Extant timetrees are consistent with a myriad of diversification histories.

Time-calibrated phylogenies of extant species (referred to here as 'extant timetrees') are widely used for estimating diversification dynamics1. However, there has been considerable debate surrounding the reliability of these inferences2-5 and, to date, this critical question remains unresolved. Here we clarify the precise information that can be extracted from extant timetrees under the generalized birth-death model, which underlies most existing methods of estimation. We prove that, for any diversification scenario, there exists an infinite number of alternative diversification scenarios that are equally likely to have generated any given extant timetree. These 'congruent' scenarios cannot possibly be distinguished using extant timetrees alone, even in the presence of infinite data. Importantly, congruent diversification scenarios can exhibit markedly different and yet similarly plausible dynamics, which suggests that many previous studies may have over-interpreted phylogenetic evidence. We introduce identifiable and easily interpretable variables that contain all available information about past diversification dynamics, and demonstrate that these can be estimated from extant timetrees. We suggest that measuring and modelling these identifiable variables offers a more robust way to study historical diversification dynamics. Our findings also make it clear that palaeontological data will continue to be crucial for answering some macroevolutionary questions.

Speciation gradients and the distribution of biodiversity.

Global patterns of biodiversity are influenced by spatial and environmental variations in the rate at which new species form. We relate variations in speciation rates to six key patterns of biodiversity worldwide, including the species-area relationship, latitudinal gradients in species and genetic diversity, and between-habitat differences in species richness. Although they sometimes mirror biodiversity patterns, recent rates of speciation, at the tip of the tree of life, are often highest where species richness is low. Speciation gradients therefore shape, but are also shaped by, biodiversity gradients and are often more useful for predicting future patterns of biodiversity than for interpreting the past.

Fundamental Identifiability Limits in Molecular Epidemiology.

Viral phylogenies provide crucial information on the spread of infectious diseases, and many studies fit mathematical models to phylogenetic data to estimate epidemiological parameters such as the effective reproduction ratio (Re) over time. Such phylodynamic inferences often complement or even substitute for conventional surveillance data, particularly when sampling is poor or delayed. It remains generally unknown, however, how robust phylodynamic epidemiological inferences are, especially when there is uncertainty regarding pathogen prevalence and sampling intensity. Here, we use recently developed mathematical techniques to fully characterize the information that can possibly be extracted from serially collected viral phylogenetic data, in the context of the commonly used birth-death-sampling model. We show that for any candidate epidemiological scenario, there exists a myriad of alternative, markedly different, and yet plausible "congruent" scenarios that cannot be distinguished using phylogenetic data alone, no matter how large the data set. In the absence of strong constraints or rate priors across the entire study period, neither maximum-likelihood fitting nor Bayesian inference can reliably reconstruct the true epidemiological dynamics from phylogenetic data alone; rather, estimators can only converge to the "congruence class" of the true dynamics. We propose concrete and feasible strategies for making more robust epidemiological inferences from viral phylogenetic data.

Unifying Phylogenetic Birth-Death Models in Epidemiology and Macroevolution.

Birth-death stochastic processes are the foundations of many phylogenetic models and are widely used to make inferences about epidemiological and macroevolutionary dynamics. There are a large number of birth-death model variants that have been developed; these impose different assumptions about the temporal dynamics of the parameters and about the sampling process. As each of these variants was individually derived, it has been difficult to understand the relationships between them as well as their precise biological and mathematical assumptions. Without a common mathematical foundation, deriving new models is nontrivial. Here, we unify these models into a single framework, prove that many previously developed epidemiological and macroevolutionary models are all special cases of a more general model, and illustrate the connections between these variants. This unification includes both models where the process is the same for all lineages and those in which it varies across types. We also outline a straightforward procedure for deriving likelihood functions for arbitrarily complex birth-death(-sampling) models that will hopefully allow researchers to explore a wider array of scenarios than was previously possible. By rederiving existing single-type birth-death sampling models, we clarify and synthesize the range of explicit and implicit assumptions made by these models. [Birth-death processes; epidemiology; macroevolution; phylogenetics; statistical inference.].

Investigating Morphological Complexes Using Informational Dissonance and Bayes Factors: A Case Study in Corbiculate Bees.

It is widely recognized that different regions of a genome often have different evolutionary histories and that ignoring this variation when estimating phylogenies can be misleading. However, the extent to which this is also true for morphological data is still largely unknown. Discordance among morphological traits might plausibly arise due to either variable convergent selection pressures or else phenomena such as hemiplasy. Here, we investigate patterns of discordance among 282 morphological characters, which we scored for 50 bee species particularly targeting corbiculate bees, a group that includes the well-known eusocial honeybees and bumblebees. As a starting point for selecting the most meaningful partitions in the data, we grouped characters as morphological modules, highly integrated trait complexes that as a result of developmental constraints or coordinated selection we expect to share an evolutionary history and trajectory. In order to assess conflict and coherence across and within these morphological modules, we used recently developed approaches for computing Bayesian phylogenetic information allied with model comparisons using Bayes factors. We found that despite considerable conflict among morphological complexes, accounting for among-character and among-partition rate variation with individual gamma distributions, rate multipliers, and linked branch lengths can lead to coherent phylogenetic inference using morphological data. We suggest that evaluating information content and dissonance among partitions is a useful step in estimating phylogenies from morphological data, just as it is with molecular data. Furthermore, we argue that adopting emerging approaches for investigating dissonance in genomic datasets may provide new insights into the integration and evolution of anatomical complexes. [Apidae; entropy; morphological modules; phenotypic integration; phylogenetic information.].

Macroevolutionary diversification rates show time dependency.

For centuries, biologists have been captivated by the vast disparity in species richness between different groups of organisms. Variation in diversity is widely attributed to differences between groups in how fast they speciate or go extinct. Such macroevolutionary rates have been estimated for thousands of groups and have been correlated with an incredible variety of organismal traits. Here we analyze a large collection of phylogenetic trees and fossil time series and describe a hidden generality among these seemingly idiosyncratic results: speciation and extinction rates follow a scaling law in which both depend on the age of the group in which they are measured, with the fastest rates in the youngest clades. Using a series of simulations and sensitivity analyses, we demonstrate that the time dependency is unlikely to be a result of simple statistical artifacts. As such, this time scaling is likely a genuine feature of the tree of life, hinting that the dynamics of biodiversity over deep time may be driven in part by surprisingly simple and general principles.

Phylogenetic history of vascular plant metabolism revealed using a macroevolutionary common garden.

While the fundamental biophysics of C3 photosynthesis is highly conserved across plants, substantial leaf structural and enzymatic variation translates into variability in rates of carbon assimilation. Although this variation is well documented, it remains poorly understood how photosynthetic rates evolve, and whether macroevolutionary changes are related to the evolution of leaf morphology and biochemistry. A substantial challenge in large-scale comparative studies is disentangling evolutionary adaptation from environmental acclimation. We overcome this by using a 'macroevolutionary common garden' approach in which we measured metabolic traits (Jmax and Vcmax) from 111 phylogenetically diverse species in a shared environment. We find substantial phylogenetic signal in these traits at moderate phylogenetic timescales, but this signal dissipates quickly at deeper scales. Morphological traits exhibit phylogenetic signal over much deeper timescales, suggesting that these are less evolutionarily constrained than metabolic traits. Furthermore, while morphological and biochemical traits (LMA, Narea and Carea) are weakly predictive of Jmax and Vcmax, evolutionary changes in these traits are mostly decoupled from changes in metabolic traits. This lack of tight evolutionary coupling implies that it may be incorrect to use changes in these functional traits in response to global change to infer that photosynthetic strategy is also evolving.

A General and Efficient Algorithm for the Likelihood of Diversification and Discrete-Trait Evolutionary Models.

As the size of phylogenetic trees and comparative data continue to grow and more complex models are developed to investigate the processes that gave rise to them, macroevolutionary analyses are becoming increasingly limited by computational requirements. Here, we introduce a novel algorithm, based on the "flow" of the differential equations that describe likelihoods along tree edges in backward time, to reduce redundancy in calculations and efficiently compute the likelihood of various macroevolutionary models. Our algorithm applies to several diversification models, including birth-death models and models that account for state- or time-dependent rates, as well as many commonly used models of discrete-trait evolution, and provides an alternative way to describe macroevolutionary model likelihoods. As a demonstration of our algorithm's utility, we implemented it for a popular class of state-dependent diversification models-BiSSE, MuSSE, and their extensions to hidden-states. Our implementation is available through the R package $\texttt{castor}$. We show that, for these models, our algorithm is one or more orders of magnitude faster than existing implementations when applied to large phylogenies. Our algorithm thus enables the fitting of state-dependent diversification models to modern massive phylogenies with millions of tips and may lead to potentially similar computational improvements for many other macroevolutionary models.

Macroevolutionary history predicts flowering time but not phenological sensitivity to temperature in grasses.

PREMISE: Long-term observations show that flowering phenology has shifted in many lineages in response to climate change. However, it remains unclear whether these results can be generalized to predict the presence, direction, or magnitude of responses in lineages for which we lack long time-series data. If phenological responses are phylogenetically conserved, we can extrapolate from species for which we have data to predict the responses of close relatives. While several studies have found that closely related species flower at similar times, fewer have evaluated whether phylogenetically proximal species respond to environmental change similarly. METHODS: We paired flowering time data from 3161 manually scored herbarium specimens of 72 species of grasses (Poaceae) with historical climate data and analyzed the phylogenetic signal and phylogenetic half-life of phenological sensitivity. We also ran these analyses on a subset of species showing statistically significant sensitivities, in order to assess the role of sampling bias on phylogenetic signal. RESULTS: Closely related grass species tend to flower at similar times, but flowering times respond to temperature changes in species-specific ways. We also show that only including species for which there is strong evidence of phenological shifts results in overestimating phylogenetic signal. CONCLUSIONS: In agreement with other recent studies, our results suggest caution in extrapolating from evidence of phylogenetic similarity to predicting shared responses in this ecologically relevant trait. Future work is needed to better understand the discrepancy between the phylogenetic signal in observed phenological shifts and absence of such signal in sensitivity.

Detecting the macroevolutionary signal of species interactions.

Species interactions lie at the heart of many theories of macroevolution, from adaptive radiation to the Red Queen. Although some theories describe the imprint that interactions will have over long timescales, we are still missing a comprehensive understanding of the effects of interactions on macroevolution. Current research shows strong evidence for the impact of interactions on macroevolutionary patterns of trait evolution and diversification, yet many macroevolutionary studies have only a tenuous relationship to ecological studies of interactions over shorter timescales. We review current research in this area, highlighting approaches that explicitly model species interactions and connect them to broad-scale macroevolutionary patterns. We also suggest that progress has been made by taking an integrative interdisciplinary look at individual clades. We focus on African cichlids as a case study of how this approach can be fruitful. Overall, although the evidence for species interactions shaping macroevolution is strong, further work using integrative and model-based approaches is needed to spur progress towards understanding the complex dynamics that structure communities over time and space.

Rethinking phylogenetic comparative methods.

As a result of the process of descent with modification, closely related species tend to be similar to one another in a myriad different ways. In statistical terms, this means that traits measured on one species will not be independent of traits measured on others. Since their introduction in the 1980s, phylogenetic comparative methods (PCMs) have been framed as a solution to this problem. In this article, we argue that this way of thinking about PCMs is deeply misleading. Not only has this sowed widespread confusion in the literature about what PCMs are doing but has led us to develop methods that are susceptible to the very thing we sought to build defenses against-unreplicated evolutionary events. Through three Case Studies, we demonstrate that the susceptibility to singular events is indeed a recurring problem in comparative biology that links several seemingly unrelated controversies. In each Case Study, we propose a potential solution to the problem. While the details of our proposed solutions differ, they share a common theme: unifying hypothesis testing with data-driven approaches (which we term "phylogenetic natural history") to disentangle the impact of singular evolutionary events from that of the factors we are investigating. More broadly, we argue that our field has, at times, been sloppy when weighing evidence in support of causal hypotheses. We suggest that one way to refine our inferences is to re-imagine phylogenies as probabilistic graphical models; adopting this way of thinking will help clarify precisely what we are testing and what evidence supports our claims.

Transitions in sex determination and sex chromosomes across vertebrate species.

Despite the prevalence of sexual reproduction across eukaryotes, there is a remarkable diversity of sex-determination mechanisms. The underlying causes of this diversity remain unclear, and it is unknown whether there are convergent trends in the directionality of turnover in sex-determination mechanisms. We used the recently assembled Tree of Sex database to assess patterns in the evolution of sex-determination systems in the remarkably diverse vertebrate clades of teleost fish, squamate reptiles and amphibians. Contrary to theoretical predictions, we find no evidence that the evolution of separate sexes is irreversible, as transitions from separate sexes to hermaphroditism occur at higher rates than the reverse in fish. We also find that transitions from environmental sex determination to genetic sex determination occur at higher rates than the reverse in both squamates and fish, suggesting that genetic sex determination is more stable. However, our data are not consistent with the hypothesis that heteromorphic sex chromosomes are an "evolutionary trap." Rather, we find similar transition rates between homomorphic and heteromorphic sex chromosomes in both fish and amphibians, and to environmental sex determination from heteromorphic vs. homomorphic sex chromosome systems in fish. Finally, we find that transitions between male and female heterogamety occur at similar rates in amphibians and squamates, while transitions to male heterogamety occur at higher rates in fish. Together, these results provide the most comprehensive view to date of the evolution of vertebrate sex determination in a phylogenetic context, providing new insight into long-standing questions about the evolution of sexual reproduction.

Conserving Phylogenetic Diversity Can Be a Poor Strategy for Conserving Functional Diversity.

For decades, academic biologists have advocated for making conservation decisions in light of evolutionary history. Specifically, they suggest that policy makers should prioritize conserving phylogenetically diverse assemblages. The most prominent argument is that conserving phylogenetic diversity (PD) will also conserve diversity in traits and features (functional diversity [FD]), which may be valuable for a number of reasons. The claim that PD-maximized ("maxPD") sets of taxa will also have high FD is often taken at face value and in cases where researchers have actually tested it, they have done so by measuring the phylogenetic signal in ecologically important functional traits. The rationale is that if traits closely mirror phylogeny, then saving the maxPD set of taxa will tend to maximize FD and if traits do not have phylogenetic structure, then saving the maxPD set of taxa will be no better at capturing FD than criteria that ignore PD. Here, we suggest that measuring the phylogenetic signal in traits is uninformative for evaluating the effectiveness of using PD in conservation. We evolve traits under several different models and, for the first time, directly compare the FD of a set of taxa that maximize PD to the FD of a random set of the same size. Under many common models of trait evolution and tree shapes, conserving the maxPD set of taxa will conserve more FD than conserving a random set of the same size. However, this result cannot be generalized to other classes of models. We find that under biologically plausible scenarios, using PD to select species can actually lead to less FD compared with a random set. Critically, this can occur even when there is phylogenetic signal in the traits. Predicting exactly when we expect using PD to be a good strategy for conserving FD is challenging, as it depends on complex interactions between tree shape and the assumptions of the evolutionary model. Nonetheless, if our goal is to maintain trait diversity, the fact that conserving taxa based on PD will not reliably conserve at least as much FD as choosing randomly raises serious concerns about the general utility of PD in conservation.

Y fuse? Sex chromosome fusions in fishes and reptiles.

Chromosomal fusion plays a recurring role in the evolution of adaptations and reproductive isolation among species, yet little is known of the evolutionary drivers of chromosomal fusions. Because sex chromosomes (X and Y in male heterogametic systems, Z and W in female heterogametic systems) differ in their selective, mutational, and demographic environments, those differences provide a unique opportunity to dissect the evolutionary forces that drive chromosomal fusions. We estimate the rate at which fusions between sex chromosomes and autosomes become established across the phylogenies of both fishes and squamate reptiles. Both the incidence among extant species and the establishment rate of Y-autosome fusions is much higher than for X-autosome, Z-autosome, or W-autosome fusions. Using population genetic models, we show that this pattern cannot be reconciled with many standard explanations for the spread of fusions. In particular, direct selection acting on fusions or sexually antagonistic selection cannot, on their own, account for the predominance of Y-autosome fusions. The most plausible explanation for the observed data seems to be (a) that fusions are slightly deleterious, and (b) that the mutation rate is male-biased or the reproductive sex ratio is female-biased. We identify other combinations of evolutionary forces that might in principle account for the data although they appear less likely. Our results shed light on the processes that drive structural changes throughout the genome.

The Evolution of Energetic Scaling across the Vertebrate Tree of Life.

Metabolism is the link between ecology and physiology-it dictates the flow of energy through individuals and across trophic levels. Much of the predictive power of metabolic theories of ecology derives from the scaling relationship between organismal size and metabolic rate. There is growing evidence that this scaling relationship is not universal, but we have little knowledge of how it has evolved over macroevolutionary time. Here we develop a novel phylogenetic comparative method to investigate how often and in which clades the macroevolutionary dynamics of the metabolic scaling have changed. We find strong evidence that the metabolic scaling relationship has shifted multiple times across the vertebrate phylogeny. However, shifts are rare and otherwise strongly constrained. Importantly, both the estimated slope and intercept values vary widely across regimes, with slopes that spanned across theoretically predicted values such as 2/3 or 3/4. We further tested whether traits such as ecto-/endothermy, genome size, and quadratic curvature with body mass (i.e., energetic constraints at extreme body sizes) could explain the observed pattern of shifts. Though these factors help explain some of the variation in scaling parameters, much of the remaining variation remains elusive. Our results lay the groundwork for further exploration of the evolutionary and ecological drivers of major transitions in metabolic strategy and for harnessing this information to improve macroecological predictions.

Warming-Induced Changes to Body Size Stabilize Consumer-Resource Dynamics.

Both body size and temperature directly influence consumer-resource dynamics. There is also widespread empirical evidence for the temperature-size rule (TSR), which creates a negative relationship between temperature and body size. However, it is not known how the TSR affects community dynamics. Here we integrate temperature- and size-dependent models to include indirect effects of warming, through changes in body size, to answer the question, How does the TSR affect the predicted response of consumer-resource systems to warming? We find that the TSR is expected to maintain consumer-resource biomass ratios and buffer the community from extinctions under warming. While our results are limited to conditions where organisms are below their thermal optimum, they hold under a range of realistic temperature-size responses and are robust to the type of functional response. Our analyses suggest that the widely observed TSR may reduce the impacts of warming on consumer-resource systems.

Comparative Analysis of Principal Components Can be Misleading.

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.

Model Adequacy and the Macroevolution of Angiosperm Functional Traits.

Making meaningful inferences from phylogenetic comparative data requires a meaningful model of trait evolution. It is thus important to determine whether the model is appropriate for the data and the question being addressed. One way to assess this is to ask whether the model provides a good statistical explanation for the variation in the data. To date, researchers have focused primarily on the explanatory power of a model relative to alternative models. Methods have been developed to assess the adequacy, or absolute explanatory power, of phylogenetic trait models, but these have been restricted to specific models or questions. Here we present a general statistical framework for assessing the adequacy of phylogenetic trait models. We use our approach to evaluate the statistical performance of commonly used trait models on 337 comparative data sets covering three key angiosperm functional traits. In general, the models we tested often provided poor statistical explanations for the evolution of these traits. This was true for many different groups and at many different scales. Whether such statistical inadequacy will qualitatively alter inferences drawn from comparative data sets will depend on the context. Regardless, assessing model adequacy can provide interesting biological insights-how and why a model fails to describe variation in a data set give us clues about what evolutionary processes may have driven trait evolution across time.

geiger v2.0: an expanded suite of methods for fitting macroevolutionary models to phylogenetic trees.

SUMMARY: Phylogenetic comparative methods are essential for addressing evolutionary hypotheses with interspecific data. The scale and scope of such data have increased dramatically in the past few years. Many existing approaches are either computationally infeasible or inappropriate for data of this size. To address both of these problems, we present geiger v2.0, a complete overhaul of the popular R package geiger. We have reimplemented existing methods with more efficient algorithms and have developed several new approaches for accomodating heterogeneous models and data types. AVAILABILITY AND IMPLEMENTATION: This R package is available on the CRAN repository http://cran.r-project.org/web/packages/geiger/. All source code is also available on github http://github.com/mwpennell/geiger-v2. geiger v2.0 depends on the ape package. CONTACT: mwpennell@gmail.com SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.