Automation and Evaluation of the SOWH Test of Phylogenetic Topologies with SOWHAT

Samuel H. Church, Joseph F. Ryan, Casey W. Dunn

The Swofford-Olsen-Waddell-Hillis (SOWH) test is a method to evaluate incongruent phylogenetic topologies. It is used, for example, when an investigator wishes to know if the maximum likelihood tree recovered in their analysis is significantly different than an alternative phylogenetic hypothesis. The SOWH test compares the observed difference in likelihood between the topologies to a null distribution of differences in likelihood generated by parametric resampling. The SOWH test is a well-established and important phylogenetic method, but it can be difficult to implement and its sensitivity to various factors is not well understood. We wrote SOWHAT, a program that automates the SOWH test. In test analyses, we find that variation in parameter estimation as well as the use of a more complex model of parameter estimation have little impact on results, but that results can be inconsistent when an insufficient number of replicates are used to estimate the null distribution. We provide methods of analyzing the sampling as well as a simple stopping criteria for sufficient bootstrap replicates, which increase the overall reliability of the approach. Applications of the SOWH test should include explicit evaluations of sampling adequacy. SOWHAT is available for download from https://github.com/josephryan/SOWHAT.

Phylogenetic confidence intervals for the optimal trait value

Krzysztof Bartoszek, Serik Sagitov

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein-Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the sample mean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean is approximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

Quantifying MCMC Exploration of Phylogenetic Tree Space
Christopher Whidden, Frederick A. Matsen IV
Comments: 30 pages, 10 figures
Subjects: Populations and Evolution (q-bio.PE)

In order to gain an understanding of the effectiveness of phylogenetic Markov chain Monte Carlo (MCMC), it is important to understand how quickly the empirical distribution of the MCMC converges to the true posterior distribution. In this paper we investigate this problem on phylogenetic tree topologies with a metric that is especially well suited to the task: the subtree-prune-regraft (SPR) metric. This metric directly corresponds to the minimum number of MCMC rearrangements required to move between trees in common phylogenetic MCMC implementations. We use a novel graph-based approach to analyze tree space and find that the SPR metric is much more informative than simpler metrics that are unrelated to MCMC moves. In doing so we show conclusively that topological peaks do occur in real Bayesian phylogenetic posteriors with standard MCMC moves, investigate the efficiency of Metropolis-coupled MCMC (MCMCMC) in traversing the valleys between peaks, and show that conditional clade probability (CCP) can have systematic problems when there are multiple peaks.

Consistency of the Maximum Likelihood Estimator of Evolutionary Tree
Arindam RoyChoudhury
Subjects: Populations and Evolution (q-bio.PE)

Maximum likelihood estimation (MLE) methods are widely used for evolutionary tree. As evolutionary tree is not a smooth parameter, the consistency of its MLE has been a topic of debate. It has been noted without proof that the classical proof of consistency by Wald holds for the MLE of evolutionary tree. Other proofs of consistency under various models were also proposed. Here we will discuss some shortcomings in some of these proofs and comment on the applicability of Wald’s proof.

Are we able to detect mass extinction events using phylogenies ?
Sacha S.J. Laurent, Marc Robinson-Rechavi, Nicolas Salamin
Comments: 14 pages, 8 figures
Subjects: Populations and Evolution (q-bio.PE)

The estimation of the rates of speciation and extinction provides important information on the macro-evolutionary processes shaping biodiversity through time (Ricklefs 2007). Since the seminal paper by Nee et al. (1994), much work have been done to extend the applicability of the birth-death process, which now allows us to test a wide range of hypotheses on the dynamics of the diversification process. Several approaches have been developed to identify the changes in rates of diversification occurring along a phylogenetic tree. Among them, we can distinguish between lineage-dependent, trait-dependent, time-dependent and density-dependent changes. Lineage specific methods identify changes in speciation and extinction rates — {\lambda} and {\mu}, respectively — at inner nodes of a phylogenetic tree (Rabosky et al. 2007; Alfaro et al. 2009; Silvestro et al. 2011). We can also identify trait-dependence in macro-evolutionary rates if the states of the particular trait of interest are known for the species under study (Maddison et al. 2007; FitzJohn et al. 2009; Mayrose et al. 2011). It is also possible to look for concerted changes in rates on independent branches of the phylogenetic tree by dividing the tree into time slices (Stadler 2011a). Finally, density-dependent effects can be detected when changes of diversification are correlated with overall species number (Etienne et al. 2012). Most methods can correct for incomplete taxon sampling, by assigning species numbers at tips of the phylogeny (Alfaro et al. 2009; Stadler and Bokma 2013), or by introducing a sampling parameter (Nee et al. 1994). By taking into account this sampling parameter at time points in the past, one can also look for events of mass extinction (Stadler 2011a).

Majority rule has transition ratio 4 on Yule trees under a 2-state symmetric model

Elchanan Mossel, Mike Steel
(Submitted on 10 Apr 2014)

Inferring the ancestral state at the root of a phylogenetic tree from states observed at the leaves is a problem arising in evolutionary biology. The simplest technique — majority rule — estimates the root state by the most frequently occurring state at the leaves. Alternative methods — such as maximum parsimony – explicitly take the tree structure into account. Since either method can outperform the other on particular trees, it is useful to consider the accuracy of the methods on trees generated under some evolutionary null model, such as a Yule pure-birth model. In this short note, we answer a recently posed question concerning the performance of majority rule on Yule trees under a symmetric 2-state Markovian substitution model of character state change. We show that majority rule is accurate precisely when the ratio of the birth (speciation) rate of the Yule process to the substitution rate exceeds the value 4. By contrast, maximum parsimony has been shown to be accurate only when this ratio is at least 6. Our proof relies on a second moment calculation, coupling, and a novel application of a reflection principle.

Estimating Phylogeny from microRNA Data: A Critical Appraisal

Robert Thomson, David Plachetzki, Luke Mahler, Brian Moore

As progress toward a highly resolved tree of life continues to expose nodes that resist resolution, interest in new sources of phylogenetic information that are informative for these most difficult relationships continues to increase. One such potential source of information, the presence and absence of microRNA families, has been vigorously promoted as an ideal phylogenetic marker and has been recently deployed to resolve several long-standing phylogenetic questions. Understanding the utility of such markers for phylogenetic inference hinges on developing a better understanding for how such markers behave under suitable evolutionary models, as well as how they perform in real inference scenarios. However, as yet, no study has rigorously characterized the statistical behavior or utility of these markers. Here we examine the behavior and performance of microRNA presence/absence data under a variety of evolutionary models and reexamine datasets from several previous studies. We find that highly heterogeneous rates of microRNA gain and loss, pervasive secondary loss, and sampling error collectively render microRNA-based inference of phylogeny difficult, and fundamentally alter the conclusions for four of the five studies that we re-examine. Our results indicate that miRNA data have far less phylogenetic utility in resolving the tree of life than is currently recognized and we urge ample caution in their interpretation.

Bias and measurement error in comparative analyses: a case study with the Ornstein Uhlenbeck model

Gavin Huw Thomas, Natalie Cooper, Chris Venditti, Andrew Meade, Robert P Freckleton

Phylogenetic comparative methods are increasingly used to give new insight into variation, causes and consequences of trait variation among species. The foundation of these methods is a suite of models that attempt to capture evolutionary patterns by extending the Brownian constant variance model. However, the parameters of these models have been hypothesised to be biased and only asymptotically behave in a statistically predictable way as datasets become large. This does not seem to be widely appreciated. We show that a commonly used model in evolutionary biology (the Ornstein-Uhlenbeck model) is biased over a wide range of conditions. Many studies fitting this model use datasets that are small and prone to substantial biases. Our results suggest that simulating fitted models and comparing with empirical results is critical when fitting OU and other extensions of the Brownian model.

PGA: A Program for Genome Annotation by Comparative Analysis of Maximum Likelihood Phylogenies of Genes and Species

Paulo Bandiera-Paiva, Marcelo R.S. Briones
(Submitted on 2 Apr 2014)

The Phylogenetic Genome Annotator (PGA) is a computer program that enables real-time comparison of ‘gene trees’ versus ‘species trees’ obtained from predicted open reading frames of whole genome data. The gene phylogenies are inferred for each individual genome predicted proteins whereas the species phylogenies are inferred from rDNA data. The correlated protein domains, defined by PFAM, are then displayed side-by-side with a phylogeny of the corresponding species. The statistical support of gene clusters (branches) is given by the quartet puzzling method. This analysis readily discriminates paralogs from orthologs, enabling the identification of proteins originated by gene duplications and the prediction of possible functional divergence in groups of similar sequences.

Phylogenetic Stochastic Mapping without Matrix Exponentiation
Jan Irvahn, Vladimir N. Minin

Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organisms carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and work well for small state spaces. The computations slow down considerably for larger state spaces (e.g. space of codons), because current methodology relies on exponentiating CTMC infinitesimal rate matrices — an operation whose computational complexity grows as the size of the CTMC state space cubed. In this work, we introduce a new approach, based on a CTMC technique called uniformization, that does not use matrix exponentiation for phylogenetic stochastic mapping. Our method is based on a new Markov chain Monte Carlo (MCMC) algorithm that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared. Moreover, in contrast to competing matrix exponentiation methods, if the rate matrix is sparse, we can leverage this sparsity and increase the computational efficiency of our algorithm further. Using simulated data, we illustrate advantages of our MCMC algorithm and investigate how large the state space needs to be for our method to outperform matrix exponentiation approaches. We show that even on the moderately large state space of codons our MCMC method can be significantly faster than currently used matrix exponentiation methods.