How can we improve accuracy of macroevolutionary rate estimates?

A Diffusion-Based Approach for Simulating Forward-in-Time State-Dependent Speciation and Extinction Dynamics

We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and three-region geographic-state speciation-extinction (GeoSSE) models. We show that the species range state dynamics simulated under tree-based and diffusion-based processes are comparable. We derive a method to infer rate parameters that are compatible with given observed stationary state frequencies and obtain an analytical result to compute stationary state frequencies for a given set of rate parameters. We also describe a procedure to find the time to reach the stationary frequencies of a ClaSSE model using our diffusion-based approach, which we demonstrate using a worked example for a two-region GeoSSE model. Finally, we discuss how the diffusion framework can be applied to formalize relationships between evolutionary patterns and processes under state-dependent diversification scenarios.

phytools 2.0: an updated R ecosystem for phylogenetic comparative methods (and other things)

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.

Inferring the ecological and evolutionary determinants of community genetic diversity

Understanding the relative contributions of ecological and evolutionary processes to the structuring of ecological communities is needed to improve our ability to predict how communities may respond to future changes in an increasingly human-modified world. Metabarcoding methods make it possible to gather population genetic data for all species within a community, unlocking a new axis of data to potentially unveil the origins and maintenance of biodiversity at local scales. Here, we present a new eco-evolutionary simulation model for investigating community assembly dynamics using metabarcoding data. The model makes joint predictions of species abundance, genetic variation, trait distributions and phylogenetic relationships under a wide range of parameter settings (e.g. high speciation/low dispersal or vice versa) and across a range of community states, from pristine and unmodified to heavily disturbed. We first demonstrate that parameters governing metacommunity and local community processes leave detectable signatures in simulated biodiversity data axes. Next, using a simulation-based machine learning approach we show that neutral and non-neutral models are distinguishable and that reasonable estimates of several model parameters within the local community can be obtained using only community-scale genetic data, while phylogenetic information is required to estimate those describing metacommunity dynamics. Finally, we apply the model to soil microarthropod metabarcoding data from the Troodos mountains of Cyprus, where we find that communities in widespread forest habitats are structured by neutral processes, while high-elevation and isolated habitats act as an abiotic filter generating non-neutral community structure. We implement our model within the ibiogen R package, a package dedicated to the investigation of island, and more generally community-scale, biodiversity using community-scale genetic data.

The Shape of Phylogenies Under Phase-Type Distributed Times to Speciation and Extinction

Phylogenetic trees describe relationships between extant species, but beyond that their shape and their relative branch lengths can provide information on broader evolutionary processes of speciation and extinction. However, currently many of the most widely used macro-evolutionary models make predictions about the shapes of phylogenetic trees that differ considerably from what is observed in empirical phylogenies. Here, we propose a flexible and biologically plausible macroevolutionary model for phylogenetic trees where times to speciation or extinction events are drawn from a Coxian phase-type (PH) distribution. First, we show that different choices of parameters in our model lead to a range of tree balances as measured by Aldous’ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}β statistic. In particular, we demonstrate that it is possible to find parameters that correspond well to empirical tree balance. Next, we provide a natural extension of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}β statistic to sets of trees. This extension produces less biased estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}β compared to using the median \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}β values from individual trees. Furthermore, we derive a likelihood expression for the probability of observing an edge-weighted tree under a model with speciation but no extinction. Finally, we illustrate the application of our model by performing both absolute and relative goodness-of-fit tests for two large empirical phylogenies (squamates and angiosperms) that compare models with Coxian PH distributed times to speciation with models that assume exponential or Weibull distributed waiting times. In our numerical analysis, we found that, in most cases, models assuming a Coxian PH distribution provided the best fit.

Phylogenomics and body shape morphometrics reveal recent diversification in the goatfishes (Syngnatharia: Mullidae)

Clades of marine fishes exhibit many patterns of diversification, ranging from relatively constant throughout time to rapid changes in the rates of speciation and extinction. The goatfishes (Syngnatharia: Mullidae) are a family of marine, reef associated fishes with a relatively recent origin, distributed globally in tropical and temperate waters. Despite their abundance and economic importance, the goatfishes remain one of the few coral reef families for which the species level relationships have not been examined using genomic techniques. Here we use phylogenomic analysis of ultra-conserved elements (UCE) and exon data to resolve a well-supported, time-calibrated phylogeny for 72 species of goatfishes, supporting a recent crown age of the goatfishes at 21.9 million years ago. We used this framework to test hypotheses about the associations among body shape morphometrics, taxonomy, and phylogeny, as well as to explore relative diversification rates across the phylogeny. Body shape was strongly associated with generic-level taxonomy of goatfishes, with morphometric analyses showing evidence for high phylogenetic signal across all morphotypes. Rates of diversification in this clade reveal a recent sharp increase in lineage accumulation, with 92% of the goatfish species sampled across all clades and major body plans having originated in just the past 5 million years. We suggest that habitat diversity in the early Pliocene oceans and the generalist ecology of goatfishes are key factors in the unusual evolutionary tempo of the family Mullidae.

The scaling of diversification rates with age is likely explained by sampling bias

Numerous phylogenetic studies reported the existence of a pervasive scaling relationship between the ages of extant eukaryotic clades and their estimated diversification rates. The causes of this age-rate-scaling (ARS), whether biological and/or artifactual, remain unresolved. Here we fit diversification models to thousands of eukaryotic time-calibrated phylogenies to explore multiple potential causes of the ARS including parameter non-identifiability, model inadequacy, biases in taxonomic practice, and an important and ubiquitous form of sampling bias-preferentially analyzing larger extant clades. We distinguish between two mechanism by which such sampling biases can cause an ARS: First, by favoring clades that happen to be unusually large merely by chance (i.e., due to the stochastic nature of the cladogenic process), thus leading to rate overestimation, and second, by favoring clades that have truly higher diversification rates. We find that, of the proposed explanations, only sampling biases are likely to contribute to the observed ARS. We develop methods for fully correcting for sampling bias mechanism 1, and find that despite these corrections a substantial ARS remains. We then confirm using simulations that preferring trees with truly higher rates (mechanism 2) likely explains this residual ARS. Since we do not have a completely unbiased sample of clades, including extinct ones, for phylogenetic analyses, it is difficult to demonstrate unambiguously that sampling biases are the sole cause of the ARS. Sampling biases are, however, a parsimonious and plausible explanation for this widely observed macroevolutionary pattern, and this has implications for how we interpret the distribution of diversification rate estimates in extant clades.

Studying speciation and extinction dynamics from phylogenies: addressing identifiability issues

A lot of what we know about past speciation and extinction dynamics is based on statistically fitting birth-death processes to phylogenies of extant species. Despite their wide use, the reliability of these tools is regularly questioned. It was recently demonstrated that vast 'congruent' sets of alternative diversification histories cannot be distinguished (i.e., are not identifiable) using extant phylogenies alone, reanimating the debate about the limits of phylogenetic diversification analysis. Here, we summarize what we know about the identifiability of the birth-death process and how identifiability issues can be addressed. We conclude that extant phylogenies, when combined with appropriate prior hypotheses and regularization techniques, can still tell us a lot about past diversification dynamics.

The causes and ecological context of rapid morphological evolution in birds

Episodic pulses in morphological diversification are a prominent feature of evolutionary history, driven by factors that remain widely disputed. Resolving this question has proved challenging because comprehensive species-level data are generally unavailable at sufficient scale. Combining global phylogenetic and morphological data for birds, we show that pulses of diversification in lineages and traits tend to occur independently and in different contexts. Speciation pulses are preceded by greater differentiation in overall morphology and habitat niche, then followed by increased rates of beak evolution. Contrary to standard hypotheses, pulses of morphological diversification tend to be associated with habitat niche stability rather than adaptation to different diets and habitat types. These patterns suggest that the timing of diversification varies across traits according to their ecological function, and that pulses of morphological evolution may occur when successful lineages subdivide niche space within particular habitat types. Our results highlight the growing potential of functional trait data sets to refine macroevolutionary models.

Causes and Consequences of Apparent Timescaling Across All Estimated Evolutionary Rates

Evolutionary rates play a central role in connecting micro- and macroevolution. All evolutionary rate estimates, including rates of molecular evolution, trait evolution, and lineage diversification, share a similar scaling pattern with time: The highest rates are those measured over the shortest time interval. This creates a disconnect between micro- and macroevolution, although the pattern is the opposite of what some might expect: Patterns of change over short timescales predict that evolution has tremendous potential to create variation and that potential is barely tapped by macroevolution. In this review, we discuss this shared scaling pattern across evolutionary rates. We break down possible explanations for scaling into two categories, estimation error and model misspecification, and discuss how both apply to each type of rate. We also discuss the consequences of this ubiquitous pattern, which can lead to unexpected results when comparing ratesover different timescales. Finally, after addressing purely statistical concerns, we explore a few possibilities for a shared unifying explanation across the three types of rates that results from a failure to fully understand and account for how biological processes scale over time.

Mesozoic origin of coleoid cephalopods and their abrupt shifts of diversification patterns

Coleoids are the most diverse group of cephalopod mollusks. While their origin is date during the Mesozoic, the diversification pattern is unknown. However, two hypotheses have been proposed. The first suggests an increasing diversification rate after the Cretaceous-Paleogene extinction event (K-Pg) as consequence of empty habitats left by the ammonites and belemnites. The second hypothesis proposes a mid-Cenozoic increase in diversification rate related to distributional changes during ice ages and biotic interactions. To test these hypotheses, we estimated a lineage through time (LTT) and the gamma-statistic along with model-based diversification rates. These analyses were conducted on a dated molecular phylogeny for coleoids that we reconstructed using five molecular markers (cytochrome b, 16S rRNA, cytochrome oxidase I, rhodopsin, and PAX-6). Our divergence time estimation suggests that coleoids originated in the Mesozoic Era (Middle Triassic) and that both main clades (Decapodiformes and Octopodiformes) diverged in the Cretaceous/Jurassic Period. The LTT, gamma statistic, and diversification rates inferred with the Bayesian Analysis of Macro-evolutionary Mixtures (BAMM), indicate an acceleration in diversification rate over time since the origin of coleoids. Additionally, BAMM allowed us to detect abrupt increases in diversification rate before and after the K-Pg boundary. Our results partially support both hypotheses as all analyses indicate that the coleoid diversification rate was increasing during the Cenozoic. However, our results also indicate increasing diversification rates before the K-Pg boundary. We propose that the radiation of coleoids has been shaped by an acceleration in diversification rate over time, including exceptional episodes of abrupt increases before and after the K-Pg boundary.

When adaptive radiations collide: Different evolutionary trajectories between and within island and mainland lizard clades

Oceanic islands are known as test tubes of evolution. Isolated and colonized by relatively few species, islands are home to many of nature's most renowned radiations from the finches of the Galápagos to the silverswords of the Hawaiian Islands. Despite the evolutionary exuberance of insular life, island occupation has long been thought to be irreversible. In particular, the presumed much tougher competitive and predatory milieu in continental settings prevents colonization, much less evolutionary diversification, from islands back to mainlands. To test these predictions, we examined the ecological and morphological diversity of neotropical Anolis lizards, which originated in South America, colonized and radiated on various islands in the Caribbean, and then returned and diversified on the mainland. We focus in particular on what happens when mainland and island evolutionary radiations collide. We show that extensive continental radiations can result from island ancestors and that the incumbent and invading mainland clades achieve their ecological and morphological disparity in very different ways. Moreover, we show that when a mainland radiation derived from island ancestors comes into contact with an incumbent mainland radiation the ensuing interactions favor the island-derived clade.

Rare and widespread: integrating Bayesian MCMC approaches, Sanger sequencing and Hyb-Seq phylogenomics to reconstruct the origin of the enigmatic Rand Flora genus Camptoloma

PREMISE

Genera that are widespread, with geographically discontinuous distributions and represented by few species, are intriguing. Is their achieved disjunct distribution recent or ancient in origin? Why are they species-poor? The Rand Flora is a continental-scale pattern in which closely related species appear codistributed in isolated regions over the continental margins of Africa. Genus Camptoloma (Scrophulariaceae) is the most notable example, comprising three species isolated from each other on the northwest, eastern, and southwest Africa.

METHODS

We employed Sanger sequencing of nuclear and plastid markers, together with genomic target sequencing of 2190 low-copy nuclear genes, to infer interspecies relationships and the position of Camptoloma within Scrophulariaceae by using supermatrix and multispecies-coalescent approaches. Lineage divergence times and ancestral ranges were inferred with Bayesian Markov chain Monte Carlo (MCMC) approaches. The population history was estimated with phylogeographic coalescent methods.

RESULTS

Camptoloma rotundifolium, restricted to Southern Africa, was shown to be a sister species to the disjunct clade formed by C. canariense, endemic to the Canary Islands, and C. lyperiiflorum, distributed in the Horn of Africa-Southern Arabia. Camptoloma was inferred to be sister to the mostly South African tribes Teedieae and Buddlejeae. Stem divergence was dated in the Late Miocene, while the origin of the extant disjunction was inferred as Early Pliocene.

CONCLUSIONS

The current disjunct distribution of Camptoloma across Africa was likely the result of fragmentation and extinction and/or population bottlenecking events associated with historical aridification cycles during the Neogene; the pattern of species divergence, from south to north, is consistent with the "climatic refugia" Rand Flora hypothesis.

Miocene Climate and Habitat Change Drove Diversification in Bicyclus, Africa's Largest Radiation of Satyrine Butterflies

Compared to other regions, the drivers of diversification in Africa are poorly understood. We studied a radiation of insects with over 100 species occurring in a wide range of habitats across the Afrotropics to investigate the fundamental evolutionary processes and geological events that generate and maintain patterns of species richness on the continent. By investigating the evolutionary history of Bicyclus butterflies within a phylogenetic framework, we inferred the group's origin at the Oligo-Miocene boundary from ancestors in the Congolian rainforests of central Africa. Abrupt climatic fluctuations during the Miocene (ca. 19-17 Ma) likely fragmented ancestral populations, resulting in at least eight early-divergent lineages. Only one of these lineages appears to have diversified during the drastic climate and biome changes of the early Miocene, radiating into the largest group of extant species. The other seven lineages diversified in forest ecosystems during the late Miocene and Pleistocene when climatic conditions were more favourable-warmer and wetter. Our results suggest changing Neogene climate, uplift of eastern African orogens, and biotic interactions might have had different effects on the various subclades of Bicyclus, producing one of the most spectacular butterfly radiations in Africa.

Detecting Lineage-Specific Shifts in Diversification: A Proper Likelihood Approach

The branching patterns of molecular phylogenies are generally assumed to contain information on rates of the underlying speciation and extinction processes. Simple birth-death models with constant, time-varying, or diversity-dependent rates have been invoked to explain these patterns. They have one assumption in common: all lineages have the same set of diversification rates at a given point in time. It seems likely, however, that there is variability in diversification rates across subclades in a phylogenetic tree. This has inspired the construction of models that allow multiple rate regimes across the phylogeny, with instantaneous shifts between these regimes. Several methods exist for calculating the likelihood of a phylogeny under a specified mapping of diversification regimes and for performing inference on the most likely diversification history that gave rise to a particular phylogenetic tree. Here, we show that the likelihood computation of these methods is not correct. We provide a new framework to compute the likelihood correctly and show, with simulations of a single shift, that the correct likelihood indeed leads to parameter estimates that are on average in much better agreement with the generating parameters than the incorrect likelihood. Moreover, we show that our corrected likelihood can be extended to multiple rate shifts in time-dependent and diversity-dependent models. We argue that identifying shifts in diversification rates is a nontrivial model selection exercise where one has to choose whether shifts in now-extinct lineages are taken into account or not. Hence, our framework also resolves the recent debate on such unobserved shifts. [Diversification; macroevolution; phylogeny; speciation].

The probability distribution of the ancestral population size conditioned on the reconstructed phylogenetic tree with occurrence data

We consider a homogeneous birth-death process with three different sampling schemes. First, individuals can be sampled through time and included in a reconstructed phylogenetic tree. Second, they can be sampled through time and only recorded as a point 'occurrence' along a timeline. Third, extant individuals can be sampled and included in the reconstructed phylogenetic tree with a fixed probability. We further consider that sampled individuals can be removed or not from the process, upon sampling, with fixed probability. We derive the probability distribution of the population size at any time in the past conditional on the joint observation of a reconstructed phylogenetic tree and a record of occurrences not included in the tree. We also provide an algorithm to simulate ancestral population size trajectories given the observation of a reconstructed phylogenetic tree and occurrences. This distribution can be readily used to draw inferences about the ancestral population size in the field of epidemiology and macroevolution. In epidemiology, these results will allow data from epidemiological case count studies to be used in conjunction with molecular sequencing data (yielding reconstructed phylogenetic trees) to coherently estimate prevalence through time. In macroevolution, it will foster the joint examination of the fossil record and extant taxa to reconstruct past biodiversity.

Macroevolutionary and macroecological approaches to understanding the evolution of stress tolerance in plants

Environmental stress response in plants has been studied using a wide range of approaches, from lab-based investigation of biochemistry and genetics, to glasshouse studies of physiology and growth rates, to field-based trials and ecological surveys. It is also possible to investigate the evolution of environmental stress responses using macroevolutionary and macroecological analyses, analysing data from many different species, providing a new perspective on the way that environmental stress shapes the evolution and distribution of biodiversity. "Macroevoeco" approaches can produce intriguing results and new ways of looking at old problems. In this review, we focus on studies using phylogenetic analysis to illuminate macroevolutionary patterns in the evolution of environmental stress tolerance in plants. We follow a particular thread from our own research-evolution of salt tolerance-as a case study that illustrates a macroevolutionary way of thinking that opens up a range of broader questions on the evolution of environmental stress tolerances. We consider some potential future applications of macroevolutionary and macroecological analyses to understanding how diverse groups of plants evolve in response to environmental stress, which may allow better prediction of current stress tolerance and a way of predicting the capacity of species to adapt to changing environmental stresses over time.

Macroevolutionary dynamics of parasite diversification: A reality check

Parasitism is often invoked as a factor explaining the variation in diversification rates across the tree of life, while also representing up to half of Earth's diversity. Yet, patterns and processes of parasite diversification remain mostly unknown. In this study, we assess the patterns of parasite diversification and specifically determine the role of life-history traits (i.e. life cycle complexity and host range) and major coevolutionary events in driving diversification across eight phylogenetic datasets spanning taxonomically different parasite groups. Aware of the degree of incomplete sampling among all parasite phylogenies, we also tested the impact of sampling bias on estimates of diversification. We show that the patterns and rates of parasite diversification differ among taxa according to life cycle complexity and to some extent major host transitions. Only directly transmitted parasites were found to be influenced by an effect of major host transitions on diversification rates. Although parasitism may be a main factor responsible for heterogeneity in diversification among the tree of life, the high degree of incomplete parasite phylogenies remains an obstacle when modelling diversification dynamics. Nevertheless, we provide the first comparative test of parasite diversification, revealing some consistent patterns and insight into the processes that shape it.

Inferring transmission heterogeneity using virus genealogies: Estimation and targeted prevention

Spread of HIV typically involves uneven transmission patterns where some individuals spread to a large number of individuals while others to only a few or none. Such transmission heterogeneity can impact how fast and how much an epidemic spreads. Further, more efficient interventions may be achieved by taking such transmission heterogeneity into account. To address these issues, we developed two phylogenetic methods based on virus sequence data: 1) to generally detect if significant transmission heterogeneity is present, and 2) to pinpoint where in a phylogeny high-level spread is occurring. We derive inference procedures to estimate model parameters, including the amount of transmission heterogeneity, in a sampled epidemic. We show that it is possible to detect transmission heterogeneity under a wide range of simulated situations, including incomplete sampling, varying levels of heterogeneity, and including within-host genetic diversity. When evaluating real HIV-1 data from different epidemic scenarios, we found a lower level of transmission heterogeneity in slowly spreading situations and a higher level of heterogeneity in data that included a rapid outbreak, while R0 and Sackin's index (overall tree shape statistic) were similar in the two scenarios, suggesting that our new method is able to detect transmission heterogeneity in real data. We then show by simulations that targeted prevention, where we pinpoint high-level spread using a coalescence measurement, is efficient when sequence data are collected in an ongoing surveillance system. Such phylogeny-guided prevention is efficient under both single-step contact tracing as well as iterative contact tracing as compared to random intervention.

Rates and Rocks: Strengths and Weaknesses of Molecular Dating Methods

I present here an in-depth, although non-exhaustive, review of two topics in molecular dating. Clock models, which describe the evolution of the rate of evolution, are considered first. Some of the shortcomings of popular approaches-uncorrelated clock models in particular-are presented and discussed. Autocorrelated models are shown to be more reasonable from a biological perspective. Some of the most recent autocorrelated models also rely on a coherent treatment of instantaneous and average substitution rates while previous models are based on implicit approximations. Second, I provide a brief overview of the processes involved in collecting and preparing fossil data. I then review the main techniques that use this data for calibrating the molecular clock. I argue that, in its current form, the fossilized birth-death process relies on assumptions about the mechanisms underlying fossilization and the data collection process that may negatively impact the date estimates. Node-dating approaches make better use of the data available, even though they rest on paleontologists' intervention to prepare raw fossil data. Altogether, this study provides indications that may help practitioners in selecting appropriate methods for molecular dating. It will also hopefully participate in defining the contour of future methodological developments in the field.

Hybridizing salamanders experience accelerated diversification

Whether hybridization generates or erodes species diversity has long been debated, but to date most studies have been conducted at small taxonomic scales. Salamanders (order Caudata) represent a taxonomic order in which hybridization plays a prevalent ecological and evolutionary role. We employed a recently developed model of trait-dependent diversification to test the hypothesis that hybridization impacts the diversification dynamics of species that are currently hybridizing. We find strong evidence supporting this hypothesis, showing that hybridizing salamander lineages have significantly greater net-diversification rates than non-hybridizing lineages. This pattern is driven by concurrently increased speciation rates and decreased extinction rates in hybridizing lineages. Our results support the hypothesis that hybridization can act as a generative force in macroevolutionary diversification.

Additional Analytical Support for a New Method to Compute the Likelihood of Diversification Models

Molecular phylogenies have been increasingly recognized as an important source of information on species diversification. For many models of macroevolution, analytical likelihood formulas have been derived to infer macroevolutionary parameters from phylogenies. A few years ago, a general framework to numerically compute such likelihood formulas was proposed, which accommodates models that allow speciation and/or extinction rates to depend on diversity. This framework calculates the likelihood as the probability of the diversification process being consistent with the phylogeny from the root to the tips. However, while some readers found the framework presented in Etienne et al. (Proc R Soc Lond B Biol Sci 279(1732):1300-1309, 2012) convincing, others still questioned it (personal communication), despite numerical evidence that for special cases the framework yields the same (i.e., within double precision) numerical value for the likelihood as analytical formulas do that were independently derived for these special cases. Here we prove analytically that the likelihoods calculated in the new framework are correct for all special cases with known analytical likelihood formula. Our results thus add substantial mathematical support for the overall coherence of the general framework.

Swapping Birth and Death: Symmetries and Transformations in Phylodynamic Models

Stochastic birth–death models provide the foundation for studying and simulating evolutionary trees in phylodynamics. A curious feature of such models is that they exhibit fundamental symmetries when the birth and death rates are interchanged. In this article, we first provide intuitive reasons for these known transformational symmetries. We then show that these transformational symmetries (encoded in algebraic identities) are preserved even when individuals at the present are sampled with some probability. However, these extended symmetries require the death rate parameter to sometimes take a negative value. In the last part of this article, we describe the relevance of these transformations and their application to computational phylodynamics, particularly to maximum likelihood and Bayesian inference methods, as well as to model selection.

Detection of HIV transmission clusters from phylogenetic trees using a multi-state birth-death model

HIV patients form clusters in HIV transmission networks. Accurate identification of these transmission clusters is essential to effectively target public health interventions. One reason for clustering is that the underlying contact network contains many local communities. We present a new maximum-likelihood method for identifying transmission clusters caused by community structure, based on phylogenetic trees. The method employs a multi-state birth–death (MSBD) model which detects changes in transmission rate, which are interpreted as the introduction of the epidemic into a new susceptible community, i.e. the formation of a new cluster. We show that the MSBD method is able to reliably infer the clusters and the transmission parameters from a pathogen phylogeny based on our simulations. In contrast to existing cutpoint-based methods for cluster identification, our method does not require that clusters be monophyletic nor is it dependent on the selection of a difficult-to-interpret cutpoint parameter. We present an application of our method to data from the Swiss HIV Cohort Study. The method is available as an easy-to-use R package.

The choice of tree prior and molecular clock does not substantially affect phylogenetic inferences of diversification rates

Comparative methods allow researchers to make inferences about evolutionary processes and patterns from phylogenetic trees. In Bayesian phylogenetics, estimating a phylogeny requires specifying priors on parameters characterizing the branching process and rates of substitution among lineages, in addition to others. Accordingly, characterizing the effect of prior selection on phylogenies is an active area of research. The choice of priors may systematically bias phylogenetic reconstruction and, subsequently, affect conclusions drawn from the resulting phylogeny. Here, we focus on the impact of priors in Bayesian phylogenetic inference and evaluate how they affect the estimation of parameters in macroevolutionary models of lineage diversification. Specifically, we simulate trees under combinations of tree priors and molecular clocks, simulate sequence data, estimate trees, and estimate diversification parameters (e.g., speciation and extinction rates) from these trees. When substitution rate heterogeneity is large, diversification rate estimates deviate substantially from those estimated under the simulation conditions when not captured by an appropriate choice of relaxed molecular clock. However, in general, we find that the choice of tree prior and molecular clock has relatively little impact on the estimation of diversification rates insofar as the sequence data are sufficiently informative and substitution rate heterogeneity among lineages is low-to-moderate.

Closing the gap between palaeontological and neontological speciation and extinction rate estimates

Measuring the pace at which speciation and extinction occur is fundamental to understanding the origin and evolution of biodiversity. Both the fossil record and molecular phylogenies of living species can provide independent estimates of speciation and extinction rates, but often produce strikingly divergent results. Despite its implications, the theoretical reasons for this discrepancy remain unknown. Here, we reveal a conceptual and methodological basis able to reconcile palaeontological and molecular evidence: discrepancies are driven by different implicit assumptions about the processes of speciation and species evolution in palaeontological and neontological analyses. We present the "birth-death chronospecies" model that clarifies the definition of speciation and extinction processes allowing for a coherent joint analysis of fossil and phylogenetic data. Using simulations and empirical analyses we demonstrate not only that this model explains much of the apparent incongruence between fossils and phylogenies, but that differences in rate estimates are actually informative about the prevalence of different speciation modes.

Comparing the rates of speciation and extinction between phylogenetic trees

Over the past decade or so it has become increasingly popular to use reconstructed evolutionary trees to investigate questions about the rates of speciation and extinction. Although the methodology of this field has grown substantially in its sophistication in recent years, here I will take a step back to present a very simple model that is designed to investigate the relatively straightforward question of whether the tempo of diversification (speciation and extinction) differs between two or more phylogenetic trees, without attempting to attribute a causal basis to this difference. It is a likelihood method, and I demonstrate that it generally shows type I error that is close to the nominal level. I also demonstrate that parameter estimates obtained with this approach are largely unbiased. As this method can be used to compare trees of unknown relationship, it will be particularly well-suited to problems in which a difference in diversification rate between clades is suspected, but in which these clades are not particularly closely related. As diversification methods can easily take into account an incomplete sampling fraction, but missing lineages are assumed to be missing at random, this method is also appropriate for cases in which we have hypothesized a difference in the process of diversification between two or more focal clades, but in which many unsampled groups separate the few of interest. The method of this study is by no means an attempt to replace more sophisticated models in which, for instance, diversification depends on the state of an observed or unobserved discrete or continuous trait. Rather, my intention is to provide a complementary approach for circumstances in which a simpler hypothesis is warranted and of biological interest.

Early Cretaceous greenhouse pumped higher taxa diversification in spiders

The Cretaceous experienced one of the most remarkable greenhouse periods in geological history. During this time, ecosystem reorganization significantly impacted the diversification of many groups of organisms. The rise of angiosperms marked a major biome turnover. Notwithstanding, relatively little remains known about how the Cretaceous global ecosystem impacted the evolution of spiders, which constitute one of the most abundant groups of predators. Herein, we evaluate the transcriptomes of 91 taxa representing more than half of the spider families. We add 23 newly sequenced taxa to the existing database to obtain a robust phylogenomic assessment. Phylogenetic reconstructions using different datasets and methods obtain novel placements of some groups, especially in the Synspermiata and the group having a retrolateral tibial apophysis (RTA). Molecular analyses indicate an expansion of the RTA clade at the Early Cretaceous with a hunting predatory strategy shift. Fossil analyses show a 7-fold increase of diversification rate at the same period, but this likely owes to the first occurrence of spiders in amber deposit. Additional analyses of fossil abundance show an accumulation of spider lineages in the Early Cretaceous. We speculate that the establishment of a warm greenhouse climate pumped the diversification of spiders, in particular among webless forms tracking the abundance of insect prey. Our study offers a new pathway for future investigations of spider phylogeny and diversification.

Estimating Age-Dependent Extinction: Contrasting Evidence from Fossils and Phylogenies

The estimation of diversification rates is one of the most vividly debated topics in modern systematics, with considerable controversy surrounding the power of phylogenetic and fossil-based approaches in estimating extinction. Van Valen's seminal work from 1973 proposed the "Law of constant extinction," which states that the probability of extinction of taxa is not dependent on their age. This assumption of age-independent extinction has prevailed for decades with its assessment based on survivorship curves, which, however, do not directly account for the incompleteness of the fossil record, and have rarely been applied at the species level. Here, we present a Bayesian framework to estimate extinction rates from the fossil record accounting for age-dependent extinction (ADE). Our approach, unlike previous implementations, explicitly models unobserved species and accounts for the effects of fossil preservation on the observed longevity of sampled lineages. We assess the performance and robustness of our method through extensive simulations and apply it to a fossil data set of terrestrial Carnivora spanning the past 40 myr. We find strong evidence of ADE, as we detect the extinction rate to be highest in young species and declining with increasing species age. For comparison, we apply a recently developed analogous ADE model to a dated phylogeny of extant Carnivora. Although the phylogeny-based analysis also infers ADE, it indicates that the extinction rate, instead, increases with increasing taxon age. The estimated mean species longevity also differs substantially, with the fossil-based analyses estimating 2.0 myr, in contrast to 9.8 myr derived from the phylogeny-based inference. Scrutinizing these discrepancies, we find that both fossil and phylogeny-based ADE models are prone to high error rates when speciation and extinction rates increase or decrease through time. However, analyses of simulated and empirical data show that fossil-based inferences are more robust. This study shows that an accurate estimation of ADE from incomplete fossil data is possible when the effects of preservation are jointly modeled, thus allowing for a reassessment of Van Valen's model as a general rule in macroevolution.

TreeSimGM: Simulating phylogenetic trees under general Bellman-Harris models with lineage-specific shifts of speciation and extinction in R

Understanding macroevolutionary processes using phylogenetic trees is a challenging and complex process that draws on mathematics, computer science and biology. Given the development of complex mathematical models and the growing computational processing power, simulation tools are becoming increasingly popular.In order to simulate phylogenetic trees, most evolutionary biologists are forced to build their own algorithms or use existing tools built on different platforms and/or as standalone programmes. The absence of a simulation tool accommodating for user-chosen model specifications limits, amongst others, model testing and pipelining with approximate Bayesian computation methods or other subsequent statistical analysis.We introduce "TreeSimGM," an r-package simulation tool for phylogenetic trees under a general Bellman and Harris model. This package allows the user to specify any desired probability distribution for the waiting times until speciation and extinction (e.g. age-dependent speciation/extinction). Upon speciation, the user can specify whether one descendant species corresponds to the ancestor species inheriting its age or whether both descendant species are new species of age 0. Moreover, it is possible to scale the waiting time to speciation/extinction for newly formed species. Thus, "TreeSimGM" not only allows the user to simulate stochastic phylogenetic trees assuming several popular existing models, such as the Yule model, the constant-rate birth-death model, and proportional to distinguishable arrangement models, but it also allows the user to formulate new models for exploration. A short explanation of the supported models and a few examples of how to use our package are presented here.As an r-package, "TreeSimGM" allows flexible and powerful stochastic phylogenetic tree simulations. Moreover, it facilitates the pipelining of outputs or inputs with other functions in r. "TreeSimGM" contributes to the tools available to the r community in the fields of ecology and evolution, is freely available under the GPL-2 licence and can be downloaded at https://cran.r-project.org/web/packages/TreeSimGM.

Biased phylodynamic inferences from analysing clusters of viral sequences

Phylogenetic methods are being increasingly used to help understand the transmission dynamics of measurably evolving viruses, including HIV. Clusters of highly similar sequences are often observed, which appear to follow a ‘power law’ behaviour, with a small number of very large clusters. These clusters may help to identify subpopulations in an epidemic, and inform where intervention strategies should be implemented. However, clustering of samples does not necessarily imply the presence of a subpopulation with high transmission rates, as groups of closely related viruses can also occur due to non-epidemiological effects such as over-sampling. It is important to ensure that observed phylogenetic clustering reflects true heterogeneity in the transmitting population, and is not being driven by non-epidemiological effects. We qualify the effect of using a falsely identified ‘transmission cluster’ of sequences to estimate phylodynamic parameters including the effective population size and exponential growth rate under several demographic scenarios. Our simulation studies show that taking the maximum size cluster to re-estimate parameters from trees simulated under a randomly mixing, constant population size coalescent process systematically underestimates the overall effective population size. In addition, the transmission cluster wrongly resembles an exponential or logistic growth model 99% of the time. We also illustrate the consequences of false clusters in exponentially growing coalescent and birth-death trees, where again, the growth rate is skewed upwards. This has clear implications for identifying clusters in large viral databases, where a false cluster could result in wasted intervention resources.

Natural Constraints to Species Diversification

Identifying modes of species diversification is fundamental to our understanding of how biodiversity changes over evolutionary time. Diversification modes are captured in species phylogenies, but characterizing the landscape of diversification has been limited by the analytical tools available for directly comparing phylogenetic trees of groups of organisms. Here, we use a novel, non-parametric approach and 214 family-level phylogenies of vertebrates representing over 500 million years of evolution to identify major diversification modes, to characterize phylogenetic space, and to evaluate the bounds and central tendencies of species diversification. We identify five principal patterns of diversification to which all vertebrate families hold. These patterns, mapped onto multidimensional space, constitute a phylogenetic space with distinct properties. Firstly, phylogenetic space occupies only a portion of all possible tree space, showing family-level phylogenies to be constrained to a limited range of diversification patterns. Secondly, the geometry of phylogenetic space is delimited by quantifiable trade-offs in tree size and the heterogeneity and stem-to-tip distribution of branching events. These trade-offs are indicative of the instability of certain diversification patterns and effectively bound speciation rates (for successful clades) within upper and lower limits. Finally, both the constrained range and geometry of phylogenetic space are established by the differential effects of macroevolutionary processes on patterns of diversification. Given these properties, we show that the average path through phylogenetic space over evolutionary time traverses several diversification stages, each of which is defined by a different principal pattern of diversification and directed by a different macroevolutionary process. The identification of universal patterns and natural constraints to diversification provides a foundation for understanding the deep-time evolution of biodiversity.

A meta-analysis of 214 family-level vertebrate trees containing more than 12,000 species and spanning 500 million years of evolution reveals general patterns of species diversification and the constraints acting on them.

Are there universal laws in the evolution of biodiversity? Why do some clades go extinct and others flourish? These questions are fundamental to our understanding of present-day biodiversity. In a meta-analysis of nearly 12,000 species spanning ~500 million years of evolution, we find that there are five principal patterns of diversification to which all vertebrate families hold, and that these patterns can be mapped into a multidimensional phylogenetic space. Importantly, because certain diversification patterns invariably lead to extinction, clades do not explore all possible phylogenetic space, and thus the evolution of biodiversity is constrained by a set of loose but inviolable rules. We characterize the biotic and abiotic factors precipitating those rules with important implications for our knowledge of the emergence and maintenance of the diversity of life around us.

Extinction in Phylogenetics and Biogeography: From Timetrees to Patterns of Biotic Assemblage

Global climate change and its impact on biodiversity levels have made extinction a relevant topic in biological research. Yet, until recently, extinction has received less attention in macroevolutionary studies than speciation; the reason is the difficulty to infer an event that actually eliminates rather than creates new taxa. For example, in biogeography, extinction has often been seen as noise, introducing homoplasy in biogeographic relationships, rather than a pattern-generating process. The molecular revolution and the possibility to integrate time into phylogenetic reconstructions have allowed studying extinction under different perspectives. Here, we review phylogenetic (temporal) and biogeographic (spatial) approaches to the inference of extinction and the challenges this process poses for reconstructing evolutionary history. Specifically, we focus on the problem of discriminating between alternative high extinction scenarios using time trees with only extant taxa, and on the confounding effect introduced by asymmetric spatial extinction – different rates of extinction across areas – in biogeographic inference. Finally, we identify the most promising avenues of research in both fields, which include the integration of additional sources of evidence such as the fossil record or environmental information in birth–death models and biogeographic reconstructions, the development of new models that tie extinction rates to phenotypic or environmental variation, or the implementation within a Bayesian framework of parametric non-stationary biogeographic models.

Total-Evidence Dating under the Fossilized Birth-Death Process

Bayesian total-evidence dating involves the simultaneous analysis of morphological data from the fossil record and morphological and sequence data from recent organisms, and it accommodates the uncertainty in the placement of fossils while dating the phylogenetic tree. Due to the flexibility of the Bayesian approach, total-evidence dating can also incorporate additional sources of information. Here, we take advantage of this and expand the analysis to include information about fossilization and sampling processes. Our work is based on the recently described fossilized birth-death (FBD) process, which has been used to model speciation, extinction, and fossilization rates that can vary over time in a piecewise manner. So far, sampling of extant and fossil taxa has been assumed to be either complete or uniformly at random, an assumption which is only valid for a minority of data sets. We therefore extend the FBD process to accommodate diversified sampling of extant taxa, which is standard practice in studies of higher-level taxa. We verify the implementation using simulations and apply it to the early radiation of Hymenoptera (wasps, ants, and bees). Previous total-evidence dating analyses of this data set were based on a simple uniform tree prior and dated the initial radiation of extant Hymenoptera to the late Carboniferous (309 Ma). The analyses using the FBD prior under diversified sampling, however, date the radiation to the Triassic and Permian (252 Ma), slightly older than the age of the oldest hymenopteran fossils. By exploring a variety of FBD model assumptions, we show that it is mainly the accommodation of diversified sampling that causes the push toward more recent divergence times. Accounting for diversified sampling thus has the potential to close the long-discussed gap between rocks and clocks. We conclude that the explicit modeling of fossilization and sampling processes can improve divergence time estimates, but only if all important model aspects, including sampling biases, are adequately addressed.

Quantifying Age-dependent Extinction from Species Phylogenies

Several ecological factors that could play into species extinction are expected to correlate with species age, i.e., time elapsed since the species arose by speciation. To date, however, statistical tools to incorporate species age into likelihood-based phylogenetic inference have been lacking. We present here a computational framework to quantify age-dependent extinction through maximum likelihood parameter estimation based on phylogenetic trees, assuming species lifetimes are gamma distributed. Testing on simulated trees shows that neglecting age dependence can lead to biased estimates of key macroevolutionary parameters. We then apply this method to two real data sets, namely a complete phylogeny of birds (class Aves) and a clade of self-compatible and -incompatible nightshades (Solanaceae), gaining initial insights into the extent to which age-dependent extinction may help explain macroevolutionary patterns. Our methods have been added to the R package TreePar.

Extinction can be estimated from moderately sized molecular phylogenies

Hundreds of studies have been dedicated to estimating speciation and extinction from phylogenies of extant species. Although it has long been known that estimates of extinction rates using trees of extant organisms are often uncertain, an influential paper by Rabosky (2010) suggested that when birth rates vary continuously across the tree, estimates of the extinction fraction (i.e., extinction rate/speciation rate) will appear strongly bimodal, with a peak suggesting no extinction and a peak implying speciation and extinction rates are approaching equality. On the basis of these results, and the realistic nature of this form of rate variation, it is now generally assumed by many practitioners that extinction cannot be understood from molecular phylogenies alone. Here, we reevaluated and extended the analyses of Rabosky (2010) and come to the opposite conclusion-namely, that it is possible to estimate extinction from molecular phylogenies, even with model violations due to heritable variation in diversification rate. Note that while it may be tempting to interpret our study as advocating the application of simple birth-death models, our goal here is to show how a particular model violation does not necessitate the abandonment of an entire field: use prudent caution, but do not abandon all hope.

Estimating the duration of speciation from phylogenies

Speciation is not instantaneous but takes time. The protracted birth–death diversification model incorporates this fact and predicts the often observed slowdown of lineage accumulation toward the present. The mathematical complexity of the protracted speciation model has barred estimation of its parameters until recently a method to compute the likelihood of phylogenetic branching times under this model was outlined (Lambert et al. 2014). Here, we implement this method and study using simulated phylogenies of extant species how well we can estimate the model parameters (rate of initiation of speciation, rate of extinction of incipient and good species, and rate of completion of speciation) as well as the duration of speciation, which is a combination of the aforementioned parameters. We illustrate our approach by applying it to a primate phylogeny. The simulations show that phylogenies often do not contain enough information to provide unbiased estimates of the speciation-initiation rate and the extinction rate, but the duration of speciation can be estimated without much bias. The estimate of the duration of speciation for the primate clade is consistent with literature estimates. We conclude that phylogenies combined with the protracted speciation model provide a promising way to estimate the duration of speciation.

Phylogenetic approaches for studying diversification

Estimating rates of speciation and extinction, and understanding how and why they vary over evolutionary time, geographical space and species groups, is a key to understanding how ecological and evolutionary processes generate biological diversity. Such inferences will increasingly benefit from phylogenetic approaches given the ever-accelerating rates of genetic sequencing. In the last few years, models designed to understand diversification from phylogenetic data have advanced significantly. Here, I review these approaches and what they have revealed about diversification in the natural world. I focus on key distinctions between different models, and I clarify the conclusions that can be drawn from each model. I identify promising areas for future research. A major challenge ahead is to develop models that more explicitly take into account ecology, in particular the interaction of species with each other and with their environment. This will not only improve our understanding of diversification; it will also present a new perspective to the use of phylogenies in community ecology, the science of interaction networks and conservation biology, and might shift the current focus in ecology on equilibrium biodiversity theories to non-equilibrium theories recognising the crucial role of history.

Phylogenetic estimates of speciation and extinction rates for testing ecological and evolutionary hypotheses

Phylogenies are used to estimate rates of speciation and extinction, reconstruct historical diversification scenarios, and link these to ecological and evolutionary factors, such as climate or organismal traits. Recent models can now estimate the effects of binary, multistate, continuous, and biogeographic characters on diversification rates. Others test for diversity dependence (DD) in speciation and extinction, which has become recognized as an important process in numerous clades. A third class incorporates flexible time-dependent functions, enabling reconstruction of major periods of both expanding and contracting diversity. Although there are some potential problems (particularly for estimating extinction), these methods hold promise for answering many classic questions in ecology and evolution, such as the origin of adaptive radiations, and the latitudinal gradient in species richness.

Dating phylogenies with sequentially sampled tips

We develop a Bayesian Markov chain Monte Carlo (MCMC) algorithm for estimating divergence times using sequentially sampled molecular sequences. This type of data is commonly collected during viral epidemics and is sometimes available from different species in ancient DNA studies. We derive the distribution of ages of nodes in the tree under a birth-death-sequential-sampling (BDSS) model and use it as the prior for divergence times in the dating analysis. We implement the prior in the MCMCtree program in the PAML package for divergence dating. The BDSS prior is very flexible and, with different parameters, can generate trees of very different shapes, suitable for examining the sensitivity of posterior time estimates. We apply the method to a data set of SIV/HIV-2 genes in comparison with a likelihood-based dating method, and to a data set of influenza H1 genes from different hosts in comparison with the Bayesian program BEAST. We examined the impact of tree topology on time estimates and suggest that multifurcating consensus trees should be avoided in dating analysis. We found posterior time estimates for old nodes to be sensitive to the priors on times and rates and suggest that previous Bayesian dating studies may have produced overconfident estimates.

Uncovering epidemiological dynamics in heterogeneous host populations using phylogenetic methods

Host population structure has a major influence on epidemiological dynamics. However, in particular for sexually transmitted diseases, quantitative data on population contact structure are hard to obtain. Here, we introduce a new method that quantifies host population structure based on phylogenetic trees, which are obtained from pathogen genetic sequence data. Our method is based on a maximum-likelihood framework and uses a multi-type branching process, under which each host is assigned to a type (subpopulation). In a simulation study, we show that our method produces accurate parameter estimates for phylogenetic trees in which each tip is assigned to a type, as well for phylogenetic trees in which the type of the tip is unknown. We apply the method to a Latvian HIV-1 dataset, quantifying the impact of the intravenous drug user epidemic on the heterosexual epidemic (known tip states), and identifying superspreader dynamics within the men-having-sex-with-men epidemic (unknown tip states).