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.     

Prolonging the past counteracts the pull of the present: protracted speciation can explain observed slowdowns in diversification

Phylogenetic trees show a remarkable slowdown in the increase of number of lineages towards the present, a phenomenon which cannot be explained by the standard birth-death model of diversification with constant speciation and extinction rates. The birth-death model instead predicts a constant or accelerating increase in the number of lineages, which has been called the pull of the present. The observed slowdown has been attributed to nonconstancy of the speciation and extinction rates due to some form of diversity dependence (i.e., species-level density dependence), but the mechanisms underlying this are still unclear. Here, we propose an alternative explanation based on the simple concept that speciation takes time to complete. We show that this idea of "protracted" speciation can be incorporated in the standard birth-death model of diversification. The protracted birth-death model predicts a realistic slowdown in the rate of increase of number of lineages in the phylogeny and provides a compelling fit to four bird phylogenies with realistic parameter values. Thus, the effect of recognizing the generally accepted fact that speciation is not an instantaneous event is significant; even if it cannot account for all the observed patterns, it certainly contributes substantially and should therefore be incorporated into future studies.     

Estimating a binary character's effect on speciation and extinction

Determining whether speciation and extinction rates depend on the state of a particular character has been of long-standing interest to evolutionary biologists. To assess the effect of a character on diversification rates using likelihood methods requires that we be able to calculate the probability that a group of extant species would have evolved as observed, given a particular model of the character's effect. Here we describe how to calculate this probability for a phylogenetic tree and a two-state (binary) character under a simple model of evolution (the "BiSSE" model, binary-state speciation and extinction). The model involves six parameters, specifying two speciation rates (rate when the lineage is in state 0; rate when in state 1), two extinction rates (when in state 0; when in state 1), and two rates of character state change (from 0 to 1, and from 1 to 0). Using these probability calculations, we can do maximum likelihood inference to estimate the model's parameters and perform hypothesis tests (e.g., is the rate of speciation elevated for one character state over the other?). We demonstrate the application of the method using simulated data with known parameter values.     

Detecting local diversity‐dependence in diversification

Whether there are ecological limits to species diversification is a hotly debated topic. Molecular phylogenies show slowdowns in lineage accumulation, suggesting that speciation rates decline with increasing diversity. A maximum‐likelihood (ML) method to detect diversity‐dependent (DD) diversification from phylogenetic branching times exists, but it assumes that diversity‐dependence is a global phenomenon and therefore ignores that the underlying species interactions are mostly local, and not all species in the phylogeny co‐occur locally. Here, we explore whether this ML method based on the nonspatial diversity‐dependence model can detect local diversity‐dependence, by applying it to phylogenies, simulated with a spatial stochastic model of local DD speciation, extinction, and dispersal between two local communities. We find that type I errors (falsely detecting diversity‐dependence) are low, and the power to detect diversity‐dependence is high when dispersal rates are not too low. Interestingly, when dispersal is high the power to detect diversity‐dependence is even higher than in the nonspatial model. Moreover, estimates of intrinsic speciation rate, extinction rate, and ecological limit strongly depend on dispersal rate. We conclude that the nonspatial DD approach can be used to detect diversity‐dependence in clades of species that live in not too disconnected areas, but parameter estimates must be interpreted cautiously.     

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.     

Simulating trees with a fixed number of extant species

In this paper, I develop efficient tools to simulate trees with a fixed number of extant species. The tools are provided in my open source R-package TreeSim available on CRAN. The new model presented here is a constant rate birth-death process with mass extinction and/or rate shift events at arbitrarily fixed times 1) before the present or 2) after the origin. The simulation approach for case (2) can also be used to simulate under more general models with fixed events after the origin. I use the developed simulation tools for showing that a mass extinction event cannot be distinguished from a model with constant speciation and extinction rates interrupted by a phase of stasis based on trees consisting of only extant species. However, once we distinguish between mass extinction and period of stasis based on paleontological data, fast simulations of trees with a fixed number of species allow inference of speciation and extinction rates using approximate Bayesian computation and allow for robustness analysis once maximum likelihood parameter estimations are available.     

Phylogenetically patterned speciation rates and extinction risks change the loss of evolutionary history during extinctions

If we are to plan conservation strategies that minimize the loss of evolutionary history through human-caused extinctions, we must understand how this loss is related to phylogenetic patterns in current extinction risks and past speciation rates. Nee & May (1997, Science 278, 692-694) showed that for a randomly evolving clade (i) a single round of random extinction removed relatively little evolutionary history, and (ii) extinction management (choosing which taxa to sacrifice) offered only marginal improvement. However, both speciation rates and extinction risks vary across lineages within real clades. We simulated evolutionary trees with phylogenetically patterned speciation rates and extinction risks (closely related lineages having similar rates and risks) and then subjected them to several biologically informed models of extinction. Increasing speciation rate variation increases the extinction-management pay-off. When extinction risks vary among lineages but are uncorrelated with speciation rates, extinction removes more history (compared with random trees), but the difference is small. When extinction risks vary and are correlated with speciation rates, history loss can dramatically increase (negative correlation) or decrease (positive correlation) with speciation rate variation. The loss of evolutionary history via human-caused extinctions may therefore be more severe, yet more manageable, than first suggested.     

Conceptual and statistical problems with the DEC+J model of founder‐event speciation and its comparison with DEC via model selection

Phylogenetic studies of geographic range evolution are increasingly using statistical model selection methods to choose among variants of the dispersal‐extinction‐cladogenesis (DEC) model, especially between DEC and DEC+J, a variant that emphasizes “jump dispersal,” or founder‐event speciation, as a type of cladogenetic range inheritance scenario. Unfortunately, DEC+J is a poor model of founder‐event speciation, and statistical comparisons of its likelihood with DEC are inappropriate. DEC and DEC+J share a conceptual flaw: cladogenetic events of range inheritance at ancestral nodes, unlike anagenetic events of dispersal and local extinction along branches, are not modelled as being probabilistic with respect to time. Ignoring this probability factor artificially inflates the contribution of cladogenetic events to the likelihood, and leads to underestimates of anagenetic, time‐dependent range evolution. The flaw is exacerbated in DEC+J because not only is jump dispersal allowed, expanding the set of cladogenetic events, its probability relative to non‐jump events is assigned a free parameter, j, that when maximized precludes the possibility of non‐jump events at ancestral nodes. DEC+J thus parameterizes the mode of speciation, but like DEC, it does not parameterize the rate of speciation. This inconsistency has undesirable consequences, such as a greater tendency towards degenerate inferences in which the data are explained entirely by cladogenetic events (at which point branch lengths become irrelevant, with estimated anagenetic rates of 0). Inferences with DEC+J can in some cases depart dramatically from intuition, e.g. when highly unparsimonious numbers of jump dispersal events are required solely because j is maximized. Statistical comparison with DEC is inappropriate because a higher DEC+J likelihood does not reflect a more close approximation of the “true” model of range evolution, which surely must include time‐dependent processes; instead, it is simply due to more weight being allocated (via j) to jump dispersal events whose time‐dependent probabilities are ignored. In testing hypotheses about the geographic mode of speciation, jump dispersal can and should instead be modelled using existing frameworks for state‐dependent lineage diversification in continuous time, taking appropriate cautions against Type I errors associated with such methods. For simple inference of ancestral ranges on a fixed phylogeny, a DEC‐based model may be defensible if statistical model selection is not used to justify the choice, and it is understood that inferences about cladogenetic range inheritance lack any relation to time, normally a fundamental axis of evolutionary models.     

Advancing the metabolic theory of biodiversity

A component of metabolic scaling theory has worked towards understanding the influence of metabolism over the generation and maintenance of biodiversity. Specific models within this ‘metabolic theory of biodiversity’ (MTB) have addressed temperature gradients in speciation rate and species richness, but the scope of MTB has been questioned because of empirical departures from model predictions. In this study, we first show that a generalized MTB is not inconsistent with empirical patterns and subsequently implement an eco‐evolutionary MTB which has thus far only been discussed qualitatively. More specifically, we combine a functional trait (body mass) approach and an environmental gradient (temperature) with a dynamic eco‐evolutionary model that builds on the current MTB. Our approach uniquely accounts for feedbacks between ecological interactions (size‐dependent competition and predation) and evolutionary rates (speciation and extinction). We investigate a simple example in which temperature influences mutation rate, and show that this single effect leads to dynamic temperature gradients in macroevolutionary rates and community structure. Early in community evolution, temperature strongly influences speciation and both speciation and extinction strongly influence species richness. Through time, niche structure evolves, speciation and extinction rates fall, and species richness becomes increasingly independent of temperature. However, significant temperature‐richness gradients may persist within emergent functional (trophic) groups, especially when niche breadths are wide. Thus, there is a strong signal of both history and ecological interactions on patterns of species richness across temperature gradients. More generally, the successful implementation of an eco‐evolutionary MTB opens the perspective that a process‐based MTB can continue to emerge through further development of metabolic models that are explicit in terms of functional traits and environmental gradients.     

FiSSE: A simple nonparametric test for the effects of a binary character on lineage diversification rates

It is widely assumed that phenotypic traits can influence rates of speciation and extinction, and several statistical approaches have been used to test for correlations between character states and lineage diversification. Recent work suggests that model‐based tests of state‐dependent speciation and extinction are sensitive to model inadequacy and phylogenetic pseudoreplication. We describe a simple nonparametric statistical test (“FiSSE”) to assess the effects of a binary character on lineage diversification rates. The method involves computing a test statistic that compares the distributions of branch lengths for lineages with and without a character state of interest. The value of the test statistic is compared to a null distribution generated by simulating character histories on the observed phylogeny. Our tests show that FiSSE can reliably infer trait‐dependent speciation on phylogenies of several hundred tips. The method has low power to detect trait‐dependent extinction but can infer state‐dependent differences in speciation even when net diversification rates are constant. We assemble a range of macroevolutionary scenarios that are problematic for likelihood‐based methods, and we find that FiSSE does not show similarly elevated false positive rates. We suggest that nonparametric statistical approaches, such as FiSSE, provide an important complement to formal process‐based models for trait‐dependent diversification.     

Species selection and random drift in macroevolution

Species selection resulting from trait‐dependent speciation and extinction is increasingly recognized as an important mechanism of phenotypic macroevolution. However, the recent bloom in statistical methods quantifying this process faces a scarcity of dynamical theory for their interpretation, notably regarding the relative contributions of deterministic versus stochastic evolutionary forces. I use simple diffusion approximations of birth‐death processes to investigate how the expected and random components of macroevolutionary change depend on phenotype‐dependent speciation and extinction rates, as can be estimated empirically. I show that the species selection coefficient for a binary trait, and selection differential for a quantitative trait, depend not only on differences in net diversification rates (speciation minus extinction), but also on differences in species turnover rates (speciation plus extinction), especially in small clades. The randomness in speciation and extinction events also produces a species‐level equivalent to random genetic drift, which is stronger for higher turnover rates. I then show how microevolutionary processes including mutation, organismic selection, and random genetic drift cause state transitions at the species level, allowing comparison of evolutionary forces across levels. A key parameter that would be needed to apply this theory is the distribution and rate of origination of new optimum phenotypes along a phylogeny.     

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.     

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.     

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.     

Likelihood methods for detecting temporal shifts in diversification rates

Maximum likelihood is a potentially powerful approach for investigating the tempo of diversification using molecular phylogenetic data. Likelihood methods distinguish between rate-constant and rate-variable models of diversification by fitting birth-death models to phylogenetic data. Because model selection in this context is a test of the null hypothesis that diversification rates have been constant over time, strategies for selecting best-fit models must minimize Type I error rates while retaining power to detect rate variation when it is present. Here I examine model selection, parameter estimation, and power to reject the null hypothesis using likelihood models based on the birth-death process. The Akaike information criterion (AIC) has often been used to select among diversification models; however, I find that selecting models based on the lowest AIC score leads to a dramatic inflation of the Type I error rate. When appropriately corrected to reduce Type I error rates, the birth-death likelihood approach performs as well or better than the widely used gamma statistic, at least when diversification rates have shifted abruptly over time. Analyses of datasets simulated under a range of rate-variable diversification scenarios indicate that the birth-death likelihood method has much greater power to detect variation in diversification rates when extinction is present. Furthermore, this method appears to be the only approach available that can distinguish between a temporal increase in diversification rates and a rate-constant model with nonzero extinction. I illustrate use of the method by analyzing a published phylogeny for Australian agamid lizards.     

Loss of sexual recombination and segregation is associated with increased diversification in evening primroses

The loss of sexual recombination and segregation in asexual organisms has been portrayed as an irreversible process that commits asexually reproducing lineages to reduced diversification. We test this hypothesis by estimating rates of speciation, extinction, and transition between sexuality and functional asexuality in the evening primroses. Specifically, we estimate these rates using the recently developed BiSSE (Binary State Speciation and Extinction) phylogenetic comparative method, which employs maximum likelihood and Bayesian techniques. We infer that net diversification rates (speciation minus extinction) in functionally asexual evening primrose lineages are roughly eight times faster than diversification rates in sexual lineages, largely due to higher speciation rates in asexual lineages. We further reject the hypothesis that a loss of recombination and segregation is irreversible because the transition rate from functional asexuality to sexuality is significantly greater than zero and in fact exceeded the reverse rate. These results provide the first empirical evidence in support of the alternative theoretical prediction that asexual populations should instead diversify more rapidly than sexual populations because they are free from the homogenizing effects of sexual recombination and segregation. Although asexual reproduction may often constrain adaptive evolution, our results show that the loss of recombination and segregation need not be an evolutionary dead end in terms of diversification of lineages.     

Tempo and mode in karyotype evolution revealed by a probabilistic model incorporating both chromosome number and morphology

Karyotype, including the chromosome and arm numbers, is a fundamental genetic characteristic of all organisms and has long been used as a species-diagnostic character. Additionally, karyotype evolution plays an important role in divergent adaptation and speciation. Centric fusion and fission change chromosome numbers, whereas the intra-chromosomal movement of the centromere, such as pericentric inversion, changes arm numbers. A probabilistic model simultaneously incorporating both chromosome and arm numbers has not been established. Here, we built a probabilistic model of karyotype evolution based on the “karyograph”, which treats karyotype evolution as a walk on the two-dimensional space representing the chromosome and arm numbers. This model enables analysis of the stationary distribution with a stable karyotype for any given parameter. After evaluating their performance using simulated data, we applied our model to two large taxonomic groups of fish, Eurypterygii and series Otophysi, to perform maximum likelihood estimation of the transition rates and reconstruct the evolutionary history of karyotypes. The two taxa significantly differed in the evolution of arm number. The inclusion of speciation and extinction rates demonstrated possibly high extinction rates in species with karyotypes other than the most typical karyotype in both groups. Finally, we made a model including polyploidization rates and applied it to a small plant group. Thus, the use of this probabilistic model can contribute to a better understanding of tempo and mode in karyotype evolution and its possible role in speciation and extinction.     

Application of Johnson et al.'s speciation threshold model to apparent colonization times of island biotas

Understanding patterns of diversity can be furthered by analysis of the dynamics of colonization, speciation, and extinction on islands using historical information provided by molecular phylogeography. The land birds of the Lesser Antilles are one of the most thoroughly described regional faunas in this context. In an analysis of colonization times, Ricklefs and Bermingham (2001) found that the cumulative distribution of lineages with respect to increasing time since colonization exhibits a striking change in slope at a genetic distance of about 2% mitochondrial DNA sequence divergence (about one million years). They further showed how this heterogeneity could be explained by either an abrupt increase in colonization rates or a mass extinction event. Cherry et al. (2002), referring to a model developed by Johnson et al. (2000), argued instead that the pattern resulted from a speciation threshold for reproductive isolation of island populations from their continental source populations. Prior to this threshold, genetic divergence is slowed by migration from the source, and species of varying age accumulate at a low genetic distance. After the threshold is reached, source and island populations diverge more rapidly, creating heterogeneity in the distribution of apparent ages of island taxa. We simulated of Johnson et al.'s speciation-threshold model, incorporating genetic divergence at rate k and fixation at rate M of genes that have migrated between the source and the island population. Fixation resets the divergence clock to zero. The speciation-threshold model fits the distribution of divergence times of Lesser Antillean birds well with biologically plausible parameter estimates. Application of the model to the Hawaiian avifauna, which does not exhibit marked heterogeneity of genetic divergence, and the West Indian herpetofauna, which does, required unreasonably high migration-fixation rates, several orders of magnitude greater than the colonization rate. However, the plausibility of the speciation-divergence model for Lesser Antillean birds emphasizes the importance of further investigation of historical biogeography on a regional scale for whole biotas, as well as the migration of genes between populations on long time scales and the achievement of reproductive isolation.     

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.     

Niche width impacts vertebrate diversification

Aim The size of the climatic niche of a species is a major factor determining its distribution and evolution. In particular, it has been proposed that niche width should be associated with the rate of species diversification. Here, we test whether species niche width affects the speciation and extinction rates of three main clades of vertebrates: amphibians, mammals and birds. Location Global. Methods We obtained the time‐calibrated phylogenies, IUCN conservation status, species distribution maps and climatic data for 2340 species of amphibians, 4563 species of mammals and 9823 species of birds. We computed the niche width for each species as the mean annual temperature across the species range. We estimated speciation, extinction and transition rates associated with lineages with either narrow (specialist) or wide (generalist) niches using phylogeny‐based birth–death models. We also tested if current conservation status was correlated with the niche width of species. Results We found higher net diversification rates in specialist species than in generalist species. This result was explained by both higher speciation rates (for the three taxonomic groups) and lower extinction rates (for mammals and birds only) in specialist than in generalist species. In contrast, current specialist species tended to be more threatened than generalist species. Main conclusions Our diversification analysis shows that the width of the climatic niche is strongly associated with diversification rates and may thus be a crucial factor for understanding the emergence of diversity patterns in vertebrates. The striking difference between our diversification results and current conservation status suggests that the current extinction process may be different from extinction rates estimated from the whole history of the group.