Root location in random trees: a polarity property of all sampling consistent phylogenetic models except one

On cherry and pitchfork distributions of random rooted and unrooted phylogenetic trees

Tree shape statistics are important for investigating evolutionary mechanisms mediating phylogenetic trees. As a step towards bridging shape statistics between rooted and unrooted trees, we present a comparison study on two subtree statistics known as numbers of cherries and pitchforks for the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models. Based on recursive formulas on the joint distribution of the number of cherries and that of pitchforks, it is shown that cherry distributions are log-concave for both rooted and unrooted trees under these two models. Furthermore, the mean number of cherries and that of pitchforks for unrooted trees converge respectively to those for rooted trees under the YHK model while there exists a limiting gap of 1∕4 for the PDA model. Finally, the total variation distances between the cherry distributions of rooted and those of unrooted trees converge for both models. Our results indicate that caution is required for conducting statistical analysis for tree shapes involving both rooted and unrooted trees.

Rooting Phylogenies and the Tree of Life While Minimizing Ad Hoc and Auxiliary Assumptions

Phylogenetic methods unearth evolutionary history when supported by three starting points of reason: (1) the continuity axiom begs the existence of a "model" of evolutionary change, (2) the singularity axiom defines the historical ground plan (phylogeny) in which biological entities (taxa) evolve, and (3) the memory axiom demands identification of biological attributes (characters) with historical information. Axiom consequences are interlinked, making the retrodiction enterprise an endeavor of reciprocal fulfillment. In particular, establishing direction of evolutionary change (character polarization) roots phylogenies and enables testing the existence of historical memory (homology). Unfortunately, rooting phylogenies, especially the "tree of life," generally follow narratives instead of integrating empirical and theoretical knowledge of retrodictive exploration. This stems mostly from a focus on molecular sequence analysis and uncertainties about rooting methods. Here, we review available rooting criteria, highlighting the need to minimize both ad hoc and auxiliary assumptions, especially argumentative ad hocness. We show that while the outgroup comparison method has been widely adopted, the generality criterion of nesting and additive phylogenetic change embodied in Weston rule offers the most powerful rooting approach. We also propose a change of focus, from phylogenies that describe the evolution of biological systems to those that describe the evolution of parts of those systems. This weakens violation of character independence, helps formalize the generality criterion of rooting, and provides new ways to study the problem of evolution.

Displayed Trees Do Not Determine Distinguishability Under the Network Multispecies Coalescent

Recent work in estimating species relationships from gene trees has included inferring networks assuming that past hybridization has occurred between species. Probabilistic models using the multispecies coalescent can be used in this framework for likelihood-based inference of both network topologies and parameters, including branch lengths and hybridization parameters. A difficulty for such methods is that it is not always clear whether, or to what extent, networks are identifiable-that is whether there could be two distinct networks that lead to the same distribution of gene trees. For cases in which incomplete lineage sorting occurs in addition to hybridization, we demonstrate a new representation of the species network likelihood that expresses the probability distribution of the gene tree topologies as a linear combination of gene tree distributions given a set of species trees. This representation makes it clear that in some cases in which two distinct networks give the same distribution of gene trees when sampling one allele per species, the two networks can be distinguished theoretically when multiple individuals are sampled per species. This result means that network identifiability is not only a function of the trees displayed by the networks but also depends on allele sampling within species. We additionally give an example in which two networks that display exactly the same trees can be distinguished from their gene trees even when there is only one lineage sampled per species. [gene tree, hybridization, identifiability, maximum likelihood, species tree, phylogeny.].

Inferring rooted species trees from unrooted gene trees using approximate Bayesian computation

Methods for inferring species trees from gene trees motivated by incomplete lineage sorting typically use either rooted gene trees to infer a rooted species tree, or use unrooted gene trees to infer an unrooted species tree, which is then typically rooted using one or more outgroups. Theoretically, however, it has been known since 2011 that it is possible to consistently infer the root of the species tree directly from unrooted gene trees without assuming an outgroup. Here, we use approximate Bayesian computation to infer the root of the species tree from unrooted gene trees assuming the multispecies coalescent model. It is hoped that this approach will be useful in cases where an appropriate outgroup is difficult to find and gene trees do not follow a molecular clock. We use approximate Bayesian computation to infer the root of the species tree from unrooted gene trees. This approach could also be useful when there is prior information that makes a small number of root locations plausible in an unrooted species tree.

Rooting Trees, Methods for

Identifying the root of a phylogenetic tree is important because incorrectly rooted phylogenetic trees may mislead evolutionary and taxonomic inferences. Many techniques for inferring the root have been proposed, but each has shortcomings that may make it inappropriate for any particular dataset. Here we outline the various ways to root phylogenetic trees, which include: outgroup, midpoint rooting, molecular clock rooting, and Bayesian molecular clock rooting. In addition, we discuss the pros and cons and also list software availability for each of the rooting methods.

Clades and clans: a comparison study of two evolutionary models

The Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model are two binary tree generating models that are widely used in evolutionary biology. Understanding the distributions of clade sizes under these two models provides valuable insights into macro-evolutionary processes, and is important in hypothesis testing and Bayesian analyses in phylogenetics. Here we show that these distributions are log-convex, which implies that very large clades or very small clades are more likely to occur under these two models. Moreover, we prove that there exists a critical value κ(n) for each n ≥ 4 such that for a given clade with size k, the probability that this clade is contained in a random tree with n leaves generated under the YHK model is higher than that under the PDA model if 1 < k < κ(n),and lower if κ(n) < k < n. Finally, we extend our results to binary unrooted trees, and obtain similar results for the distributions of clan sizes.

Unrooted tree reconciliation: a unified approach

Tree comparison functions are widely used in phylogenetics for comparing evolutionary trees. Unrooted trees can be compared with rooted trees by identifying all rootings of the unrooted tree that minimize some provided comparison function between two rooted trees. The plateau property is satisfied by the provided function, if all optimal rootings form a subtree, or plateau, in the unrooted tree, from which the rootings along every path toward a leaf have monotonically increasing costs. This property is sufficient for the linear-time identification of all optimal rootings and rooting costs. However, the plateau property has only been proven for a few rooted comparison functions, requiring individual proofs for each function without benefitting from inherent structural features of such functions. Here, we introduce the consistency condition that is sufficient for a general function to satisfy the plateau property. For consistent functions, we introduce general linear-time solutions that identify optimal rootings and all rooting costs. Further, we identify novel relationships between consistent functions in terms of plateaus, especially the plateau of the well-studied duplication-loss function is part of a plateau of every other consistent function. We introduce a novel approach for identifying consistent cost functions by defining a formal language of Boolean costs. Formulas in this language can be interpreted as cost functions. Finally, we demonstrate the performance of our general linear-time solutions in practice using empirical and simulation studies.