Likelihood Inference of Non-Constant Diversification Rates with Incomplete Taxon Sampling

Large-scale phylogenies provide a valuable source to study background diversification rates and investigate if the rates have changed over time. Unfortunately most large-scale, dated phylogenies are sparsely sampled (fewer than 5% of the described species) and taxon sampling is not uniform. Instead, taxa are frequently sampled to obtain at least one representative per subgroup (e.g. family) and thus to maximize diversity (diversified sampling). So far, such complications have been ignored, potentially biasing the conclusions that have been reached. In this study I derive the likelihood of a birth-death process with non-constant (time-dependent) diversification rates and diversified taxon sampling. Using simulations I test if the true parameters and the sampling method can be recovered when the trees are small or medium sized (fewer than 200 taxa). The results show that the diversification rates can be inferred and the estimates are unbiased for large trees but are biased for small trees (fewer than 50 taxa). Furthermore, model selection by means of Akaike''s Information Criterion favors the true model if the true rates differ sufficiently from alternative models (e.g. the birth-death model is recovered if the extinction rate is large and compared to a pure-birth model). Finally, I applied six different diversification rate models – ranging from a constant-rate pure birth process to a decreasing speciation rate birth-death process but excluding any rate shift models – on three large-scale empirical phylogenies (ants, mammals and snakes with respectively 149, 164 and 41 sampled species). All three phylogenies were constructed by diversified taxon sampling, as stated by the authors. However only the snake phylogeny supported diversified taxon sampling. Moreover, a parametric bootstrap test revealed that none of the tested models provided a good fit to the observed data. The model assumptions, such as homogeneous rates across species or no rate shifts, appear to be violated.     

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.     

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.     

Bats, clocks, and rocks: diversification patterns in Chiroptera

Identifying nonrandom clade diversification is a critical first step toward understanding the evolutionary processes underlying any radiation and how best to preserve future phylogenetic diversity. However, differences in diversification rates have not been quantitatively assessed for the majority of groups because of the lack of necessary analytical tools (e.g., complete species-level phylogenies, estimates of divergence times, and robust statistics which incorporate phylogenetic uncertainty and test appropriate null models of clade growth). Here, for the first time, we investigate diversification rate heterogeneity in one of the largest groups studied thus far, the bats (Mammalia: Chiroptera). We use a recent, robust statistical approach (whole-tree likelihood-based relative rate tests) on complete dated species-level supertree phylogenies. As has been demonstrated previously for most other groups, among-lineage diversification rate within bats has not been constant. However, we show that bat diversification is more heterogeneous than in other mammalian clades thus far studied. The whole-tree likelihood-based relative rates tests suggest that clades within the families Phyllostomidae and Molossidae underwent a number of significant changes in relative diversification rate. There is also some evidence for rate shifts within Pteropodidae, Emballonuridae, Rhinolophidae, Hipposideridae, and Vespertilionidae, but the significance of these shifts depends on polytomy resolution within each family. Diversification rate in bats has also not been constant, with the largest diversification rate shifts occurring 30-50 million years ago, a time overlapping with the greatest number of shifts in flowering plant diversification rates.     

Investigating the timing of origin and evolutionary processes shaping regional species diversity: Insights from simulated data and neotropical butterfly diversification rates

Different diversification scenarios have been proposed to explain the origin of extant biodiversity. However, most existing meta‐analyses of time‐calibrated phylogenies rely on approaches that do not quantitatively test alternative diversification processes. Here, I highlight the shortcomings of using species divergence ranks, which is a method widely used in meta‐analyses. Divergence ranks consist of categorizing cladogenetic events to certain periods of time, typically to either Pleistocene or to pre‐Pleistocene ages. This approach has been claimed to shed light on the origin of most extant species and the timing and dynamics of diversification in any biogeographical region. However, interpretations drawn from such method often confound two fundamental questions in macroevolutionary studies, tempo (timing of evolutionary rate shifts) and mode (“how” and “why” of speciation). By using simulated phylogenies under four diversification scenarios, constant‐rate, diversity‐dependence, high extinction, and high speciation rates in the Pleistocene, I showed that interpretations based on species divergence ranks might have been seriously misleading. Future meta‐analyses of dated phylogenies need to be aware of the impacts of incomplete taxonomic sampling, tree topology, and divergence time uncertainties, as well as they might be benefited by including quantitative tests of alternative diversification models that acknowledge extinction and diversity dependence.     

Sampling-through-time in birth-death trees

I consider the constant rate birth-death process with incomplete sampling. I calculate the density of a given tree with sampled extant and extinct individuals.This density is essential for analyzing datasets which are sampled through time. Such datasets are common in virus epidemiology as viruses in infected individuals are sampled through time. Further, such datasets appear in phylogenetics when extant and extinct species data is available.I show how the derived tree density can be used (i) as a tree prior in a Bayesian method to reconstruct the evolutionary past of the sequence data on a calender-timescale, (ii) to infer the birth- and death-rates for a reconstructed evolutionary tree, and (iii) for simulating trees with a given number of sampled extant and extinct individuals which is essential for testing evolutionary hypotheses for the considered datasets.     

Diversity Dynamics in Nymphalidae Butterflies: Effect of Phylogenetic Uncertainty on Diversification Rate Shift Estimates

The species rich butterfly family Nymphalidae has been used to study evolutionary interactions between plants and insects. Theories of insect-hostplant dynamics predict accelerated diversification due to key innovations. In evolutionary biology, analysis of maximum credibility trees in the software MEDUSA (modelling evolutionary diversity using stepwise AIC) is a popular method for estimation of shifts in diversification rates. We investigated whether phylogenetic uncertainty can produce different results by extending the method across a random sample of trees from the posterior distribution of a Bayesian run. Using the MultiMEDUSA approach, we found that phylogenetic uncertainty greatly affects diversification rate estimates. Different trees produced diversification rates ranging from high values to almost zero for the same clade, and both significant rate increase and decrease in some clades. Only four out of 18 significant shifts found on the maximum clade credibility tree were consistent across most of the sampled trees. Among these, we found accelerated diversification for Ithomiini butterflies. We used the binary speciation and extinction model (BiSSE) and found that a hostplant shift to Solanaceae is correlated with increased net diversification rates in Ithomiini, congruent with the diffuse cospeciation hypothesis. Our results show that taking phylogenetic uncertainty into account when estimating net diversification rate shifts is of great importance, as very different results can be obtained when using the maximum clade credibility tree and other trees from the posterior distribution.     

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.     

Phylogenetic evidence of a rapid radiation of pleurocarpous mosses (Bryophyta)

Abstract Pleurocarpous mosses, characterized by lateral female gametangia and highly branched, interwoven stems, comprise three orders and some 5000 species, or almost half of all moss diversity. Recent phylogenetic analyses resolve the Ptychomniales as sister to the Hypnales plus Hookeriales. Species richness is highly asymmetric with approximately 100 Ptychomniales, 750 Hookeriales, and 4400 Hypnales. Chloroplast DNA (cpDNA) sequences were obtained to compare partitioning of molecular diversity among the orders with estimates of species richness, and to test the hypothesis that either the Hookeriales or Hypnales underwent a period (or periods) of exceptionally rapid diversification. Levels of biodiversity were quantified using explicitly historical "phylogenetic diversity" and non-historical estimates of standing sequence diversity. Diversification rates were visualized using lineage-through-time (LTT) plots, and statistical tests of alternative diversification models were performed using the methods of Paradis (1997). The effects of incomplete sampling on the shape of LTT plots and performance of statistical tests were investigated using simulated phylogenies with incomplete sampling. Despite a much larger number of accepted species, the Hypnales contain lower levels of (cpDNA) biodiversity than their sister group, the Hookeriales, based on all molecular measures. Simulations confirm previous results that incomplete sampling yields diversification patterns that appear to reflect a decreasing rate through time, even when the true phylogenies were simulated with constant rates. Comparisons between simulated results and empirical data indicate that a constant rate of diversification cannot be rejected for the Hookeriales. The Hypnales, however, appear to have undergone a period of exceptionally rapid diversification for the earliest 20% of their history.     

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.     

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.     

Understanding angiosperm diversification using small and large phylogenetic trees

How will the emerging possibility of inferring ultra-large phylogenies influence our ability to identify shifts in diversification rate? For several large angiosperm clades (Angiospermae, Monocotyledonae, Orchidaceae, Poaceae, Eudicotyledonae, Fabaceae, and Asteraceae), we explore this issue by contrasting two approaches: (1) using small backbone trees with an inferred number of extant species assigned to each terminal clade and (2) using a mega-phylogeny of 55473 seed plant species represented in GenBank. The mega-phylogeny approach assumes that the sample of species in GenBank is at least roughly proportional to the actual species diversity of different lineages, as appears to be the case for many major angiosperm lineages. Using both approaches, we found that diversification rate shifts are not directly associated with the major named clades examined here, with the sole exception of Fabaceae in the GenBank mega-phylogeny. These agreements are encouraging and may support a generality about angiosperm evolution: major shifts in diversification may not be directly associated with major named clades, but rather with clades that are nested not far within these groups. An alternative explanation is that there have been increased extinction rates in early-diverging lineages within these clades. Based on our mega-phylogeny, the shifts in diversification appear to be distributed quite evenly throughout the angiosperms. Mega-phylogenetic studies of diversification hold great promise for revealing new patterns, but we will need to focus more attention on properly specifying null expectation.     

Trees of unusual size: biased inference of early bursts from large molecular phylogenies

An early burst of speciation followed by a subsequent slowdown in the rate of diversification is commonly inferred from molecular phylogenies. This pattern is consistent with some verbal theory of ecological opportunity and adaptive radiations. One often-overlooked source of bias in these studies is that of sampling at the level of whole clades, as researchers tend to choose large, speciose clades to study. In this paper, we investigate the performance of common methods across the distribution of clade sizes that can be generated by a constant-rate birth-death process. Clades which are larger than expected for a given constant-rate branching process tend to show a pattern of an early burst even when both speciation and extinction rates are constant through time. All methods evaluated were susceptible to detecting this false signature when extinction was low. Under moderate extinction, both the [Formula: see text]-statistic and diversity-dependent models did not detect such a slowdown but only because the signature of a slowdown was masked by subsequent extinction. Some models which estimate time-varying speciation rates are able to detect early bursts under higher extinction rates, but are extremely prone to sampling bias. We suggest that examining clades in isolation may result in spurious inferences that rates of diversification have changed through time.     

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.     

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.     

A conceptual and statistical framework for adaptive radiations with a key role for diversity dependence

Abstract In this article we propose a new framework for studying adaptive radiations in the context of diversity-dependent diversification. Diversity dependence causes diversification to decelerate at the end of an adaptive radiation but also plays a key role in the initial pulse of diversification. In particular, key innovations (which in our definition include novel traits as well as new environments) may cause decoupling of the diversity-dependent dynamics of the innovative clade from the diversity-dependent dynamics of its ancestral clade. We present a likelihood-based inference method to test for decoupling of diversity dependence using molecular phylogenies. The method, which can handle incomplete phylogenies, identifies when the decoupling took place and which diversification parameters are affected. We illustrate our approach by applying it to the molecular phylogeny of the North American clade of the legume tribe Psoraleeae (47 extant species, of which 4 are missing). Two diversification rate shifts were previously identified for this clade; our analysis shows that the first, positive shift can be associated with decoupling of two Pediomelum subgenera from the other Psoraleeae lineages, while we argue that the second, negative shift can be attributed to speciation being protracted. The latter explanation yields nonzero extinction rates, in contrast to previous findings. Our framework offers a new perspective on macroevolution: new environments and novel traits (ecological opportunity) and diversity dependence (ecological limits) cannot be considered separately.     

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.     

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.     

Ecological and Ecomorphological Specialization Are Not Associated with Diversification Rates in Muroid Rodents (Rodentia: Muroidea)

Multiple diversification rate shifts explain uneven clade richness in muroid rodents. Previous muroid studies have shown that extrinsic factors, notwithstanding ecological opportunity, are poor predictors of clade diversity. Here, we use a 297-muroid species chronogram that is sampled proportional to total clade diversity, along with various trait-dependent diversification approaches to investigate the association between diversification rates with intrinsic attributes—diet, habitat, body mass, and relative tail length. We found some association between both dietary specialization and body mass, as well as between habitat specialization with relative tail lengths using phylogenetic analyses of variance. However, there was no significant association between diversification rates with the evolution of these traits in muroid rodents. We also show that several of the state-dependent diversification approaches are highly susceptible to Type I error—a result that is in accordance with recent criticisms of these methods. Finally, we discuss several potential causes for the lack of association between the examined trait data with diversification rates, ranging from methodological biases (e.g. method conservativism) to biology (e.g. behavioral plasticity and ecological opportunism of muroid rodents).