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.     

Primate diversification inferred from phylogenies and fossils

Biodiversity arises from the balance between speciation and extinction. Fossils record the origins and disappearance of organisms, and the branching patterns of molecular phylogenies allow estimation of speciation and extinction rates, but the patterns of diversification are frequently incongruent between these two data sources. I tested two hypotheses about the diversification of primates based on ～600 fossil species and 90% complete phylogenies of living species: (1) diversification rates increased through time; (2) a significant extinction event occurred in the Oligocene. Consistent with the first hypothesis, analyses of phylogenies supported increasing speciation rates and negligible extinction rates. In contrast, fossils showed that while speciation rates increased, speciation and extinction rates tended to be nearly equal, resulting in zero net diversification. Partially supporting the second hypothesis, the fossil data recorded a clear pattern of diversity decline in the Oligocene, although diversification rates were near zero. The phylogeny supported increased extinction ～34 Ma, but also elevated extinction ～10 Ma, coinciding with diversity declines in some fossil clades. The results demonstrated that estimates of speciation and extinction ignoring fossils are insufficient to infer diversification and information on extinct lineages should be incorporated into phylogenetic analyses.     

Testing macro-evolutionary models using incomplete molecular phylogenies.

Phylogenies reconstructed from gene sequences can be used to investigate the tempo and mode of species diversification. Here we develop and use new statistical methods to infer past patterns of speciation and extinction from molecular phylogenies. Specifically, we test the null hypothesis that per-lineage speciation and extinction rates have remained constant through time. Rejection of this hypothesis may provide evidence for evolutionary events such as adaptive radiations or key adaptations. In contrast to previous approaches, our methods are robust to incomplete taxon sampling and are conservative with respect to extinction. Using simulation we investigate, first, the adverse effects of failing to take incomplete sampling into account and, second, the power and reliability of our tests. When applied to published phylogenies our tests suggest that, in some cases, speciation rates have decreased through time.     

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.      

Analysis of diversification: combining phylogenetic and taxonomic data

The estimation of diversification rates using phylogenetic data has attracted a lot of attention in the past decade. In this context, the analysis of incomplete phylogenies (e.g. phylogenies resolved at the family level but unresolved at the species level) has remained difficult. I present here a likelihood-based method to combine partly resolved phylogenies with taxonomic (species-richness) data to estimate speciation and extinction rates. This method is based on fitting a birth-and-death model to both phylogenetic and taxonomic data. Some examples of the method are presented with data on birds and on mammals. The method is compared with existing approaches that deal with incomplete phylogenies. Some applications and generalizations of the approach introduced in this paper are further discussed.     

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.     

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.     

Artificial neural networks can learn to estimate extinction rates from molecular phylogenies

Molecular phylogenies typically consist of only extant species, yet they allow inference of past rates of extinction, because recently originated species are less likely to be extinct than ancient species. Despite the simple structure of the assumed underlying speciation-extinction process, parametric functions to estimate extinction rates from phylogenies turned out to be complex and often difficult to derive. Moreover, these parametric functions are specific to a particular process (e.g. complete species level phylogeny with constant birth and death rates) and a particular type of data (e.g. times between bifurcations). Here, it is shown that artificial neural networks can substitute for parametric estimation functions once they have been sufficiently trained on simulated data. This technique can in principle be used for different processes and data types, and because it circumvents the time-consuming and difficult task of deriving parametric estimation functions, it may greatly extend the possibilities to make macro-evolutionary inferences from molecular phylogenies. This novel approach is explained, applied to estimate speciation and extinction rates from a molecular phylogeny of the reef fish genus Naso (Acanturidae), and its performance is compared to that of maximum likelihood estimation.     

Detection of "punctuated equilibrium" by bayesian estimation of speciation and extinction rates, ancestral character states, and rates of anagenetic and cladogenetic evolution on a molecular phylogeny

Algorithms are presented to simultaneously estimate probabilities of speciation and extinction, rates of anagenetic and cladogenetic phenotypic evolution, as well as ancestral character states, from a complete ultrametric species-level phylogeny with dates assigned to all bifurcations and one or more phenotypes in three or more extant species, using Metropolis-Hastings Markov Chain Monte Carlo sampling. The algorithms also estimate missing phenotypes of extant species and numbers of speciation events that occurred on all branches of the phylogeny. The algorithms are discussed and their performance is evaluated using simulated data. That evaluation shows that precise estimation of rates of evolution of one or a few phenotypes requires large phylogenies. Estimation accuracy improves with the number of species on the phylogeny.     

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.     

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.     

Incomplete lineage sorting impacts the inference of macroevolutionary regimes from molecular phylogenies when concatenation is employed: An analysis based on Cetacea

Interest in methods that estimate speciation and extinction rates from molecular phylogenies has increased over the last decade. The application of such methods requires reliable estimates of tree topology and node ages, which are frequently obtained using standard phylogenetic inference combining concatenated loci and molecular dating. However, this practice disregards population‐level processes that generate gene tree/species tree discordance. We evaluated the impact of employing concatenation and coalescent‐based phylogeny inference in recovering the correct macroevolutionary regime using simulated data based on the well‐established diversification rate shift of delphinids in Cetacea. We found that under scenarios of strong incomplete lineage sorting, macroevolutionary analysis of phylogenies inferred by concatenating loci failed to recover the delphinid diversification shift, while the coalescent‐based tree consistently retrieved the correct rate regime. We suggest that ignoring microevolutionary processes reduces the power of methods that estimate macroevolutionary regimes from molecular data.     

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.     

Detecting shifts in diversity limits from molecular phylogenies: what can we know?

Large complete species-level molecular phylogenies can provide the most direct information about the macroevolutionary history of clades having poor fossil records. However, extinction will ultimately erode evidence of pulses of rapid speciation in the deep past. Assessment of how well, and for how long, phylogenies retain the signature of such pulses has hitherto been based on a--probably untenable--model of ongoing diversity-independent diversification. Here, we develop two new tests for changes in diversification 'rules' and evaluate their power to detect sudden increases in equilibrium diversity in clades simulated with diversity-dependent speciation and extinction rates. Pulses of diversification are only detected easily if they occurred recently and if the rate of species turnover at equilibrium is low; rates reported for fossil mammals suggest that the power to detect a doubling of species diversity falls to 50 per cent after less than 50 Myr even with a perfect phylogeny of extant species. Extinction does eventually draw a veil over past dynamics, suggesting that some questions are beyond the limits of inference, but sudden clade-wide pulses of speciation can be detected after many millions of years, even when overall diversity is constrained. Applying our methods to existing phylogenies of mammals and angiosperms identifies intervals of elevated diversification in each.     

The quality of the fossil record and the accuracy of phylogenetic inferences about sampling and diversity

Because phylogenies can be estimated without stratigraphic data and because estimated phylogenies also infer gaps in sampling, some workers have used phylogeny estimates as templates for evaluating sampling from the fossil record and for "correcting" historical diversity patterns. However, it is not known how sampling intensity (the probability of sampling taxa per unit time) and completeness (the proportion of taxa sampled) affect the accuracy of phylogenetic inferences, nor how phylogenetically inferred estimates of sampling and diversity respond to inaccurate estimates of phylogeny. Both issues are addressed with a series of simulations using simple models of character evolution, varying speciation patterns, and various rates of speciation, extinction, character change, and preservation. Parsimony estimates of simulated phylogenies become less accurate as sampling decreases, and inaccurate trees chronically underestimate sampling. Biotic factors such as rates of morphologic change and extinction both affect the accuracy of phylogenetic estimates and thus affect estimated gaps in sampling, indicating that differences in implied sampling need not reflect actual differences in sampling. Errors in inferred diversity are concentrated early in the history of a clade. This, coupled with failure to account for true extinction times (i.e., the Signor-Lipps effect), inflates relative diversity levels early in clade histories. Because factors other than differences in sampling predict differences in the numbers of gaps implied by phylogeny estimates, inferred phylogenies can be misleading templates for evaluating sampling or historical diversity patterns.     

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.     

Modeling colonization rates over time: Generating null models and testing model adequacy in phylogenetic analyses of species assemblages*

A central theme connecting macroevolutionary processes to macroecological patterns is the shaping of regional biodiversity over time through speciation, extinction, migration, and range shifts. The use of phylogenies to explore the dynamics of diversification due to variation in speciation and extinction rates has been well-developed and there are established methods for inferring speciation times from phylogenies and generating its null distributions (as represented by node heights on molecular phylogenies). But inferring colonization events from phylogenies is more challenging. Unlike speciation events, represented by nodes, colonization events could occur at any point along a branch connecting species in the assemblage to the regional pool. We account for uncertainty in identification of colonization lineages and timing of colonization events by using an efficient analytical solution to inferring the distribution of colonization times from an assemblage phylogeny. Using the same solution, we efficiently derive the null distribution of colonization times, which provides us with a general approach to testing the adequacy of a model to describe colonization events into the assemblage. We illustrate this approach by demonstrating how the movement of squamate lineages into Madagascar has been uneven over time, peaking in the early Cenozoic when ocean conditions favored colonization.     

The ecological dynamics of clade diversification and community assembly

Clades diversify in an ecological context, but most macroevolutionary models do not directly encapsulate ecological mechanisms that influence speciation and extinction. A data set of 245 chordate, arthropod, mollusk, and magnoliophyte phylogenies had a majority of clades that showed rapid lineage accumulation early with a slowing more recently, whereas a small but significant minority showed accelerated lineage accumulation in their recent histories. Previous analyses have demonstrated that macroevolutionary birth-death models can replicate the pattern of slowing lineage accumulation only by a strong decrease in speciation rate with increasing species richness and extinction rate held extremely low or absent. In contrast, the metacommunity model presented here could generate the full range of patterns seen in the real phylogenies by simply manipulating the degree of ecological differentiation of new species at the time of speciation. Specifically, the metacommunity model predicts that clades showing decelerating lineage accumulation rates are those that have diversified by ecological modes of speciation, whereas clades showing accelerating lineage accumulation rates are those that have diversified primarily by modes of speciation that generate little or no ecological diversification. A number of testable predictions that integrate data from molecular systematics, community ecology, and biogeography are also discussed.     

Probability distribution of molecular evolutionary trees: A new method of phylogenetic inference

A new method is presented for inferring evolutionary trees using nucleotide sequence data. The birth-death process is used as a model of speciation and extinction to specify the prior distribution of phylogenies and branching times. Nucleotide substitution is modeled by a continuous-time Markov process. Parameters of the branching model and the substitution model are estimated by maximum likelihood. The posterior probabilities of different phylogenies are calculated and the phylogeny with the highest posterior probability is chosen as the best estimate of the evolutionary relationship among species. We refer to this as the maximum posterior probability (MAP) tree. The posterior probability provides a natural measure of the reliability of the estimated phylogeny. Two example data sets are analyzed to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The best trees estimated by the new method are the same as those from the maximum likelihood analysis of separate topologies, but the posterior probabilities are quite different from the bootstrap proportions. The results of the method are found to be insensitive to changes in the rate parameter of the branching process. Correspondence to: Z. Yang