A new method for handling missing species in diversification analysis applicable to randomly or nonrandomly sampled phylogenies

Chronograms from molecular dating are increasingly being used to infer rates of diversification and their change over time. A major limitation in such analyses is incomplete species sampling that moreover is usually nonrandom. While the widely used γ statistic with the Monte Carlo constant-rates test or the birth-death likelihood analysis with the δ AICrc test statistic are appropriate for comparing the fit of different diversification models in phylogenies with random species sampling, no objective automated method has been developed for fitting diversification models to nonrandomly sampled phylogenies. Here, we introduce a novel approach, CorSiM, which involves simulating missing splits under a constant rate birth-death model and allows the user to specify whether species sampling in the phylogeny being analyzed is random or nonrandom. The completed trees can be used in subsequent model-fitting analyses. This is fundamentally different from previous diversification rate estimation methods, which were based on null distributions derived from the incomplete trees. CorSiM is automated in an R package and can easily be applied to large data sets. We illustrate the approach in two Araceae clades, one with a random species sampling of 52% and one with a nonrandom sampling of 55%. In the latter clade, the CorSiM approach detects and quantifies an increase in diversification rate, whereas classic approaches prefer a constant rate model; in the former clade, results do not differ among methods (as indeed expected since the classic approaches are valid only for randomly sampled phylogenies). The CorSiM method greatly reduces the type I error in diversification analysis, but type II error remains a methodological problem.     

EXTINCTION RATES SHOULD NOT BE ESTIMATED FROM MOLECULAR PHYLOGENIES

Molecular phylogenies contain information about the tempo and mode of species diversification through time. Because extinction leaves a characteristic signature in the shape of molecular phylogenetic trees, many studies have used data from extant taxa only to infer extinction rates. This is a promising approach for the large number of taxa for which extinction rates cannot be estimated from the fossil record. Here, I explore the consequences of violating a common assumption made by studies of extinction from phylogenetic data. I show that when diversification rates vary among lineages, simple estimators based on the birth–death process are unable to recover true extinction rates. This is problematic for phylogenetic trees with complete taxon sampling as well as for the simpler case of clades with known age and species richness. Given the ubiquity of variation in diversification rates among lineages and clades, these results suggest that extinction rates should not be estimated in the absence of fossil data.     

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.     

The shape and temporal dynamics of phylogenetic trees arising from geographic speciation

Phylogenetic trees often depart from the expectations of stochastic models, exhibiting imbalance in diversification among lineages and slowdowns in the rate of lineage accumulation through time. Such departures have led to a widespread perception that ecological differences among species or adaptation and subsequent niche filling are required to explain patterns of diversification. However, a key element missing from models of diversification is the geographical context of speciation and extinction. In this study, we develop a spatially explicit model of geographic range evolution and cladogenesis, where speciation arises via vicariance or peripatry, and explore the effects of these processes on patterns of diversification. We compare the results with those observed in 41 reconstructed avian trees. Our model shows that nonconstant rates of speciation and extinction are emergent properties of the apportioning of geographic ranges that accompanies speciation. The dynamics of diversification exhibit wide variation, depending on the mode of speciation, tendency for range expansion, and rate of range evolution. By varying these parameters, the model is able to capture many, but not all, of the features exhibited by birth-death trees and extant bird clades. Under scenarios with relatively stable geographic ranges, strong slowdowns in diversification rates are produced, with faster rates of range dynamics leading to constant or accelerating rates of apparent diversification. A peripatric model of speciation with stable ranges also generates highly unbalanced trees typical of bird phylogenies but fails to produce realistic range size distributions among the extant species. Results most similar to those of a birth-death process are reached under a peripatric speciation scenario with highly volatile range dynamics. Taken together, our results demonstrate that considering the geographical context of speciation and extinction provides a more conservative null model of diversification and offers a very different perspective on the phylogenetic patterns expected in the absence of ecology.     

Quantitative traits and diversification

Quantitative traits have long been hypothesized to affect speciation and extinction rates. For example, smaller body size or increased specialization may be associated with increased rates of diversification. Here, I present a phylogenetic likelihood-based method (quantitative state speciation and extinction [QuaSSE]) that can be used to test such hypotheses using extant character distributions. This approach assumes that diversification follows a birth-death process where speciation and extinction rates may vary with one or more traits that evolve under a diffusion model. Speciation and extinction rates may be arbitrary functions of the character state, allowing much flexibility in testing models of trait-dependent diversification. I test the approach using simulated phylogenies and show that a known relationship between speciation and a quantitative character could be recovered in up to 80% of the cases on large trees (500 species). Consistent with other approaches, detecting shifts in diversification due to differences in extinction rates was harder than when due to differences in speciation rates. Finally, I demonstrate the application of QuaSSE to investigate the correlation between body size and diversification in primates, concluding that clade-specific differences in diversification may be more important than size-dependent diversification in shaping the patterns of diversity within this group.     

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.     

Bayesian Inference of Sampled Ancestor Trees for Epidemiology and Fossil Calibration

Phylogenetic analyses which include fossils or molecular sequences that are sampled through time require models that allow one sample to be a direct ancestor of another sample. As previously available phylogenetic inference tools assume that all samples are tips, they do not allow for this possibility. We have developed and implemented a Bayesian Markov Chain Monte Carlo (MCMC) algorithm to infer what we call sampled ancestor trees, that is, trees in which sampled individuals can be direct ancestors of other sampled individuals. We use a family of birth-death models where individuals may remain in the tree process after sampling, in particular we extend the birth-death skyline model [Stadler et al., 2013] to sampled ancestor trees. This method allows the detection of sampled ancestors as well as estimation of the probability that an individual will be removed from the process when it is sampled. We show that even if sampled ancestors are not of specific interest in an analysis, failing to account for them leads to significant bias in parameter estimates. We also show that sampled ancestor birth-death models where every sample comes from a different time point are non-identifiable and thus require one parameter to be known in order to infer other parameters. We apply our phylogenetic inference accounting for sampled ancestors to epidemiological data, where the possibility of sampled ancestors enables us to identify individuals that infected other individuals after being sampled and to infer fundamental epidemiological parameters. We also apply the method to infer divergence times and diversification rates when fossils are included along with extant species samples, so that fossilisation events are modelled as a part of the tree branching process. Such modelling has many advantages as argued in the literature. The sampler is available as an open-source BEAST2 package (https://github.com/CompEvol/sampled-ancestors).     

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.     

Testing for temporal variation in diversification rates when sampling is incomplete and nonrandom

A common pattern found in phylogeny-based empirical studies of diversification is a decrease in the rate of lineage accumulation toward the present. This early-burst pattern of cladogenesis is often interpreted as a signal of adaptive radiation or density-dependent processes of diversification. However, incomplete taxonomic sampling is also known to artifactually produce patterns of rapid initial diversification. The Monte Carlo constant rates (MCCR) test, based upon Pybus and Harvey's gamma (γ)-statistic, is commonly used to accommodate incomplete sampling, but this test assumes that missing taxa have been randomly pruned from the phylogeny. Here we use simulations to show that preferentially sampling disparate lineages within a clade can produce severely inflated type-I error rates of the MCCR test, especially when taxon sampling drops below 75%. We first propose two corrections for the standard MCCR test, the proportionally deeper splits that assumes missing taxa are more likely to be recently diverged, and the deepest splits only MCCR that assumes that all missing taxa are the youngest lineages in the clade, and assess their statistical properties. We then extend these two tests into a generalized form that allows the degree of nonrandom sampling (NRS)to be controlled by a scaling parameter, α. This generalized test is then applied to two recent studies. This new test allows systematists to account for nonrandom taxonomic sampling when assessing temporal patterns of lineage diversification in empirical trees. Given the dramatic affect NRS can have on the behavior of the MCCR test, we argue that evaluating the sensitivity of this test to NRS should become the norm when investigating patterns of cladogenesis in incompletely sampled phylogenies.     

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.     

Recent diversification rates in North American tiger beetles estimated from a dated mtDNA phylogenetic tree

Species-level phylogenies derived from DNA sequence data provide a tool for estimating diversification rates and how these rates change over time, but to date there have been few empirical studies, particularly on insect groups. We use a densely sampled phylogenetic tree based on mitochondrial DNA to investigate diversification rates in the North American tiger beetles (genus Cicindela). Using node ages estimated from sequence data and calibrated by biogeographical evidence, we estimate an average per-lineage diversification rate of at least 0.22 +/- 0.08 species/Myr over the time interval since the most recent colonization that led to a radiation within the continent. In addition, we find evidence for a weak, recent increase in the net diversification rate. This is more consistent with a late Pleistocene increase in the speciation rate than with a constant rate of background extinction, but the results are sensitive to the dating method and taxon sampling. We discuss practical limitations to phylogenetic studies of diversification rates.     

COMPARISONS OF OBSERVED PHYLOGENETIC TOPOLOGIES WITH NULL EXPECTATIONS AMONG THREE MONOPHYLETIC LINEAGES

Three null models have been proposed to predict the relative frequencies of topologies of phylogenetic trees. One null model assumes each distinguishable n-member tree is equally likely (proportional-to-distinguishable-arrangements model). A second model assumes that each topological type is equally likely (equiprobable model). A third model assumes that the probability of each topological type is determined by random speciation (Markov model). We sampled published phylogenetic trees from three major groups of organisms: division Angiospermae, class Insecta, and superclass Tetrapoda. Our sampling was more restricted than previous studies and was designed to test whether observed topological frequencies were distinguishable from those predicted by the three null models. The pattern of evolution reflected in five-member phylogenetic trees is different from predictions of the equiprobable and Markov model but is indistinguishable from the proportional-to-distinguishable-arrangements model. This indicates that 1) speciation (and/or extinction) is not equally likely among all taxa, even for small phylogenies; or 2) systematists' attempts at reconstructing small phylogenies are, on average, indistinguishable from those expected if they had merely selected a tree at random from the pool of all possible trees. The topology frequencies were not different among the three groups of organisms, suggesting that factors shaping patterns of speciation and extinction are consistent among major taxonomic groups.     

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%.      

Can extinction rates be estimated without fossils?

There is considerable interest in the possibility of using molecular phylogenies to estimate extinction rates. The present study aims at assessing the statistical performance of the birth-death model fitting approach to estimate speciation and extinction rates by comparison to the approach considering fossil data. A simulation-based approach was used. The diversification of a large number of lineages was simulated under a wide range of speciation and extinction rate values. The estimators obtained with fossils performed better than those without fossils. In the absence of fossils (e.g. with a molecular phylogeny), the speciation rate was correctly estimated in a wide range of situations; the bias of the corresponding estimator was close to zero for the largest trees. However, this estimator was substantially biased when the simulated extinction rate was high. On the other hand the estimator of extinction rate was biased in a wide range of situations. Surprisingly, this bias was lesser with medium-sized trees. Some recommendations for interpreting results from a diversification analysis are given.     

Lineages-through-time plots of neutral models for speciation

Drawing inferences about macroevolutionary processes from phylogenetic trees is a fundamental challenge in evolutionary biology. Understanding stochastic models for speciation is an essential step in solving this challenge. We consider a neutral class of stochastic models for speciation, the constant rate birth-death process. For trees with n extant species - which might be derived from bigger trees via random taxon sampling - we calculate the expected time of the kth speciation event (k=1,...,n-1). Further, for a tree with n extant species, we calculate the density and expectation for the number of lineages at any time between the origin of the process and the present. With the developed methods, expected lineages-through-time (LTT) plots can be drawn analytically. The effect of random taxon sampling on LTT plots is discussed.     

Inferring speciation and extinction rates under different sampling schemes

The birth-death process is widely used in phylogenetics to model speciation and extinction. Recent studies have shown that the inferred rates are sensitive to assumptions about the sampling probability of lineages. Here, we examine the effect of the method used to sample lineages. Whereas previous studies have assumed random sampling (RS), we consider two extreme cases of biased sampling: "diversified sampling" (DS), where tips are selected to maximize diversity and "cluster sampling (CS)," where sample diversity is minimized. DS appears to be standard practice, for example, in analyses of higher taxa, whereas CS may occur under special circumstances, for example, in studies of geographically defined floras or faunas. Using both simulations and analyses of empirical data, we show that inferred rates may be heavily biased if the sampling strategy is not modeled correctly. In particular, when a diversified sample is treated as if it were a random or complete sample, the extinction rate is severely underestimated, often close to 0. Such dramatic errors may lead to serious consequences, for example, if estimated rates are used in assessing the vulnerability of threatened species to extinction. Using Bayesian model testing across 18 empirical data sets, we show that DS is commonly a better fit to the data than complete, random, or cluster sampling (CS). Inappropriate modeling of the sampling method may at least partly explain anomalous results that have previously been attributed to variation over time in birth and death rates.     

Dealing with incomplete taxon sampling and diversification of a large clade of mushroom-forming fungi

The absence of an adequate fossil record can hinder understanding the process of diversification that underlies the evolutionary history of a given group. In such cases, investigators have used ultrametric trees derived from molecular data from extant taxa to gain insights into processes of speciation and extinction over time. Inadequate taxon sampling, however, impairs such inferences. In this study, we use simulations to investigate the effect of incomplete taxon sampling on the accumulation of lineages through time for a clade of mushroom-forming fungi, the Hebelomateae. To achieve complete taxon sampling, we use a new Bayesian approach that incorporates substitute lineages to estimate diversification rates. Unlike many studies of animals and plants, we find no evidence of a slowdown in speciation. This indicates the Hebelomateae has not undergone an adaptive radiation. Rather, these fungi have evolved under a relatively constant rate of diversification since their most recent common ancestor, which we date back to the Eocene. The estimated net diversification rate (0.08-0.19 spp./lineage/Ma) is comparable with that of many plants and animals. We suggest that continuous diversification in the Hebelomateae has been facilitated by climatic and vegetation changes throughout the Cenozoic. We also caution against modeling multiple genes as a single partition when performing phylogenetic dating analyses.     

Taxon sampling effects on the quantification and comparison of community phylogenetic diversity

Ecologists are increasingly making use of molecular phylogenies, especially in the fields of community ecology and conservation. However, these phylogenies are often used without full appreciation of their underlying assumptions and uncertainties. A frequent practice in ecological studies is inferring a phylogeny with molecular data from taxa only within the community of interest. These “inferred community phylogenies” are inherently biased in their taxon sampling. Despite the importance of comprehensive sampling in constructing phylogenies, the implications of using inferred community phylogenies in ecological studies have not been examined. Here, we evaluate how taxon sampling affects the quantification and comparison of community phylogenetic diversity using both simulated and empirical data sets. We demonstrate that inferred community trees greatly underestimate phylogenetic diversity and that the probability of incorrectly ranking community diversity can reach up to 25%, depending on the dating methods employed. We argue that to reach reliable conclusions, ecological studies must improve their taxon sampling and generate the best phylogeny possible.     

Quaternary diversification in European alpine plants: pattern and process

Molecular clock approaches applied previously to European alpine plants suggest that Primula sect. Auricula, Gentiana sect. Ciminalis and Soldanella diversified at the beginning of the Quaternary or well within this period, whereas Globularia had already started diversifying in the (Late-)Tertiary. In the first part of this paper we present evidence that, in contrast to Globularia and Soldanella, the branching patterns of the molecular internal transcribed spacer phylogenies of both Primula and Gentiana are incompatible with a constant-rates birth-death model. In both of these last two taxa, speciation probably decreased through Quaternary times, perhaps because of some niche-filling process and/or a decrease in specific range size. In the second part, we apply nonlinear regression analyses to the lineage-through-time plots of P. sect. Auricula to test a range of capacity-dependent models of diversification, and the effect of Quaternary climatic oscillations on diversification and extinction. At least for one major clade of sect. Auricula there is firm evidence that both diversification and extinction are a function of temperature. Intriguingly, temperature appears to be correlated positively with extinction, but negatively with diversification. This suggests that diversification did not take place, as previously assumed, in geographical isolation in high-altitude interglacial refugia, but rather at low altitudes in geographically isolated glacial refugia.