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This book presents a history of microbial evolutionary biology from the 19th century to the present. It follows the research of molecular evolutionists who explore the origins of the genetic system and the primary life forms: three domains and multiple kingdoms, created by mechanisms very unlike those considered by Darwin and his followers.

Phylogenetic comparative methods comprise the general endeavor of using an estimated phylogenetic tree (or set of trees) to make secondary inferences: about trait evolution, diversification dynamics, biogeography, community ecology, and a wide range of other phenomena or processes. Over the past ten years or so, the phytools R package has grown to become an important research tool for phylogenetic comparative analysis. phytools is a diverse contributed R library now consisting of hundreds of different functions covering a variety of methods and purposes in phylogenetic biology. As of the time of writing, phytools included functionality for fitting models of trait evolution, for reconstructing ancestral states, for studying diversification on trees, and for visualizing phylogenies, comparative data, and fitted models, as well numerous other tasks related to phylogenetic biology. Here, I describe some significant features of and recent updates to phytools , while also illustrating several popular workflows of the phytools computational software.

PhyloNetworks is a Julia package for the inference, manipulation, visualization, and use of phylogenetic networks in an interactive environment. Inference of phylogenetic networks is done with maximum pseudolikelihood from gene trees or multi-locus sequences (SNaQ), with possible bootstrap analysis. PhyloNetworks is the first software providing tools to summarize a set of networks (from a bootstrap or posterior sample) with measures of tree edge support, hybrid edge support, and hybrid node support. Networks can be used for phylogenetic comparative analysis of continuous traits, to estimate ancestral states or do a phylogenetic regression. The software is available in open source and with documentation at https://github.com/crsl4/PhyloNetworks.jl

Phylogenetic signal is the tendency for closely related species to display similar trait values due to their common ancestry. Several methods have been developed for quantifying phylogenetic signal in univariate traits and for sets of traits treated simultaneously, and the statistical properties of these approaches have been extensively studied. However, methods for assessing phylogenetic signal in high-dimensional multivariate traits like shape are less well developed, and their statistical performance is not well characterized. In this article, I describe a generalization of the statistic of Blomberg et al. that is useful for quantifying and evaluating phylogenetic signal in highly dimensional multivariate data. The method (Kmult) is found from the equivalency between statistical methods based on covariance matrices and those based on distance matrices. Using computer simulations based on Brownian motion, I demonstrate that the expected value of Kmult remains at 1.0 as trait variation among species is increased or decreased, and as the number of trait dimensions is increased. By contrast, estimates of phylogenetic signal found with a squared-change parsimony procedure for multivariate data change with increasing trait variation among species and with increasing numbers of trait dimensions, confounding biological interpretations. I also evaluate the statistical performance of hypothesis testing procedures based on and find that the method displays appropriate Type I error and high statistical power for detecting phylogenetic signal in highdimensional data. Statistical properties of Kmult were consistent for simulations using bifurcating and random phylogenies, for simulations using different numbers of species, for simulations that varied the number of trait dimensions, and for different underlying models of trait covariance structure. Overall these findings demonstrate that provides a useful means of evaluating phylogenetic signal in high-dimensional multivariate traits. Finally, I illustrate the utility of the new approach by evaluating the strength of phylogenetic signal for head shape in a lineage of Plethodon salamanders.

Recent years have seen increased interest in phylogenetic comparative analyses of multivariate data sets, but to date the varied proposed approaches have not been extensively examined. Here we review the mathematical properties required of any multivariate method, and specifically evaluate existing multivariate phylogenetic comparative methods in this context. Phylogenetic comparative methods based on the full multivariate likelihood are robust to levels of covariation among trait dimensions and are insensitive to the orientation of the data set, but display increasing model misspecification as the number of trait dimensions increases. This is because the expected evolutionary covariance matrix (V) used in the likelihood calculations becomes more ill-conditioned as trait dimensionality increases, and as evolutionary models become more complex. Thus, these approaches are only appropriate for data sets with few traits and many species. Methods that summarize patterns across trait dimensions treated separately (e.g., SURFACE) incorrectly assume independence among trait dimensions, resulting in nearly a 100% model misspecification rate. Methods using pairwise composite likelihood are highly sensitive to levels of trait covariation, the orientation of the data set, and the number of trait dimensions. The consequences of these debilitating deficiencies are that a user can arrive at differing statistical conclusions, and therefore biological inferences, simply from a dataspace rotation, like principal component analysis. By contrast, algebraic generalizations of the standard phylogenetic comparative toolkit that use the trace of covariance matrices are insensitive to levels of trait covariation, the number of trait dimensions, and the orientation of the data set. Further, when appropriate permutation tests are used, these approaches display acceptable Type I error and statistical power. We conclude that methods summarizing information across trait dimensions, as well as pairwise composite likelihood methods should be avoided, whereas algebraic generalizations of the phylogenetic comparative toolkit provide a useful means of assessing macroevolutionary patterns in multivariate data. Finally, we discuss areas in which multivariate phylogenetic comparative methods are still in need of future development; namely highly multivariate Ornstein–Uhlenbeck models and approaches for multivariate evolutionary model comparisons.

Many questions in evolutionary biology require the quantification and comparison of rates of phenotypic evolution. Recently, phylogenetic comparative methods have been developed for comparing evolutionary rates on a phylogeny for single, univariate traits (σ²), and evolutionary rate matrices (R) for sets of traits treated simultaneously. However, high-dimensional traits like shape remain under-examined with this framework, because methods suited for such data have not been fully developed. In this article, I describe a method to quantify phylogenetic evolutionary rates for high-dimensional multivariate data $\\left( {\\sigma _{mult}^2} \\right)$, found from the equivalency between statistical methods based on covariance matrices and those based on distance matrices (R-mode and Q-mode methods). I then use simulations to evaluate the statistical performance of hypothesis-testing procedures that compare $\\sigma _{mult}^1$ for two or more groups of species on a phylogeny. Under both isotropic and non-isotropic conditions, and for differing numbers of trait dimensions, the proposed method displays appropriate Type I error and high statistical power for detecting known differences in $\\sigma _{mult}^1$ among groups. In contrast, the Type I error rate of likelihood tests based on the evolutionary rate matrix (R) increases as the number of trait dimensions (p) increases, and becomes unacceptably large when only a few trait dimensions are considered. Further, likelihood tests based on R cannot be computed when the number of trait dimensions equals or exceeds the number of taxa in the phylogeny (i.e., when p> N). These results demonstrate that tests based on $\\sigma _{mult}^1$ provide a useful means of comparing evolutionary rates for high-dimensional data that are otherwise not analytically accessible to methods based on the evolutionary rate matrix. This advance thus expands the phylogenetic comparative toolkit for high-dimensional phenotypic traits like shape. Finally, I illustrate the utility of the new approach by evaluating rates of head shape evolution in a lineage of Plethodon salamanders.

Studies of evolutionary correlations commonly use phylogenetic regression (i.e., independent contrasts and phylogenetic generalized least squares) to assess trait covariation in a phylogenetic context. However, while this approach is appropriate for evaluating trends in one or a few traits, it is incapable of assessing patterns in highly multivariate data, as the large number of variables relative to sample size prohibits parametric test statistics from being computed. This poses serious limitations for comparative biologists, who must either simplify how they quantify phenotypic traits, or alter the biological hypotheses they wish to examine. In this article, I propose a new statistical procedure for performing ANOVA and regression models in a phylogenetic context that can accommodate high-dimensional datasets. The approach is derived from the statistical equivalency between parametric methods using covariance matrices and methods based on distance matrices. Using simulations under Brownian motion, I show that the method displays appropriate Type I error rates and statistical power, whereas standard parametric procedures have decreasing power as data dimensionality increases. As such, the new procedure provides a useful means of assessing trait covariation across a set of taxa related by a phylogeny, enabling macroevolutionary biologists to test hypotheses of adaptation, and phenotypic change in high-dimensional datasets.

Evolutionary biology is multivariate, and advances in phylogenetic comparative methods for multivariate phenotypes have surged to accommodate this fact. Evolutionary trends in multivariate phenotypes are derived from distances and directions between species in a multivariate phenotype space. For these patterns to be interpretable, phenotypes should be characterized by traits in commensurate units and scale. Visualizing such trends, as is achieved with phylomorphospaces, should continue to play a prominent role in macroevolutionary analyses. Evaluating phylogenetic generalized least squares (PGLS) models (e.g., phylogenetic analysis of variance and regression) is valuable, but using parametric procedures is limited to only a few phenotypic variables. In contrast, nonparametric, permutation-based PGLS methods provide a flexible alternative and are thus preferred for high-dimensional multivariate phenotypes. Permutation-based methods for evaluating covariation within multivariate phenotypes are also well established and can test evolutionary trends in phenotypic integration. However, comparing evolutionary rates and modes in multivariate phenotypes remains an important area of future development.

Most existing methods for modeling trait evolution are univariate, although researchers are often interested in investigating evolutionary patterns and processes across multiple traits. Principal components analysis (PCA) is commonly used to reduce the dimensionality of multivariate data so that univariate trait models can be fit to individual principal components. The problem with using standard PCA on phylogenetically structured data has been previously pointed out yet it continues to be widely used in the literature. Here we demonstrate precisely how using standard PCA can mislead inferences: The first few principal components of traits evolved under constant-rate multivariate Brownian motion will appear to have evolved via an \"early burst\" process. A phylogenetic PCA (pPCA) has been proprosed to alleviate these issues. However, when the true model of trait evolution deviates from the model assumed in the calculation of the pPCA axes, we find that the use of pPCA suffers from similar artifacts as standard PCA. We show that data sets with high effective dimensionality are particularly likely to lead to erroneous inferences. Ultimately, all of the problems we report stem from the same underlying issue—by considering only the first few principal components as univariate traits, we are effectively examining a biased sample of a multivariate pattern. These results highlight the need for truly multivariate phylogenetic comparative methods. As these methods are still being developed, we discuss potential alternative strategies for using and interpreting models fit to univariate axes of multivariate data.

Phylogenetic regression is frequently used in macroevolutionary studies, and its statistical properties have been thoroughly investigated. By contrast, phylogenetic ANOVA has received relatively less attention, and the conditions leading to incorrect statistical and biological inferences when comparing multivariate phenotypes among groups remain underexplored. Here, we propose a refined method of randomizing residuals in a permutation procedure (RRPP) for evaluating phenotypic differences among groups while conditioning the data on the phylogeny. We show that RRPP displays appropriate statistical properties for both phylogenetic ANOVA and regression models, and for univariate and multivariate datasets. For ANOVA, we find that RRPP exhibits higher statistical power than methods utilizing phylogenetic simulation. Additionally, we investigate how group dispersion across the phylogeny affects inferences, and reveal that highly aggregated groups generate strong and significant correlations with the phylogeny, which reduce statistical power and subsequently affect biological interpretations. We discuss the broader implications of this phylogenetic group aggregation, and its relation to challenges encountered with other comparative methods where one or a few transitions in discrete traits are observed on the phylogeny. Finally, we recommend that phylogenetic comparative studies of continuous trait data use RRPP for assessing the significance of indicator variables as sources of trait variation.