Challenges in the estimation of extinction from molecular phylogenies: A response to Beaulieu and O'Meara

Time‐calibrated phylogenies that contain only living species have been widely used to study the dynamics of speciation and extinction. Concerns about the reliability of phylogenetic extinction estimates were raised by Rabosky (2010), where I suggested that unaccommodated heterogeneity in speciation rate could lead to positively biased extinction estimates. In a recent article, Beaulieu and O'Meara (2015a) correctly point out several technical errors in the execution of my 2010 study and concluded that phylogenetic extinction estimates are robust to speciation rate heterogeneity under a range of model parameters. I demonstrate that Beaulieu and O'Meara underestimated the magnitude of speciation rate variation in real phylogenies and consequently did not incorporate biologically meaningful levels of rate heterogeneity into their simulations. Using parameter values drawn from the recent literature, I find that modest levels of heterogeneity in speciation rate result in a consistent, positive bias in extinction estimates that are exacerbated by phylogenetic tree size. This bias, combined with the inherent lack of information about extinction in molecular phylogenies, suggests that extinction rate estimates from phylogenies of extant taxa only should be treated with caution.     

Time-dependent speciation and extinction from phylogenies: a least squares approach

Molecular phylogenies contribute to the study of the patterns and processes of macroevolution even though past events (fossils) are not recorded in these data. In this article, I consider the general time-dependent birth-death model to fit any model of temporal variation in speciation and extinction to phylogenies. I establish formulae to compute the expected cumulative distribution function of branching times for any model, and, building on previous published works, I derive maximum likelihood estimators. Some limitations of the likelihood approach are described, and a fitting procedure based on least squares is developed that alleviates the shortcomings of maximum likelihood in the present context. Parametric and nonparametric bootstrap procedures are developed to assess uncertainty in the parameter estimates, the latter version giving narrower confidence intervals and being faster to compute. I also present several general algorithms of tree simulation in continuous time. I illustrate the application of this approach with the analysis of simulated datasets, and two published phylogenies of primates (Catarrhinae) and lizards (Agamidae).     

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.     

Inferring speciation rates from phylogenies

Abstract It is possible to estimate the rate of diversification of clades from phylogenies with a temporal dimension. First, I present several methods for constructing confidence intervals for the speciation rate under the simple assumption of a pure birth process. I discuss the relationships among these methods in the hope of clarifying some fundamental theory in this area. Their performances are compared in a simulation study and one is recommended for use as a result. A variety of other questions that may, in fact, be the questions of primary interest (e.g., Has the rate of cladogenesis been declining?) are then recast as biological variants of the purely statistical question—Is the birth process model appropriate for my data? Seen in this way, a preexisting arsenal of statistical techniques is opened up for use in this area: in particular, techniques developed for the analysis of Poisson processes and the analysis of survival data. These two approaches start from different representations of the data—the branch lengths in the tree—and I explicitly relate the two. Aiming for a synoptic account of useful theory in this area, I briefly discuss some important results from the analysis of two distinct birth‐death processes: the one introduced into this area by Hey (1992) is refitted with some powerful statistical tools.     

QUANTIFYING VARIATION IN SPECIATION AND EXTINCTION RATES WITH CLADE DATA

High‐level phylogenies are very common in evolutionary analyses, although they are often treated as incomplete data. Here, we provide statistical tools to analyze what we name “clade data,” which are the ages of clades together with their numbers of species. We develop a general approach for the statistical modeling of variation in speciation and extinction rates, including temporal variation, unknown variation, and linear and nonlinear modeling. We show how this approach can be generalized to a wide range of situations, including testing the effects of life‐history traits and environmental variables on diversification rates. We report the results of an extensive simulation study to assess the performance of some statistical tests presented here as well as of the estimators of speciation and extinction rates. These latter results suggest the possibility to estimate correctly extinction rate in the absence of fossils. An example with data on fish is presented.     

Exploring the power of Bayesian birth‐death skyline models to detect mass extinction events from phylogenies with only extant taxa

Mass extinction events (MEEs), defined as significant losses of species diversity in significantly short time periods, have attracted the attention of biologists because of their link to major environmental change. MEEs have traditionally been studied through the fossil record, but the development of birth‐death models has made it possible to detect their signature based on extant‐taxa phylogenies. Most birth‐death models consider MEEs as instantaneous events where a high proportion of species are simultaneously removed from the tree (“single pulse” approach), in contrast to the paleontological record, where MEEs have a time duration. Here, we explore the power of a Bayesian Birth‐Death Skyline (BDSKY) model to detect the signature of MEEs through changes in extinction rates under a “time‐slice” approach. In this approach, MEEs are time intervals where the extinction rate is greater than the speciation rate. Results showed BDSKY can detect and locate MEEs but that precision and accuracy depend on the phylogeny's size and MEE intensity. Comparisons of BDSKY with the single‐pulse Bayesian model, CoMET, showed a similar frequency of Type II error and neither model exhibited Type I error. However, while CoMET performed better in detecting and locating MEEs for smaller phylogenies, BDSKY showed higher accuracy in estimating extinction and speciation rates.     

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.     

Evolutionary diversification of reef corals: a comparison of the molecular and fossil records

Understanding historical patterns of diversity dynamics is of paramount importance for many evolutionary questions. The fossil record has long been the only source of information on patterns of diversification, but the molecular record, derived from time-calibrated phylogenies, is becoming an important additional resource. Both fossil and molecular approaches have shortcomings and biases. These have been well studied for fossil data but much less so for molecular data and empirical comparisons between approaches are lacking. Here, we compare the patterns of diversification derived from fossil and molecular data in scleractinian reef coral species. We also assess the robustness of molecular diversification rates to poor taxon sampling. We find that the temporal pattern of molecular diversification rates is robust to incomplete sampling when rates are calculated per interval. The major obstacle of molecular methods is that rate estimates are distorted because diversification rates can never be negative, whereas the fossil record suffers from incomplete preservation and inconsistent taxonomy. Nevertheless, the molecular pattern of diversification is comparable to the pattern we observe in the fossil record, with the timing of major diversification pulses coinciding in each dataset. For example, both agree that the end-Triassic coral extinction was a catastrophic bottleneck in scleractinian evolution.     

The geography of mammalian speciation: mixed signals from phylogenies and range maps

The importance of geographic isolation in speciation has been debated since the 19th century. Since the beginning of the 20th century, the consensus has been that most speciation involves divergence in allopatry. This consensus was based largely on decades of observations by naturalists and verbal arguments against speciation without isolation. Recent attempts to quantify the importance of allopatric versus sympatric speciation using comparative methods called "age-range correlation" (ARC) suggest that allopatric speciation is more common than sympatric speciation. However, very few taxa have been studied and there are concerns about the adequacy of the methods. We propose methodological improvements including changes in the way overlap between clades is quantified and Monte Carlo methods to test the null hypothesis of no relationship between phylogenetic relatedness and geographic range overlap. We analyze 14 clades of mammals, chosen because of the availability of data and the consensus among mammalogists that speciation is routinely allopatric. Although data from a few clades clearly indicate allopatric speciation, divergence with gene flow is plausible in others and many results are inconclusive. The relative rarity of significant correlations between phylogenetic distance and range overlap may have three distinct causes: (1) post-speciation range changes, (2) relative rarity of range overlap, and (3) a mixture of geographic modes of speciation. Our results support skepticism about ARC's power for inferring the biogeography of speciation. Yet, even if few clades provide clear signals, meta-analytic approaches such as ARC may set bounds on the prevalence of alternative modes of speciation.     

Molecular phylogenies reveal host-specific divergence of Ophiocordyceps unilateralis sensu lato following its host ants

Ophiocordyceps unilateralis (Hypocreales, Ascomycetes) is an entomopathogenic fungus specific to formicine ants (Formicinae, Hymenoptera). Previous works have shown that the carpenter ant Camponotus leonardi acts as the principal host with occasional infections of ants from the genus Polyrhachis (sister genus of Camponotus). Observations were made on the permanent plots of Mo Singto, Khao Yai National Park of Thailand according to which O. unilateralis was found to occur predominantly on three host species: C. leonardi, C. saundersi and P. furcata. Molecular phylogenies of the elongation factor 1-α and β-Tubulin genes indicate a separation of O. unilateralis samples into three clades, reflecting specificity to each of the three different ant species. Samples collected from P. furcata and from C. leonardi were found to form sister groups with samples from C. saundersi forming an outgroup to the latter. Additional samples collected from unidentified ant species of Camponotus and Polyrhachis were positioned as outgroups to those samples on identified species. These results demonstrate that O. unilateralis is clearly not a single phylogenetic species and comprises at least three species that are specific to different host ant species. These cryptic species may arise through recent events of speciation driven by their specificity to host ant species.     

EXTINCTION DURING EVOLUTIONARY RADIATIONS: RECONCILING THE FOSSIL RECORD WITH MOLECULAR PHYLOGENIES

Recent application of time‐varying birth–death models to molecular phylogenies suggests that a decreasing diversification rate can only be observed if there was a decreasing speciation rate coupled with extremely low or no extinction. However, from a paleontological perspective, zero extinction rates during evolutionary radiations seem unlikely. Here, with a more comprehensive set of computer simulations, we show that substantial extinction can occur without erasing the signal of decreasing diversification rate in a molecular phylogeny. We also find, in agreement with the previous work, that a decrease in diversification rate cannot be observed in a molecular phylogeny with an increasing extinction rate alone. Further, we find that the ability to observe decreasing diversification rates in molecular phylogenies is controlled (in part) by the ratio of the initial speciation rate (Lambda) to the extinction rate (Mu) at equilibrium (the LiMe ratio), and not by their absolute values. Here we show in principle, how estimates of initial speciation rates may be calculated using both the fossil record and the shape of lineage through time plots derived from molecular phylogenies. This is important because the fossil record provides more reliable estimates of equilibrium extinction rates than initial speciation rates.     

Diversity-dependence brings molecular phylogenies closer to agreement with the fossil record

The branching times of molecular phylogenies allow us to infer speciation and extinction dynamics even when fossils are absent. Troublingly, phylogenetic approaches usually return estimates of zero extinction, conflicting with fossil evidence. Phylogenies and fossils do agree, however, that there are often limits to diversity. Here, we present a general approach to evaluate the likelihood of a phylogeny under a model that accommodates diversity-dependence and extinction. We find, by likelihood maximization, that extinction is estimated most precisely if the rate of increase in the number of lineages in the phylogeny saturates towards the present or first decreases and then increases. We demonstrate the utility and limits of our approach by applying it to the phylogenies for two cases where a fossil record exists (Cetacea and Cenozoic macroperforate planktonic foraminifera) and to three radiations lacking fossil evidence (Dendroica, Plethodon and Heliconius). We propose that the diversity-dependence model with extinction be used as the standard model for macro-evolutionary dynamics because of its biological realism and flexibility.     

Inferring biogeographic history from molecular phylogenies

The present study illustrates a method for analysing the biogeography of a group that is based on the group's phylogeny but does not invoke founder dispersal or centre of origin. The case studies presented include groups from many different parts of the world, but most are from the south‐west Pacific. The idea that basal groups are ancestral is not valid as a generalization. Neither the basal group, nor the oldest fossil represents the centre of origin, the time of origin or the ancestral ecology. Basal groups comprise less diverse sister groups and their distributions occur around centres of differentiation in already widespread ancestors, and not centres of origin for the whole group. Thus, the sequence of nodes in a phylogeny may indicate the spatial sequence of differentiation in a widespread ancestor rather than a series of founder dispersal events. Allocation of clades to a priori geographic areas, such as the continents, in the initial stages of biogeographic analysis has often involved incorrect assumptions of sympatry. This has led to the idea that the ‘areas of sympatry’ were centres of origin. Areas other than those defined by the taxa themselves need not be used in analysis. The fossil‐calibrated molecular clock, with dates transmogrified from minimum to maximum dates, has been used to test for vicariance. Recent work in population genetics, however, indicates that allopatry is caused by vicariance rather than founder dispersal, and so vicariance can instead be used to test the clock. Deriving evolutionary chronology by calibrating spatial vicariance in molecular clades with associated tectonic events is more reasonable than relying on the fossil record to give maximum (absolute) dates. © 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 98 , 757–774.     

Detection of punctuated equilibrium from molecular phylogenies

Abstract The theory of ‘punctuated equilibrium’ hypothesises that most morphological change in species takes place in rapid bursts triggered by speciation. Eldregde and Gould postulated the theory in 1972, as an alternative to the idea that morphological change slowly accumulates in the course of time, a then common belief they dubbed ‘phyletic gradualism’. Ever since its introduction the theory of punctuated equilibrium has been the subject of speculation rather than empirical validation. Here I present a method to detect punctuated evolution without reference to fossil data, based on the phenotypes of extant species and on their relatedness as revealed by molecular phylogeny. The method involves a general mathematical model describing morphological differentiation of two species over time. The two parameters in the model, the rates of punctual (cladogenetic) and gradual (anagenetic) change, are estimated from plots of morphological diversification against time since divergence of extant species.     

Estimating diversification rates for higher taxa: BAMM can give problematic estimates of rates and rate shifts

Estimates of diversification rates are invaluable for many macroevolutionary studies. Recently, an approach called BAMM (Bayesian Analysis of Macro‐evolutionary Mixtures) has become widely used for estimating diversification rates and rate shifts. At the same time, several articles have concluded that estimates of net diversification rates from the method‐of‐moments (MS) estimators are inaccurate. Yet, no studies have compared the ability of these two methods to accurately estimate clade diversification rates. Here, we use simulations to compare their performance. We found that BAMM yielded relatively weak relationships between true and estimated diversification rates. This occurred because BAMM underestimated the number of rates shifts across each tree, and assigned high rates to small clades with low rates. Errors in both speciation and extinction rates contributed to these errors, showing that using BAMM to estimate only speciation rates is also problematic. In contrast, the MS estimators (particularly using stem group ages), yielded stronger relationships between true and estimated diversification rates, by roughly twofold. Furthermore, the MS approach remained relatively accurate when diversification rates were heterogeneous within clades, despite the widespread assumption that it requires constant rates within clades. Overall, we caution that BAMM may be problematic for estimating diversification rates and rate shifts.     

Asymmetries in phylogenetic diversification and character change can be untangled

The analysis of diversification and character evolution using phylogenetic data attracts increasing interest from biologists. Recent statistical developments have resulted in a variety of tools for the inference of macroevolutionary processes in a phylogenetic context. In a recent paper Maddison (2006 Evolution, 60: 1743-1746) pointed out that uncareful use of some of these tools could lead to misleading conclusions on diversification or character evolution, and thus to difficulties in distinguishing both phenomena. I here present guidelines for the analyses of macroevolutionary data that may help to avoid these problems. The proper use of recently developed statistical methods may help to untangle diversification and character change, and so will allow us to address important evolutionary questions.     

Positive correlation between diversification rates and phenotypic evolvability can mimic punctuated equilibrium on molecular phylogenies

The hypothesis of punctuated equilibrium proposes that most phenotypic evolution occurs in rapid bursts associated with speciation events. Several methods have been developed that can infer punctuated equilibrium from molecular phylogenies in the absence of paleontological data. These methods essentially test whether the variance in phenotypes among extant species is better explained by evolutionary time since common ancestry or by the number of estimated speciation events separating taxa. However, apparent "punctuational" trait change can be recovered on molecular phylogenies if the rate of phenotypic evolution is correlated with the rate of speciation. Strong support for punctuational models can arise even if the underlying mode of trait evolution is strictly gradual, so long as rates of speciation and trait evolution covary across the branches of phylogenetic trees, and provided that lineages vary in their rate of speciation. Species selection for accelerated rates of ecological or phenotypic divergence can potentially lead to the perception that most trait divergence occurs in association with speciation events.     

EXPLOSIVE EVOLUTIONARY RADIATIONS: DECREASING SPECIATION OR INCREASING EXTINCTION THROUGH TIME?

A common pattern in time-calibrated molecular phylogenies is a signal of rapid diversification early in the history of a radiation. Because the net rate of diversification is the difference between speciation and extinction rates, such "explosive-early" diversification could result either from temporally declining speciation rates or from increasing extinction rates through time. Distinguishing between these alternatives is challenging but important, because these processes likely result from different ecological drivers of diversification. Here we develop a method for estimating speciation and extinction rates that vary continuously through time. By applying this approach to real phylogenies with explosive-early diversification and by modeling features of lineage-accumulation curves under both declining speciation and increasing extinction scenarios, we show that a signal of explosive-early diversification in phylogenies of extant taxa cannot result from increasing extinction and can only be explained by temporally declining speciation rates. Moreover, whenever extinction rates are high, "explosive early" patterns become unobservable, because high extinction quickly erases the signature of even large declines in speciation rates. Although extinction may obscure patterns of evolutionary diversification, these results show that decreasing speciation is often distinguishable from increasing extinction in the numerous molecular phylogenies of radiations that retain a preponderance of early lineages.     

Extinction, ecological opportunity, and the origins of global snake diversity

Snake diversity varies by at least two orders of magnitude among extant lineages, with numerous groups containing only one or two species, and several young clades exhibiting exceptional richness (>700 taxa). With a phylogeny containing all known families and subfamilies, we find that these patterns cannot be explained by background rates of speciation and extinction. The majority of diversity appears to derive from a radiation within the superfamily Colubroidea, potentially stemming from the colonization of new areas and the evolution of advanced venom-delivery systems. In contrast, negative relationships between clade age, clade size, and diversification rate suggest the potential for possible bias in estimated diversification rates, interpreted by some recent authors as support for ecologically mediated limits on diversity. However, evidence from the fossil record indicates that numerous lineages were far more diverse in the past, and that extinction has had an important impact on extant diversity patterns. Thus, failure to adequately account for extinction appears to prevent both rate- and diversity-limited models from fully characterizing richness dynamics in snakes. We suggest that clade-level extinction may provide a key mechanism for explaining negative or hump-shaped relationships between clade age and diversity, and the prevalence of ancient, species-poor lineages in numerous groups.     

Some problems in the study of the origin of neotropical biodiversity using palaeoecological and molecular phylogenetic evidence

This study contends that progress in the understanding of the origin and maintenance of extant neotropical biodiversity by means of empirical evidence is hampered by the persistence of anachronistic conceptual approaches, notably the adherence to closed paradigms or ruling theories. The topic is discussed from three main perspectives: (1) the tendency to shift from one paradigm to another, (2) the use and abuse of broad generalizations from a single or a few case studies and (3) the use of inadequate phylogenetic dating (usually crown dating alone) for a sound appraisal of diversification timing. The origin of neotropical biodiversity is a complex subject that requires an open-minded attitude to be fully captured. The solution proposed is fairly easy, somewhat trivial, and rooted in the classical multiple working hypotheses (MWH) approach. The MWH seeks to explore any explanation possible for observed phenomena and develop every testable hypothesis in relation to their possible causes. The MWH approach promotes thoroughness, suggests lines of inquiry that might otherwise be overlooked and develops the habit of parallel and complex thought that, unfortunately, is not fully developed in the empirical study of neotropical biodiversity.