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# Reconciling molecular phylogenies with the fossil record

Edited* by Robert E. Ricklefs, University of Missouri, St. Louis, MO, and approved August 1, 2011 (received for review February 14, 2011)

## Abstract

Historical patterns of species diversity inferred from phylogenies typically contradict the direct evidence found in the fossil record. According to the fossil record, species frequently go extinct, and many clades experience periods of dramatic diversity loss. However, most analyses of molecular phylogenies fail to identify any periods of declining diversity, and they typically infer low levels of extinction. This striking inconsistency between phylogenies and fossils limits our understanding of macroevolution, and it undermines our confidence in phylogenetic inference. Here, we show that realistic extinction rates and diversity trajectories can be inferred from molecular phylogenies. To make this inference, we derive an analytic expression for the likelihood of a phylogeny that accommodates scenarios of declining diversity, time-variable rates, and incomplete sampling; we show that this likelihood expression reliably detects periods of diversity loss using simulation. We then study the cetaceans (whales, dolphins, and porpoises), a group for which standard phylogenetic inferences are strikingly inconsistent with fossil data. When the cetacean phylogeny is considered as a whole, recently radiating clades, such as the Balaneopteridae, Delphinidae, Phocoenidae, and Ziphiidae, mask the signal of extinctions. However, when isolating these groups, we infer diversity dynamics that are consistent with the fossil record. These results reconcile molecular phylogenies with fossil data, and they suggest that most extant cetaceans arose from four recent radiations, with a few additional species arising from clades that have been in decline over the last ∼10 Myr.

Inferring rates of speciation and extinction and the resulting pattern of diversity over geological time scales is one of the most fundamental but challenging questions in biodiversity studies (1–4). Traditionally, biologists have relied on the fossil record to study long-term diversity dynamics (4–7). However, many groups, including terrestrial insects, birds, and plants, lack an adequate fossil record. Methods have therefore been developed to estimate speciation and extinction rates and test hypotheses about the mechanisms governing diversification using phylogenies of extant species reconstructed from molecular data (1, 8–14). These methods have raised the possibility of inferring diversity dynamics for groups that lack a detailed fossil record.

Given the large number of taxonomic groups that lack fossil data, approaches that rely on extant taxa alone are critically important. However, recent studies have highlighted major inconsistencies between the diversity dynamics inferred from phylogenies and those dynamics inferred from the fossil record (4, 11, 15). For example, the fossil record clearly shows that the diversity of cetaceans has declined over the last 10 Myr (4, 16), whereas two recent phylogeny-based maximum likelihood analyses of this group would suggest that cetacean diversity has been expanding (17, 18). More generally, phylogeny-based maximum likelihood estimates of extinction rates are often close to zero, which is not realistic given that extinctions do, in fact, occur and can be frequent in many groups (1, 9, 11, 15, 19).

The current inconsistency between phylogenies and fossils is puzzling, and it casts serious doubt on phylogenetic techniques for inferring the history of species diversity (4). These concerns are especially problematic for groups that lack sufficient fossil data. There are several possible reasons for this inconsistency. On the one hand, because phylogenies of extant taxa lack direct information about extinct lineages, they simply may lack sufficient information to accurately estimate extinction rates or infer diversity dynamics (15, 20, 21). If this is the case, there is little hope for us to ever understand the history of diversification in groups or places lacking fossil data. On the other hand, there is also a possibility that the apparent inconsistency between phylogenies and the fossil record is a methodological artifact, which could be overcome if we develop the appropriate tools.

There is no doubt that the information provided by a reconstructed phylogeny is limited. It is well-recognized that alternative diversification scenarios can produce phylogenies with similar shapes, such that phylogenies may have little discriminatory power (4, 13, 14, 22, 23). It is, thus, understandable that phylogenetic inferences based on a single summary statistic, such as the widely used γ-statistic describing the temporal distribution of nodes in a phylogeny (24–27), fail to properly infer past diversity dynamics (4, 20, 21). It is more worrisome, however, that likelihood-based inferences, which use most of the information contained in phylogenies, also yield unrealistically low extinction rate estimates (9, 11, 19). However, this inconsistency likely arises from limitations in the current methods of phylogenetic inference, which typically assume that speciation rates are constant through time or across lineages and that speciation rates exceed extinction rates (1, 4).

Here, we begin by deriving an exact analytic expression for the likelihood of observing a given phylogeny that simultaneously accommodates undersampling of extant taxa, rate variation over time, and potential periods of declining diversity. Our derivation is based on the birth–death framework introduced in the work by Nee et al. (8) and further developed by Rabosky and Lovette (11) and by Maddison et al. (10, 28). Using Monte Carlo simulations, we quantify the ability of our likelihood-based inferences to detect clades in decline. We then apply this phylogenetic method to the cetaceans, and we compare the diversity dynamics inferred from their phylogeny with the dynamics inferred from the fossil record.

## Results

We developed a method to infer diversity dynamics from phylogenies using a birth–death model of cladogenesis (1, 8, 9, 11). We assume that a clade has evolved according to a birth–death process, with per-lineage speciation and extinction rates, *λ*(*t*) and *μ*(*t*), respectively, that can vary over time. We consider the phylogeny of *n* species sampled at present from this clade. We allow for the possibility that some extant species are not included in the sample by assuming that each extant species was sampled with probability *f* ≤ 1. We measure time from the present to the past. Thus, *t* = 0 denotes the present, and *t* increases into the past. *t*_{1} denotes the first time at which the ancestral species came into existence, and {*t*_{2}, *t*_{3}, … , *t _{n}*} denote the times of branching events in the phylogeny, with

*t*

_{1}>

*t*

_{2}> … >

*t*. In particular,

_{n}*t*

_{2}is the time of the most recent common ancestor of the sampled species (Fig. 1 has a schematic illustration of notations).

The probability density of observing such a phylogeny, conditioned on the presence of at least one descendant in the sample, is proportional to (*Materials and Methods* has details)

where Ψ(*s*, *t*) denotes the probability that a lineage alive at time *t* leaves exactly one descendant lineage at time *s* < *t* in the reconstructed phylogeny, and Φ(*t*) denotes the probability that a lineage alive at time *t* has no descendant in the sample. *s _{i}*

_{,1}and

*s*

_{i}_{,2}denote the times at which the daughter lineages introduced at time

*t*themselves branch (or zero if the daughter lineage survives to the present without branching) (Fig. 1).

_{i}Adapting the approaches by Maddison et al. (10) and FitzJohn et al. (28), we derived the following exact likelihood expressions:

and

Substituting Eqs. **2** and **3** into Eq. **1** gives the likelihood of the phylogeny in terms of the sampling fraction *f* and the speciation and extinction rates *λ*(*t*) and *μ*(*t*), respectively. The net diversification rate at any given time, *λ*(*t*) − *μ*(*t*), can be positive, corresponding to a period of expanding diversity, or negative, corresponding to a period of declining diversity. The likelihood expression given by Eq. **1** is directly comparable with those expressions derived in the seminal work by Nee et al. (8) and in more recent works by Rabosky and Lovette (11), Maddison et al. (10), and FitzJohn et al. (28). When phylogenies are fully sampled and diversification rates are assumed constant over time and independent of a specific character, these likelihood expressions differ from one another only by the conditioning on the birth–death process (*Materials and Methods* and *SI Results*). Eq. **1** is, however, an exact analytical expression that simultaneously accounts for rate variation through time and undersampling, although FitzJohn (29) and Rabosky and Glor (30) proposed numerical procedures associated with this scenario, and Stadler (31) derived the likelihood analytically in the case of discrete rate shifts.

If we no longer assume that diversification rates are constant across lineages but, instead, assume that they change at a fixed set of branching points, Eq. **1** can readily be modified to take into account this rate heterogeneity. Under the assumption that rates vary only at a fixed set of observed branching points, our expression for Φ(*t*) and Ψ(*s*, *t*) holds (*SI Results*). If a clade first appears at the branching point (Fig. 1 clarifies the notation), the likelihood function of the subtree corresponding to this clade is given by Eq. **1** with the clade-specific rates of speciation and extinction. The likelihood function of the remaining pruned parent tree (i.e., the whole tree minus the clade) is also given by Eq. **1** if we replace all terms corresponding to the subclade, such as

with the probability that the subclade did not go extinct (*SI Results*). The likelihood of the whole tree is then the product of the likelihood of the subtree and the pruned tree. More generally, the likelihood of a phylogeny in which various subclades have different diversification rates is obtained by multiplying together the likelihoods of each subclade and the likelihood of the remaining pruned parent tree. Hence, given a phylogeny, Eq. **1** can be used to estimate rates in multiple subclades as well as compare the performance of various parametric models for how these rates vary over time and across clades.

Applying the likelihood expression in Eq. **1** to phylogenies simulated with time-variable speciation and extinction rates, we found that diversity dynamics can be accurately inferred across a wide range of parameter values, including scenarios that feature periods of declining diversity (*Materials and Methods*, *SI Results*, and Figs. S1–S3). For example, one such simulated parameter set featured a constant extinction rate (*μ*_{0} = 0.5 events per arbitrary time unit) and a speciation rate that decayed exponentially over time (from *λ* = 3 at 10 time units in the past to *λ*_{0} = 0.25 at present), and therefore, the net diversification rate switched from positive to negative over the clade's history. Even in this scenario of diversity expansion followed by diversity collapse, which is similar to the scenario of waxing and waning observed in the fossil record, our method produced unbiased parameter estimates (Figs. S1, rightmost data point, and S2), and we correctly inferred a negative diversification rate at present for 70% of such simulated phylogenies. This percentage increases to 81% and 92% when we consider only the subset of phylogenies with at least 10 or 20 species at present, respectively. We found similar results when the speciation rate was held constant and the extinction rate increased over time (Fig. S3).

Although our method produces unbiased parameter estimates, the confidence intervals around these estimates can be broad, especially when a phylogeny is small (*Materials and Methods* and Figs. S4 and S5). Figs. S4 and S5 show how tree size influences the confidence interval for estimates of the net diversification rate at present for an example set of parameters. These figures reflect the fact that even the most powerful asymptotically unbiased procedure (i.e., maximum likelihood) may require relatively large tree sizes to reject one model of diversification in favor of another model. Nonetheless, we will show below that our method allows us to confidently reject positive net diversification rates for some important empirical phylogenies, notably the cetaceans.

Confident that our likelihood expression (Eq. **1**) produces unbiased estimates and can accurately detect periods of declining diversity under our model assumptions, we used this expression to estimate diversification rates from a recently published phylogeny of the cetaceans (17) (*Materials and Methods*). This dated molecular phylogeny includes 87 of 89 extant cetacean species, missing only two species in the Delphinidae family. According to the fossil record, the global diversity of the cetaceans increased steadily during the late Oligocene to mid Miocene and subsequently declined monotonically over the past ∼10 Myr (Fig. 2*D*) (4).

When we analyzed the cetacean phylogeny as a whole, a pure birth model was selected over all other models, including models that allowed speciation and extinction rates to vary exponentially or linearly through time (*Materials and Methods* and Table S1). In particular, the most likely, pure-birth model suggests that cetacean diversity has increased over the last 30 Myr—in direct contradiction to the fossil record. Similar results were found in previous phylogenetic studies of this group (17, 18). The striking discrepancy with the fossil record is not caused by a large number of extinct taxa in the stem group, because most Oligocene and all Miocene and younger taxa belong to the crown group (4). Thus, even when we allow speciation and extinction rates to vary over time, allow the extinction rate to exceed the speciation rate, and account for undersampling of extant taxa, the levels of extinction estimated from the phylogeny are unrealistically low (Fig. S6*A*), and we fail to identify known periods of diversity loss.

By analyzing the cetaceans as a whole, we have implicitly assumed that the pattern of diversification, *λ*(*t*) and *μ*(*t*), is homogeneous across clades. This assumption is likely violated, as suggested by the different temporal distributions of nodes in species-rich families compared with the rest of the tree (Fig. 2*A*). Whereas the four most speciose families (the Delphinidae, Balaenopteridae, Phocoenidae, and Ziphiidae) exhibit many recent nodes, the rest of the tree, comprising 10 other families, exhibits relatively few recent speciation events. This pattern suggests that the four species-rich families may have diversified faster than the smaller families, at least recently. To test this hypothesis, we compared the likelihoods of models that allow for different patterns of rate variation in different clades. In particular, we allowed for rate shifts at some or all of the nodes corresponding to the four largest families (*SI Results*); we found that the model allowing distinct patterns of rate variation in each of these families was strongly supported over alternative models (Table S2). When we isolated the four largest families using the rate heterogeneous approach outlined above, we found that the phylogeny of the remaining 16 cetacean species is consistent with a decline in diversity over the past ∼10 Myr (Figs. 2*B* and S6*F*). In particular, the most likely model for these 16 species featured a constant speciation rate through time and an exponentially increasing extinction rate, such that the net diversification rate switched from positive to negative over time (Fig. S6*F*); this model was strongly supported over all alternative patterns of diversification (Table 1 and Table S3). Using the most likely parameter values, we inferred that the diversity of the cetaceans, excluding the four largest families at present, peaked at more than 200 species about 10 Mya, and it subsequently crashed to its present value of 16 extant species (Fig. 2*B*).

The boom-then-bust pattern of diversity that we inferred for the cetaceans, excluding the four largest extant families, is especially notable given the well-known difficulty of inferring nonzero extinction rates from molecular phylogenies. Not only did we infer a positive extinction rate for these groups, we inferred an extinction rate significantly higher than the speciation rate over the past ∼10 Myr [inferred net diversification rate at present: *λ*(0) − *μ*(0) = −0.69]. We performed a series of tests to determine the robustness of these inferences. First, the 95% χ^{2} confidence interval around the estimated net diversification rate at present is (−1.54; −0.28), which allows us to confidently reject the hypothesis that diversity is increasing at present (*P* < 0.05). Second, assuming linear rather than exponential variation in diversification rates through time produced a similar boom-then-bust pattern of diversity (Fig. S7). Third, the diversity trajectory that we inferred was not qualitatively affected if we considered models with two or three rate shifts instead of the model with four shifts (Fig. S8). Finally, if we chose to analyze the mysticetes (excluding the Balaneopteridae) and odontocetes (excluding the Delphinidae, Phocoenidae, and Ziphiidae) separately rather than as a whole (i.e., if we allow for different rates in each of these two clades), then the inferred diversity trajectories are hump-shaped for both groups (Fig. 2*C*), and the present net diversification rates are both significantly negative [−0.26 (−0.49; −0.06) and −0.88 (−1.59; −0.18), respectively]. Under the most likely parameter values, the mysticete group peaked at about 80 species ∼9 Mya, and it then crashed to its present value of 6 extant species. Similarly, the odontocetes peaked at more than 120 species around 9 Mya, and this group retains only 10 species today. Summing these two diversity trajectories, we obtain a diversity curve qualitatively similar to the one obtained when treating the mysticetes and odontocetes as a single clade (Fig. S9). These results all suggest that the boom-then-bust pattern of diversity that we have inferred is not an artifact of the various choices that we made in our analysis.

The history of species diversity in the cetaceans as a whole has been extensively studied using the fossil record (4, 16). To compare our phylogenetic inferences with the fossil record, we summed the diversity trajectories of each individual group (the four largest extant families plus the remaining species). For each of the Balaneopteridae, Delphinidae, Phocoenidae, and Ziphiidae families, we used their best fit models (specified in Fig. 2), which all feature expanding diversity at present (Figs. 2 *B* and *C* and Fig. S6). However, the diversity expansion of these four families does not compensate for the diversity loss in the remaining cetaceans. As a result, the trajectory that we inferred for the cetaceans as a whole features a maximum diversity of almost 250 species about 9 Mya, with only 89 species surviving today (Fig. 2*D*). This trajectory is consistent with the history of diversity inferred from the fossil record (4), which shows a long period of steady species accumulation followed by a sharp decline in diversity starting ∼10 Mya (Fig. 2*D*).

Aside from analyzing historical patterns of net diversity, our phylogenetic inference technique allows us to study how speciation and extinction rates themselves have varied over time (11). Different groups feature different patterns of temporal variation in speciation and extinction rates (Fig. S6 *B–F*). The phylogenies of the Delphinidae, Phocoenidae, and Ziphiidae exhibit relatively constant speciation and suggest that diversity is expanding at present (Fig. S6 *C–F*). The phylogeny of the Balaenopteridae, by contrast, indicates a decay in the net diversification rate caused by a decay in the speciation rate (Fig. S6*B*), so that the Balaenopteridae are currently reaching a point of equilibrium diversity (zero net diversification rate) (14, 30). For the remaining cetaceans, the extinction rate has increased over time, whereas the speciation rate has remained relatively constant, resulting in a negative net diversification rate at present (Fig. S6*F*); the same pattern holds for the odontocetes analyzed separately (Fig. S10). Finally, the mysticete phylogeny indicates a constant extinction rate with a decaying speciation rate (Fig. S10). Thus, a variety of different scenarios operating in different taxonomic groups combine to produce the net diversity trajectories that we observed.

## Discussion

Phylogenies of extant taxa are increasingly used to infer macroevolutionary patterns. However, few studies have directly compared diversity patterns inferred from phylogenies with those patterns estimated from the fossil record. The few studies attempting this comparison have uncovered major inconsistencies, suggesting that phylogenetic inferences are not reliable on their own (4). In this paper, we have shown that diversity dynamics inferred from phylogenies can be consistent with the fossil record if rate variation through time and among major taxonomic groups is taken into account.

The correspondence that we found between the diversity dynamics inferred from molecular phylogenies and the fossil record is remarkable given that we analyzed the cetaceans, a group that has been used specifically to illustrate major inconsistencies between phylogenies and fossil data (4). Our analysis indicates an important role for species turnover in shaping biodiversity, which is generally found in the fossil record (6) but has rarely been evidenced in molecular phylogenies (12, 32, 33). In addition, our analysis suggests that the net diversification rate has decreased over time in several taxonomic groups, which is often interpreted as a feature of evolutionary radiations (11, 25, 27). Our modeling approach has allowed us to unravel complex historical patterns, such as boom-then-bust patterns of species diversity. These patterns of diversity would have been difficult to discern simply by inspecting the phylogenies without the use of a quantitative cladogenesis model and a corresponding inference procedure.

When the cetacean phylogeny was considered as a whole, with the implicit assumption that diversification rates are homogeneous across lineages, we did not detect any extinction. However, after isolating recently radiating clades from the phylogeny, we recovered realistic extinction rates and diversity trajectories. This finding suggests an important general principle—recently radiating clades mask the signal of extinctions in other clades, but extinctions can be detected from a phylogeny after accounting for rate heterogeneity. These results support the view in Rabosky (15) that different tempos of diversification across lineages are responsible for the current inconsistency between phylogenies and the fossil record, and they suggest that this issue can be overcome (12). When accounting for rate heterogeneity, it is inherently difficult to identify which clades should be analyzed separately. Here, realistic diversity trajectories were obtained by separating the largest extant families. In other situations, more systematic ways to detect rate shifts may be needed (12).

Whereas the historical trajectory of species diversity that we have inferred from the cetacean phylogeny matches the fossil record, our analyses also make more specific inferences than this pattern alone. In particular, we have inferred that the vast majority of cetacean species present about 10 Mya were not within the Balaenopteridae, Delphinidae, Phocoenidae, or Ziphiidae families. In the future, this phylogenetic inference could be tested by detailed examination of the fossil record, with historical specimens identified to the family level.

If we are to extract meaningful information from phylogenies, it is crucial that we understand the strengths and limitations of various analytical approaches. There has been a recent focus on using the γ-statistic to detect declines in speciation rates (20, 21, 24–27). Although the γ-statistic has the advantage of simplicity, it was originally designed only to test deviations from the pure birth Yule process (24). As a result, it is typically not powerful enough to analyze complex diversity trajectories (4, 20, 21). The distribution of phylogenetic branch lengths (13), by contrast, allows us to test whether diversification rates depend on species’ age, which is not accommodated by other methods. However, this approach is not powerful for testing more traditional hypotheses, such as whether diversification rates vary over absolute time (14). A recent method based on coalescent theory allows us to compare a variety of scenarios with constant vs. expanding diversity (14). However, this approach does not yet accommodate scenarios of declining diversity, and it relies on an approximate likelihood expression. The approach described here, which is closely related to the approaches used in refs. 8, 10, 11, and 28, rectifies several of these issues simultaneously.

Inferring long-term diversity dynamics without fossils is challenging. Obviously, any incorporation of fossil data to phylogenetic inference will improve our ability to understand diversity dynamics (20, 21, 34–36), and our likelihood expressions can be modified to incorporate some types of fossil information (*SI Results*). However, we have shown here that molecular phylogenies alone can recover diversity dynamics that are consistent with the fossil record. Thus, there is hope for us to reconstruct the history of species diversity in groups or regions that lack a reliable fossil record.

## Materials and Methods

### Likelihood of Observing a Given Phylogeny.

To obtain our likelihood expression (Eq. **1**), we conditioned the cladogenesis process on having at least one lineage surviving to the present and being sampled. The denominator in the likelihood function accounts for this conditioning. Conditioning the process on survival is critical to obtain unbiased parameter estimates, particularly when the probability of survival is low (i.e., when extinction rates exceed speciation rates) (35). Our conditioning is different from the conditioning used by Nee et al. (8) and implemented in both the laser (37) and diversitree (28, 29) packages. Nee et al. (8) conditioned the process on the existence of a root node (i.e., a speciation event occurring at the time of the most recent common ancestor and the two descendant lineages surviving to the present). Modifying Eq. **1** to obtain the likelihood conditioned on the existence of a root node as in Nee et al. (8) is straightforward. Our conditioning allows for taking into account information on the root length (i.e., *t*_{1} − *t*_{2}) when available, which is the case for subclades within the cetaceans. This form of conditioning also allows us to relax the assumption (8) that all lineages trace back to a single common ancestor at a given time *T* in the past. In future studies, this flexibility may allow for the combination of phylogenetic and fossil data to gain a more precise understanding of diversity dynamics (*SI Results*).

In Eq. **1**, the factor *f ^{n}* accounts for the fact that each extant species was sampled with probability

*f*. The factor Ψ(

*t*

_{2},

*t*

_{1}) corresponds to the probability of observing the given root. The

*n*− 1 other factors correspond to the probabilities of observing a speciation event and the two descendant branch lengths at each of the

*n*− 1 nodes. To obtain maximum likelihood estimates for a given model, we used the Nelder–Mead simplex algorithm implemented in R (38). R codes computing the likelihood and estimating the maximum likelihood parameters are provided in Dataset S1.

To determine an analytic expression for Ψ(*s*, *t*), we first find

which following ref. 10, can be obtained through an ordinary differential equation. Notice that

Subtracting Φ(*t*), dividing by Δ*t*, and taking Δ*t* → 0 yields

whereas

Set *F*(*t*) = 1 − Φ(*t*). Then, *F*(*t*) satisfies the Bernoulli equation

Letting *G*(*t*) = 1/*F*(*t*), we have

which is readily solved as

where *G*(0) = 1/*f*. Solving for Φ(*t*) produces Eq. **2**. To determine Ψ(*s*, *t*) itself, following ref. 10, we note that

Subtracting Ψ(*s*, *t*), dividing by Δ*t*, and taking Δ*t* → 0 yields

whereas Ψ(*s*, *s*) = 1, because the lineage can neither disappear nor give birth at a single instant. Solving this ordinary differential equation yields

Substituting Eq. **2** into Eq. **14**, we get Eq. **3** (*SI Results*).

### Models of Diversification.

We considered models with time-constant diversification rates and models with time-variable diversification rates. When rates varied through time, we assumed one of two variations: either exponential variation, such that *λ*(*t*) = *λ*_{0}*e ^{αt}* and

*μ*(

*t*) =

*μ*

_{0}

*e*, where

^{βt}*λ*

_{0}and

*μ*

_{0}are the speciation and extinction rates at present, respectively, and

*α*and

*β*are the rates of change, or linear variation, such that

*λ*(

*t*) = max(0,

*λ*

_{0}+

*αt*) and

*μ*(

*t*) = max(0,

*μ*

_{0}+

*βt*).

### Computing Confidence Intervals.

Given a phylogeny (simulated or empirical), we computed the 95% confidence interval around the maximum likelihood estimate of the net diversification rate according to the χ^{2} distribution. To perform this computation, we changed variables to parameterize the likelihood function in terms of the net diversification rate and speciation rate. We then computed the confidence interval corresponding to a likelihood ratio test, with 1 degree of freedom and *P* = 0.05, by finding the minimum and maximal values of the net diversification rate within 3.84/2 log-likelihood units of the maximal log-likelihood value (39).

### Cetacean Phylogeny.

We analyzed the dated cetacean phylogeny constructed by Steeman et al. (17), which consists of 87 of 89 extant cetacean species. This phylogeny was derived from six mitochondrial and nine nuclear genes using the Bayesian phylogenetic inference implemented in MrBayes (40). It was calibrated using seven paleontological age constraints and the relaxed molecular clock approach implemented in r8S (41).

## Acknowledgments

We thank L. Harmon, C. Marshall, T. Quental, D. Rabosky, and M. Sanderson for discussions and/or comments on our manuscript, and we thank A. Chen-Plotkin for the scientific illustrations in Fig. 2. We also thank the editor and two anonymous reviewers for very constructive comments. H.M. acknowledges support from the Centre National de la Recherche Scientifique, and J.B.P. acknowledges funding from the Burroughs Wellcome Fund, the David and Lucile Packard Foundation, the Alfred P. Sloan Foundation, and the James S. McDonnell Foundation.

## Footnotes

- ↵
^{1}To whom correspondence should be addressed. E-mail: helene.morlon{at}polytechnique.edu.

Author contributions: H.M. and J.B.P. designed research; H.M., T.L.P., and J.B.P. performed research; H.M. and T.L.P. contributed new reagents/analytic tools; H.M. analyzed data; and H.M., T.L.P., and J.B.P. wrote the paper.

The authors declare no conflict of interest.

See Commentary on page 16145.

↵*This Direct Submission article had a prearranged editor.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1102543108/-/DCSupplemental.

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