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.     

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.     

Inferring the Dynamics of Diversification: A Coalescent Approach

Recent analyses of the fossil record and molecular phylogenies suggest that there are fundamental limits to biodiversity, possibly arising from constraints in the availability of space, resources, or ecological niches. Under this hypothesis, speciation rates decay over time and biodiversity eventually saturates, with new species emerging only when others are driven to extinction. This view of macro-evolution contradicts an alternative hypothesis that biodiversity is unbounded, with species ever accumulating as they find new niches to occupy. These contrasting theories of biodiversity dynamics yield fundamentally different explanations for the disparity in species richness across taxa and regions. Here, we test whether speciation rates have decayed or remained constant over time, and whether biodiversity is saturated or still expanding. We first derive a general likelihood expression for internode distances in a phylogeny, based on the well-known coalescent process from population genetics. This expression accounts for either time-constant or time-variable rates, time-constant or time-variable diversity, and completely or incompletely sampled phylogenies. We then compare the performance of different diversification scenarios in explaining a set of 289 phylogenies representing amphibians, arthropods, birds, mammals, mollusks, and flowering plants. Our results indicate that speciation rates typically decay over time, but that diversity is still expanding at present. The evidence for expanding-diversity models suggests that an upper limit to biodiversity has not yet been reached, or that no such limit exists.     

Fossil‐based comparative analyses reveal ancient marine ancestry erased by extinction in ray‐finned fishes

The marine‐freshwater boundary is a major biodiversity gradient and few groups have colonised both systems successfully. Fishes have transitioned between habitats repeatedly, diversifying in rivers, lakes and oceans over evolutionary time. However, their history of habitat colonisation and diversification is unclear based on available fossil and phylogenetic data. We estimate ancestral habitats and diversification and transition rates using a large‐scale phylogeny of extant fish taxa and one containing a massive number of extinct species. Extant‐only phylogenetic analyses indicate freshwater ancestry, but inclusion of fossils reveal strong evidence of marine ancestry in lineages now restricted to freshwaters. Diversification and colonisation dynamics vary asymmetrically between habitats, as marine lineages colonise and flourish in rivers more frequently than the reverse. Our study highlights the importance of including fossils in comparative analyses, showing that freshwaters have played a role as refuges for ancient fish lineages, a signal erased by extinction in extant‐only phylogenies.     

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.     

Fossil calibrations and molecular divergence time estimates in centrarchid fishes (Teleostei: Centrarchidae)

Molecular clock methods allow biologists to estimate divergence times, which in turn play an important role in comparative studies of many evolutionary processes. It is well known that molecular age estimates can be biased by heterogeneity in rates of molecular evolution, but less attention has been paid to the issue of potentially erroneous fossil calibrations. In this study we estimate the timing of diversification in Centrarchidae, an endemic major lineage of the diverse North American freshwater fish fauna, through a new approach to fossil calibration and molecular evolutionary model selection. Given a completely resolved multi-gene molecular phylogeny and a set of multiple fossil-inferred age estimates, we tested for potentially erroneous fossil calibrations using a recently developed fossil cross-validation. We also used fossil information to guide the selection of the optimal molecular evolutionary model with a new fossil jackknife method in a fossil-based model cross-validation. The centrarchid phylogeny resulted from a mixed-model Bayesian strategy that included 14 separate data partitions sampled from three mtDNA and four nuclear genes. Ten of the 31 interspecific nodes in the centrarchid phylogeny were assigned a minimal age estimate from the centrarchid fossil record. Our analyses identified four fossil dates that were inconsistent with the other fossils, and we removed them from the molecular dating analysis. Using fossil-based model cross-validation to determine the optimal smoothing value in penalized likelihood analysis, and six mutually consistent fossil calibrations, the age of the most recent common ancestor of Centrarchidae was 33.59 million years ago (mya). Penalized likelihood analyses of individual data partitions all converged on a very similar age estimate for this node, indicating that rate heterogeneity among data partitions is not confounding our analyses. These results place the origin of the centrarchid radiation at a time of major faunal turnover as the fossil record indicates that the most diverse lineages of the North American freshwater fish fauna originated at the Eocene-Oligocene boundary, approximately 34 mya. This time coincided with major global climate change from warm to cool temperatures and a signature of elevated lineage extinction and origination in the fossil record across the tree of life. Our analyses demonstrate the utility of fossil cross-validation to critically assess individual fossil calibration points, providing the ability to discriminate between consistent and inconsistent fossil age estimates that are used for calibrating molecular phylogenies.     

Time-dependent speciation and extinction from phylogenies: a least squares approach

Molecular phylogenies contribute to the study of the patterns and processes of macroevolution even though past events (fossils) are not recorded in these data. In this article, I consider the general time-dependent birth-death model to fit any model of temporal variation in speciation and extinction to phylogenies. I establish formulae to compute the expected cumulative distribution function of branching times for any model, and, building on previous published works, I derive maximum likelihood estimators. Some limitations of the likelihood approach are described, and a fitting procedure based on least squares is developed that alleviates the shortcomings of maximum likelihood in the present context. Parametric and nonparametric bootstrap procedures are developed to assess uncertainty in the parameter estimates, the latter version giving narrower confidence intervals and being faster to compute. I also present several general algorithms of tree simulation in continuous time. I illustrate the application of this approach with the analysis of simulated datasets, and two published phylogenies of primates (Catarrhinae) and lizards (Agamidae).     

Assessment of available anatomical characters for linking living mammals to fossil taxa in phylogenetic analyses

Analyses of living and fossil taxa are crucial for understanding biodiversity through time. The total evidence method allows living and fossil taxa to be combined in phylogenies, using molecular data for living taxa and morphological data for living and fossil taxa. With this method, substantial overlap of coded anatomical characters among living and fossil taxa is vital for accurately inferring topology. However, although molecular data for living species are widely available, scientists generating morphological data mainly focus on fossils. Therefore, there are fewer coded anatomical characters in living taxa, even in well-studied groups such as mammals. We investigated the number of coded anatomical characters available in phylogenetic matrices for living mammals and how these were phylogenetically distributed across orders. Eleven of 28 mammalian orders have less than 25% species with available characters; this has implications for the accurate placement of fossils, although the issue is less pronounced at higher taxonomic levels. In most orders, species with available characters are randomly distributed across the phylogeny, which may reduce the impact of the problem. We suggest that increased morphological data collection efforts for living taxa are needed to produce accurate total evidence phylogenies.     

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.     

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.     

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.     

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.     

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.     

Ancient tropical extinctions at high latitudes contributed to the latitudinal diversity gradient*

Global biodiversity currently peaks at the equator and decreases toward the poles. Growing fossil evidence suggest this hump-shaped latitudinal diversity gradient (LDG) has not been persistent through time, with similar diversity across latitudes flattening out the LDG during past greenhouse periods. However, when and how diversity declined at high latitudes to generate the modern LDG remains an open question. Although diversity-loss scenarios have been proposed, they remain mostly undemonstrated. We outline the “asymmetric gradient of extinction and dispersal” framework that contextualizes previous ideas behind the LDG under a time-variable scenario. Using phylogenies and fossils of Testudines, Crocodilia, and Lepidosauria, we find that the hump-shaped LDG could be explained by (1) disproportionate extinctions of high-latitude tropical-adapted clades when climate transitioned from greenhouse to icehouse, and (2) equator-ward biotic dispersals tracking their climatic preferences when tropical biomes became restricted to the equator. Conversely, equivalent diversification rates across latitudes can account for the formation of an ancient flat LDG. The inclusion of fossils in macroevolutionary studies allows revealing time-dependent extinction rates hardly detectable from phylogenies only. This study underscores that the prevailing evolutionary processes generating the LDG during greenhouses differed from those operating during icehouses.     

Partially incorrect fossil data augment analyses of discrete trait evolution in living species

Ancestral state reconstruction of discrete character traits is often vital when attempting to understand the origins and homology of traits in living species. The addition of fossils has been shown to alter our understanding of trait evolution in extant taxa, but researchers may avoid using fossils alongside extant species if only few are known, or if the designation of the trait of interest is uncertain. Here, I investigate the impacts of fossils and incorrectly coded fossils in the ancestral state reconstruction of discrete morphological characters under a likelihood model. Under simulated phylogenies and data, likelihood-based models are generally accurate when estimating ancestral node values. Analyses with combined fossil and extant data always outperform analyses with extant species alone, even when around one quarter of the fossil information is incorrect. These results are especially pronounced when model assumptions are violated, such as when there is a trend away from the root value. Fossil data are of particular importance when attempting to estimate the root node character state. Attempts should be made to include fossils in analysis of discrete traits under likelihood, even if there is uncertainty in the fossil trait data.     

Understanding mammalian evolution using Bayesian phylogenetic inference

1. Phylogenetic trees are critical in addressing evolutionary hypotheses; however, the reconstruction of a phylogeny is no easy task. This process has recently been made less arduous by using a Bayesian statistical approach. This method offers the advantage that one can determine the probability of some hypothesis (i.e. a phylogeny), conditional on the observed data (i.e. nucleotide sequences). 2. By reconstructing phylogenies using Bayes’ theorem in combination with Markov chain Monte Carlo, phylogeneticists are able to test hypotheses more quickly compared with using standard methods such as neighbour-joining, maximum likelihood or parsimony. Critics of the Bayesian approach suggest that it is not a panacea, and argue that the prior probability is too subjective and the resulting posterior probability is too liberal compared with maximum likelihood. 3. These issues are currently debated in the arena of mammalian evolution. Recently, proponents and opponents of the Bayesian approach have constructed the mammalian phylogeny using different methods under different conditions and with a variety of parameters. These analyses showed the robustness (or lack of) of the Bayesian approach. In the end, consensus suggests that Bayesian methods are robust and give essentially the same answer as maximum likelihood methods but in less time. 4. Approaches based on fossils and molecules typically agree on ordinal-level relationships among mammals but not on higher-level relationships, as Bayesian analyses recognize the African radiation, Afrotheria, and the two Laurasian radiations, Laurasiatheria and Euarchontoglires, whereas fossils did not predict Afrotheria.     

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.     

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     

The molecular phylogenetic signature of clades in decline

Molecular phylogenies have been used to study the diversification of many clades. However, current methods for inferring diversification dynamics from molecular phylogenies ignore the possibility that clades may be decreasing in diversity, despite the fact that the fossil record shows this to be the case for many groups. Here we investigate the molecular phylogenetic signature of decreasing diversity using the most widely used statistic for inferring diversity dynamics from molecular phylogenies, the γ statistic. We show that if a clade is in decline its molecular phylogeny may show evidence of the decrease in the diversification rate that occurred between its diversification and decline phases. The ability to detect the change in diversification rate depends largely on the ratio of the speciation rates of the diversification and decline phases, the higher the ratio the stronger the signal of the change in diversification rate. Consequently, molecular phylogenies of clades in relative rapid decline do not carry a signature of their decreasing diversification. Further, the signal of the change in diversification rate, if present, declines as the diversity drop. Unfortunately, the molecular signature of clades in decline is the same as the signature produced by diversity dependent diversification. Given this similarity, and the inability of current methods to detect declining diversity, it is likely that some of the extant clades that show a decrease in diversification rate, currently interpreted as evidence for diversity dependent diversification, are in fact in decline. Unless methods can be developed that can discriminate between the different modes of diversification, specifically diversity dependent diversification and declining diversity, we will need the fossil record, or data from some other source, to distinguish between these very different diversity trajectories.     

Phylogeny of extant and fossil Juglandaceae inferred from the integration of molecular and morphological data sets

It is widely acknowledged that integrating fossils into data sets of extant taxa is imperative for proper placement of fossils, resolution of relationships, and a better understanding of character evolution. The importance of this process has been further magnified because of the crucial role of fossils in dating divergence times. Outstanding issues remain, including appropriate methods to place fossils in phylogenetic trees, the importance of molecules versus morphology in these analyses, as well as the impact of potentially large amounts of missing data for fossil taxa. In this study we used the angiosperm clade Juglandaceae as a model for investigating methods of integrating fossils into a phylogenetic framework of extant taxa. The clade has a rich fossil record relative to low extant diversity, as well as a robust molecular phylogeny and morphological database for extant taxa. After combining fossil organ genera into composite and terminal taxa, our objectives were to (1) compare multiple methods for the integration of the fossils and extant taxa (including total evidence, molecular scaffolds, and molecular matrix representation with parsimony [MRP]); (2) explore the impact of missing data (incomplete taxa and characters) and the evidence for placing fossils on the topology; (3) simulate the phylogenetic effect of missing data by creating "artificial fossils"; and (4) place fossils and compare the impact of single and multiple fossil constraints in estimating the age of clades. Despite large and variable amounts of missing data, each of the methods provided reasonable placement of both fossils and simulated "artificial fossils" in the phylogeny previously inferred only from extant taxa. Our results clearly show that the amount of missing data in any given taxon is not by itself an operational guideline for excluding fossils from analysis. Three fossil taxa (Cruciptera simsonii, Paleoplatycarya wingii, and Platycarya americana) were placed within crown clades containing living taxa for which relationships previously had been suggested based on morphology, whereas Polyptera manningii, a mosaic taxon with equivocal affinities, was placed firmly as sister to two modern crown clades. The position of Paleooreomunnea stoneana was ambiguous with total evidence but conclusive with DNA scaffolds and MRP. There was less disturbance of relationships among extant taxa using a total evidence approach, and the DNA scaffold approach did not provide improved resolution or internal support for clades compared to total evidence, whereas weighted MRP retained comparable levels of support but lost crown clade resolution. Multiple internal minimum age constraints generally provided reasonable age estimates, but the use of single constraints provided by extinct genera tended to underestimate clade ages.