance of tree rearrangement distance that is tractable. Our experiments show that the HOP distance is better correlated to the Subtree-Prune-and-Regraft distance than the widely used Robinson-Foulds distance. We also describe how the proposed tree representation can be further generalized to tree-child networks, showcasing its versatility and potential applications in broader evolutionary analyses.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

The paper written in 1925 by G. Udny Yule that we celebrate in this special issue introduces several novelties and results that we recall in detail. First, we discuss Yule's (1925)main legacies over the past century, focusing on empirical frequency distributions with heavy tails and random tree models for phylogenies. We estimate the year when Yule's work was re-discovered by scientists interested in stochastic processes of population growth (1948) and the year from which it began to be cited (1951, Yule's death). We highlight overlooked aspects of Yule's work (e.g. the Yule process of Yule processes) and correct some common misattributions (e.g. the Yule tree). Second, we generalize Yule's results on the average frequency of genera of a given age and size (number of species). We show that his formula also applies to the age [Formula: see text] and size [Formula: see text] of any randomly chosen genus and that the pairs [Formula: see text] are equally distributed and independent across genera. This property extends to triples [Formula: see text], where [Formula: see text] are the coalescence times of the genus phylogeny, even when species diversification within genera follows any integer-valued process, including species extinctions. Studying [Formula: see text] in this broader context allows us to identify cases where [Formula: see text] has a power-law tail distribution, with new applications to urn schemes.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture. Computing the likelihood of data observed at the leaves is costly as the size and complexity of the phylogeny grows. Efficient algorithms exist for trees, but cannot be applied to networks. We show that a vast array of models for trait evolution along phylogenetic networks can be reformulated as graphical models, for which efficient belief propagation algorithms exist. We provide a brief review of belief propagation on general graphical models, then focus on linear Gaussian models for continuous traits. We show how belief propagation techniques can be applied for exact or approximate (but more scalable) likelihood and gradient calculations, and prove novel results for efficient parameter inference of some models. We highlight the possible fruitful interactions between graphical models and phylogenetic methods. For example, approximate likelihood approaches have the potential to greatly reduce computational costs for phylogenies with reticulations.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

A wide variety of stochastic models of cladogenesis (based on speciation and extinction) lead to an identical distribution on phylogenetic tree shapes once the edge lengths are ignored. By contrast, the distribution of the tree's edge lengths is generally quite sensitive to the underlying model. In this paper, we review the impact of different model choices on tree shape and edge length distribution, and its impact for studying the properties of phylogenetic diversity (PD) as a measure of biodiversity, and the loss of PD as species become extinct at the present. We also compare PD with a stochastic model of feature diversity, and investigate some mathematical links and inequalities between these two measures plus their predictions concerning the loss of biodiversity under extinction at the present.This article is part of the theme issue "'A mathematical theory of evolution": phylogenetic models dating back 100 years'.

Shape parameters, e.g. balance indices, of evolutionary trees have been extensively studied under the Yule model in phylogenetics. Independently, many of the same parameters have also been studied for random binary search trees in computer science, where they measure the running time of algorithms. In fact, under the Yule and binary search tree models, these parameters have the same distribution, resulting in many identical discoveries. In this survey, we explain these connections and introduce some of the tools that have been used in computer science to derive stochastic results for shape parameters.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

Models of random phylogenetic networks have been used since the inception of the field, but the introduction and rigorous study of mathematically tractable models is a much more recent topic that has gained momentum in the last 5 years. This manuscript discusses some recent developments in the field through a selection of examples. The emphasis is on the techniques rather than on the results themselves, and on probabilistic tools rather than on combinatorial ones.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

The phylogenetic inference package GCtree uses abundance of sampled sequences to improve the performance of parsimony-based inference, using a branching process model. Our previous work showed that GCtree performs competitively on B-cell receptor data, compared with other similar tools. In this article, we describe recent enhancements to GCtree, including an efficient tree storage data structure that discovers additional diversity of parsimonious trees with negligible additional computational cost. We also describe a suite of new objective functions that can be used to rank these trees, including a Poisson context likelihood function that models sequence evolution in a context-sensitive way. We validate these additions to GCtree with simulated B-cell receptor data, and benchmark performance against other phylogenetic inference tools.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

The birth-death process (BDP) is widely used in evolutionary biology as a model for generating phylogenetic trees of species. The generalized birth-death process (GBDP) allows rate variation over time, with speciation and extinction rates to be arbitrary functions of time. Here we review the probability theory underpinning the GBDP as a model of cladogenesis and recent findings concerning its identifiability. The GBDP with arbitrary continuous rate functions has been shown to be non-identifiable from lineage-through-time data: even with species phylogenies of infinite size the parameters cannot be estimated. However, a restricted class of BDPs with piecewise-constant rates has been shown to be identifiable. We review and illustrate these results using simple examples and discuss their implications for biologists interested in inferring the past tempo and mode of evolution using reconstructed phylogenetic trees.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

Standard birth-death (BD) processes used in macroevolutionary studies assume instantaneous speciation, an unrealistic premise that limits the interpretation of speciation and extinction rates. The protracted birth-death (PBD) model instead assumes that speciation involves two steps: initiation and completion. In order to understand their respective influence on macroevolutionary speciation rates, we compute a standard time-varying BD scenario that is 'equivalent' to the PBD model in terms of speciation and extinction probabilities. First, we find a sharp decline in the equivalent birth rate near the present, indicating that rates estimated at the tips of phylogenies may not accurately reflect the underlying speciation process. Second, the completion rate controls the timing of the decay rather than the asymptotic equivalent rates. The equivalent birth rate in the past scales with the speciation initiation rate, with a scaling factor depending mostly on the population extinction rate. Our results suggest that the rates of population formation and extinction may often play a larger role than the speed of accumulation of reproductive isolation in modulating speciation rates. Our study establishes a theoretical framework for understanding how microevolutionary processes combine to explain the diversification of species on macroevolutionary time scales.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.