FiSSE: A simple nonparametric test for the effects of a binary character on lineage diversification rates

It is widely assumed that phenotypic traits can influence rates of speciation and extinction, and several statistical approaches have been used to test for correlations between character states and lineage diversification. Recent work suggests that model‐based tests of state‐dependent speciation and extinction are sensitive to model inadequacy and phylogenetic pseudoreplication. We describe a simple nonparametric statistical test (“FiSSE”) to assess the effects of a binary character on lineage diversification rates. The method involves computing a test statistic that compares the distributions of branch lengths for lineages with and without a character state of interest. The value of the test statistic is compared to a null distribution generated by simulating character histories on the observed phylogeny. Our tests show that FiSSE can reliably infer trait‐dependent speciation on phylogenies of several hundred tips. The method has low power to detect trait‐dependent extinction but can infer state‐dependent differences in speciation even when net diversification rates are constant. We assemble a range of macroevolutionary scenarios that are problematic for likelihood‐based methods, and we find that FiSSE does not show similarly elevated false positive rates. We suggest that nonparametric statistical approaches, such as FiSSE, provide an important complement to formal process‐based models for trait‐dependent diversification.     

Heterogeneity, speciation/extinction history and climate: explaining regional plant diversity patterns in the Cape Floristic Region

This paper investigates the role of heterogeneity and speciation/extinction history in explaining variation in regional scale (c. 0.1–3000 km²) plant diversity in the Cape Floristic Region of south‐western Africa, a species‐ and endemic‐rich biogeographical region. We used species‐area analysis and analysis of covariance to investigate geographical (east vs. west) and topographic (lowland vs. montane) patterns of diversity. We used community diversity as a surrogate for biological heterogeneity, and the diversity of naturally rare species in quarter degree squares as an indicator of differences in speciation/extinction histories across the study region. We then used standard statistical methods to analyse geographical and topographic patterns of these two measures. There was a clear geographical diversity pattern (richer in the west), while a topographic pattern (richer in mountains) was evident only in the west. The geographical boundary coincided with a transition from the reliable winter‐rainfall zone (west) to the less reliable non‐seasonal rainfall zone (east). Community diversity, or biological heterogeneity, showed no significant variation in relation to geography and topography. Diversity patterns of rare species mirrored the diversity pattern for all species. We hypothesize that regional diversity patterns are the product of different speciation and extinction histories, leading to different steady‐state diversities. Greater Pleistocene climatic stability in the west would have resulted in higher rates of speciation and lower rates of extinction than in the east, where for the most, Pleistocene climates would not have favoured Cape lineages. A more parsimonious hypothesis is that the more predictable seasonal rainfall of the west would have favoured non‐sprouting plants and that this, in turn, resulted in higher speciation and lower extinction rates. Both hypotheses are consistent with the higher incidence of rare species in the west, and higher levels of beta and gamma diversity there, associated with the turnover of species along environmental and geographical gradients, respectively. These rare species do not contribute to community patterns; hence, biological heterogeneity is uniform across the region. The weak topography pattern of diversity in the west arises from higher speciation rates and lower extinction rates in the topographically complex mountains, rather than from the influence of environmental heterogeneity on diversity.     

EXPLOSIVE EVOLUTIONARY RADIATIONS: DECREASING SPECIATION OR INCREASING EXTINCTION THROUGH TIME?

A common pattern in time-calibrated molecular phylogenies is a signal of rapid diversification early in the history of a radiation. Because the net rate of diversification is the difference between speciation and extinction rates, such "explosive-early" diversification could result either from temporally declining speciation rates or from increasing extinction rates through time. Distinguishing between these alternatives is challenging but important, because these processes likely result from different ecological drivers of diversification. Here we develop a method for estimating speciation and extinction rates that vary continuously through time. By applying this approach to real phylogenies with explosive-early diversification and by modeling features of lineage-accumulation curves under both declining speciation and increasing extinction scenarios, we show that a signal of explosive-early diversification in phylogenies of extant taxa cannot result from increasing extinction and can only be explained by temporally declining speciation rates. Moreover, whenever extinction rates are high, "explosive early" patterns become unobservable, because high extinction quickly erases the signature of even large declines in speciation rates. Although extinction may obscure patterns of evolutionary diversification, these results show that decreasing speciation is often distinguishable from increasing extinction in the numerous molecular phylogenies of radiations that retain a preponderance of early lineages.     

Species selection and random drift in macroevolution

Species selection resulting from trait‐dependent speciation and extinction is increasingly recognized as an important mechanism of phenotypic macroevolution. However, the recent bloom in statistical methods quantifying this process faces a scarcity of dynamical theory for their interpretation, notably regarding the relative contributions of deterministic versus stochastic evolutionary forces. I use simple diffusion approximations of birth‐death processes to investigate how the expected and random components of macroevolutionary change depend on phenotype‐dependent speciation and extinction rates, as can be estimated empirically. I show that the species selection coefficient for a binary trait, and selection differential for a quantitative trait, depend not only on differences in net diversification rates (speciation minus extinction), but also on differences in species turnover rates (speciation plus extinction), especially in small clades. The randomness in speciation and extinction events also produces a species‐level equivalent to random genetic drift, which is stronger for higher turnover rates. I then show how microevolutionary processes including mutation, organismic selection, and random genetic drift cause state transitions at the species level, allowing comparison of evolutionary forces across levels. A key parameter that would be needed to apply this theory is the distribution and rate of origination of new optimum phenotypes along a phylogeny.     

Phylogenetically patterned speciation rates and extinction risks change the loss of evolutionary history during extinctions

If we are to plan conservation strategies that minimize the loss of evolutionary history through human-caused extinctions, we must understand how this loss is related to phylogenetic patterns in current extinction risks and past speciation rates. Nee & May (1997, Science 278, 692-694) showed that for a randomly evolving clade (i) a single round of random extinction removed relatively little evolutionary history, and (ii) extinction management (choosing which taxa to sacrifice) offered only marginal improvement. However, both speciation rates and extinction risks vary across lineages within real clades. We simulated evolutionary trees with phylogenetically patterned speciation rates and extinction risks (closely related lineages having similar rates and risks) and then subjected them to several biologically informed models of extinction. Increasing speciation rate variation increases the extinction-management pay-off. When extinction risks vary among lineages but are uncorrelated with speciation rates, extinction removes more history (compared with random trees), but the difference is small. When extinction risks vary and are correlated with speciation rates, history loss can dramatically increase (negative correlation) or decrease (positive correlation) with speciation rate variation. The loss of evolutionary history via human-caused extinctions may therefore be more severe, yet more manageable, than first suggested.     

Interactions within and between clades shaped the diversification of terrestrial carnivores

A longstanding debate in evolutionary biology and paleontology is whether ecological interactions such as competition impose diversity dependence on speciation and extinction rates. Here, we analyze the fossil record of terrestrial mammalian carnivores in North America and Eurasia using a Bayesian framework to assess whether their diversity dynamics were affected by diversity dependence within and between families (12 in Eurasia, 10 in North America). We found eight instances of within‐clade diversity dependence suppressing speciation rates and detected between‐clade effects increasing extinction rates in six instances. Diversity dependence often involved lineages that migrated between continents and we found that speciation was more responsive to diversity changes within the clade, whereas extinction responded to diversity of taxa in other clades. The analysis of the fossil record of Carnivora suggests that interactions within and between clades are associated with different speciation and extinction regimes, opening room for a broader theory of diversity dependence.     

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.     

Robustness of the approximate likelihood of the protracted speciation model

The protracted speciation model presents a realistic and parsimonious explanation for the observed slowdown in lineage accumulation through time, by accounting for the fact that speciation takes time. A method to compute the likelihood for this model given a phylogeny is available and allows estimation of its parameters (rate of initiation of speciation, rate of completion of speciation and extinction rate) and statistical comparison of this model to other proposed models of diversification. However, this likelihood computation method makes an approximation of the protracted speciation model to be mathematically tractable: it sometimes counts fewer species than one would do from a biological perspective. This approximation may have large consequences for likelihood‐based inferences: it may render any conclusions based on this method completely irrelevant. Here, we study to what extent this approximation affects parameter estimations. We simulated phylogenies from which we reconstructed the tree of extant species according to the original, biologically meaningful protracted speciation model and according to the approximation. We then compared the resulting parameter estimates. We found that the differences were larger for high values of extinction rates and small values of speciation‐completion rates. Indeed, a long speciation‐completion time and a high extinction rate promote the appearance of cases to which the approximation applies. However, surprisingly, the deviation introduced is largely negligible over the parameter space explored, suggesting that this approximate likelihood can be applied reliably in practice to estimate biologically relevant parameters under the original protracted speciation model.     

Phylogenetic extinction rates and comparative methodology

Species are not independent points for comparative analyses because closely related species share more evolutionary history and are therefore more similar to each other than distantly related species. The extent to which independent-contrast analysis reduces type I and type II statistical error in comparison with cross-species analysis depends on the relative branch lengths in the phylogenetic tree: as deeper branches get relatively long, cross-species analyses have more statistical type I and type II error. Phylogenetic trees reconstructed from extant species, under the assumptions of a branching process with speciation (branching) and extinction rates remaining constant through time, will have relatively longer deep branches as the extinction rate increases relative to the speciation rate. We compare the statistical performance of cross-species and independent-contrast analyses with varying relative extinction rates, and conclude that cross-species comparisons have unacceptable statistical performance, particularly when extinction rates are relatively high.     

Niche width impacts vertebrate diversification

Aim The size of the climatic niche of a species is a major factor determining its distribution and evolution. In particular, it has been proposed that niche width should be associated with the rate of species diversification. Here, we test whether species niche width affects the speciation and extinction rates of three main clades of vertebrates: amphibians, mammals and birds. Location Global. Methods We obtained the time‐calibrated phylogenies, IUCN conservation status, species distribution maps and climatic data for 2340 species of amphibians, 4563 species of mammals and 9823 species of birds. We computed the niche width for each species as the mean annual temperature across the species range. We estimated speciation, extinction and transition rates associated with lineages with either narrow (specialist) or wide (generalist) niches using phylogeny‐based birth–death models. We also tested if current conservation status was correlated with the niche width of species. Results We found higher net diversification rates in specialist species than in generalist species. This result was explained by both higher speciation rates (for the three taxonomic groups) and lower extinction rates (for mammals and birds only) in specialist than in generalist species. In contrast, current specialist species tended to be more threatened than generalist species. Main conclusions Our diversification analysis shows that the width of the climatic niche is strongly associated with diversification rates and may thus be a crucial factor for understanding the emergence of diversity patterns in vertebrates. The striking difference between our diversification results and current conservation status suggests that the current extinction process may be different from extinction rates estimated from the whole history of the group.     

Advancing the metabolic theory of biodiversity

A component of metabolic scaling theory has worked towards understanding the influence of metabolism over the generation and maintenance of biodiversity. Specific models within this ‘metabolic theory of biodiversity’ (MTB) have addressed temperature gradients in speciation rate and species richness, but the scope of MTB has been questioned because of empirical departures from model predictions. In this study, we first show that a generalized MTB is not inconsistent with empirical patterns and subsequently implement an eco‐evolutionary MTB which has thus far only been discussed qualitatively. More specifically, we combine a functional trait (body mass) approach and an environmental gradient (temperature) with a dynamic eco‐evolutionary model that builds on the current MTB. Our approach uniquely accounts for feedbacks between ecological interactions (size‐dependent competition and predation) and evolutionary rates (speciation and extinction). We investigate a simple example in which temperature influences mutation rate, and show that this single effect leads to dynamic temperature gradients in macroevolutionary rates and community structure. Early in community evolution, temperature strongly influences speciation and both speciation and extinction strongly influence species richness. Through time, niche structure evolves, speciation and extinction rates fall, and species richness becomes increasingly independent of temperature. However, significant temperature‐richness gradients may persist within emergent functional (trophic) groups, especially when niche breadths are wide. Thus, there is a strong signal of both history and ecological interactions on patterns of species richness across temperature gradients. More generally, the successful implementation of an eco‐evolutionary MTB opens the perspective that a process‐based MTB can continue to emerge through further development of metabolic models that are explicit in terms of functional traits and environmental gradients.     

How diversification rates and diversity limits combine to create large-scale species-area relationships

Species-area relationships (SARs) have mostly been treated from an ecological perspective, focusing on immigration, local extinction and resource-based limits to species coexistence. However, a full understanding across large regions is impossible without also considering speciation and global extinction. Rates of both speciation and extinction are known to be strongly affected by area and thus should contribute to spatial patterns of diversity. Here, we explore how variation in diversification rates and ecologically mediated diversity limits among regions of different sizes can result in the formation of SARs. We explain how this area-related variation in diversification can be caused by either the direct effects of area or the effects of factors that are highly correlated with area, such as habitat diversity and population size. We also review environmental, clade-specific and historical factors that affect diversification and diversity limits but are not highly correlated with region area, and thus are likely to cause scatter in observed SARs. We present new analyses using data on the distributions, ages and traits of mammalian species to illustrate these mechanisms; in doing so we provide an integrated perspective on the evolutionary processes shaping SARs.     

Extinction and time help drive the marine‐terrestrial biodiversity gradient: is the ocean a deathtrap?

The marine‐terrestrial richness gradient is among Earth's most dramatic biodiversity patterns, but its causes remain poorly understood. Here, we analyse detailed phylogenies of amniote clades, paleontological data and simulations to reveal the mechanisms underlying low marine richness, emphasising speciation, extinction and colonisation. We show that differences in diversification rates (speciation minus extinction) between habitats are often weak and inconsistent with observed richness patterns. Instead, the richness gradient is explained by limited time for speciation in marine habitats, since all extant marine clades are relatively young. Paleontological data show that older marine invasions have consistently ended in extinction. Simulations show that marine extinctions help drive the pattern of young, depauperate marine clades. This role for extinction is not discernible from molecular phylogenies alone, and not predicted by most previously hypothesised explanations for this gradient. Our results have important implications for the marine‐terrestrial biodiversity gradient, and studies of biodiversity gradients in general.     

High speciation rate at temperate latitudes explains unusual diversity gradients in a clade of ectomycorrhizal fungi

Understanding the patterns of biodiversity through time and space is a challenging task. However, phylogeny‐based macroevolutionary models allow us to account and measure many of the processes responsible for diversity buildup, namely speciation and extinction. The general latitudinal diversity gradient (LDG) is a well‐recognized pattern describing a decline in species richness from the equator polewards. Recent macroecological studies in ectomycorrhizal (EM) fungi have shown that their LDG is shifted, peaking at temperate rather than tropical latitudes. Here we investigate this phenomenon from a macroevolutionary perspective, focusing on a well‐sampled group of edible EM mushrooms from the genus Amanita—the Caesar's mushrooms, which follow similar diversity patterns. Our approach consisted in applying a suite of models including (1) nontrait‐dependent time‐varying diversification (Bayesian analysis of macroevolutionary mixtures [BAMM]), (2) continuous trait‐dependent diversification (quantitative‐state speciation and extinction [QuaSSE]), and (3) diversity‐dependent diversification. In short, results give strong support for high speciation rates at temperate latitudes (BAMM and QuaSSE). We also find some evidence for different diversity‐dependence thresholds in “temperate” and “tropical” subclades, and little differences in diversity due to extinction. We conclude that our analyses on the Caesar's mushrooms give further evidence of a temperate‐peaking LDG in EM fungi, highlighting the importance and the implications of macroevolutionary processes in explaining diversity gradients in microorganisms.     

Exploring the power of Bayesian birth‐death skyline models to detect mass extinction events from phylogenies with only extant taxa

Mass extinction events (MEEs), defined as significant losses of species diversity in significantly short time periods, have attracted the attention of biologists because of their link to major environmental change. MEEs have traditionally been studied through the fossil record, but the development of birth‐death models has made it possible to detect their signature based on extant‐taxa phylogenies. Most birth‐death models consider MEEs as instantaneous events where a high proportion of species are simultaneously removed from the tree (“single pulse” approach), in contrast to the paleontological record, where MEEs have a time duration. Here, we explore the power of a Bayesian Birth‐Death Skyline (BDSKY) model to detect the signature of MEEs through changes in extinction rates under a “time‐slice” approach. In this approach, MEEs are time intervals where the extinction rate is greater than the speciation rate. Results showed BDSKY can detect and locate MEEs but that precision and accuracy depend on the phylogeny's size and MEE intensity. Comparisons of BDSKY with the single‐pulse Bayesian model, CoMET, showed a similar frequency of Type II error and neither model exhibited Type I error. However, while CoMET performed better in detecting and locating MEEs for smaller phylogenies, BDSKY showed higher accuracy in estimating extinction and speciation rates.     

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.     

Can we continue to neglect genomic variation in introgression rates when inferring the history of speciation? A case study in a Mytilus hybrid zone

The use of molecular data to reconstruct the history of divergence and gene flow between populations of closely related taxa represents a challenging problem. It has been proposed that the long‐standing debate about the geography of speciation can be resolved by comparing the likelihoods of a model of isolation with migration and a model of secondary contact. However, data are commonly only fit to a model of isolation with migration and rarely tested against the secondary contact alternative. Furthermore, most demographic inference methods have neglected variation in introgression rates and assume that the gene flow parameter (Nm) is similar among loci. Here, we show that neglecting this source of variation can give misleading results. We analysed DNA sequences sampled from populations of the marine mussels, Mytilus edulis and M. galloprovincialis, across a well‐studied mosaic hybrid zone in Europe and evaluated various scenarios of speciation, with or without variation in introgression rates, using an Approximate Bayesian Computation (ABC) approach. Models with heterogeneous gene flow across loci always outperformed models assuming equal migration rates irrespective of the history of gene flow being considered. By incorporating this heterogeneity, the best‐supported scenario was a long period of allopatric isolation during the first three‐quarters of the time since divergence followed by secondary contact and introgression during the last quarter. By contrast, constraining migration to be homogeneous failed to discriminate among any of the different models of gene flow tested. Our simulations thus provide statistical support for the secondary contact scenario in the European Mytilus hybrid zone that the standard coalescent approach failed to confirm. Our results demonstrate that genomic variation in introgression rates can have profound impacts on the biological conclusions drawn from inference methods and needs to be incorporated in future studies.     

Linking the investigations of character evolution and species diversification

Variation in diversification rates is often studied by investigating traits related to species' ecology and life history. Often, however, it is unknown whether these traits evolve gradually or in punctuated bursts during speciation. Using phylogenetic data and species' present-day trait information, we present a novel approach to assessing the mode of character change while accounting for trait-dependent speciation and extinction. Our model, "Binary-State Speciation and Extinction-node enhanced state shift" (BiSSE-ness), estimates both the rate of change occurring along lineages and the probability of change occurring during speciation, as well as independent speciation and extinction rates for each character state. Using simulations, we found that BiSSE-ness is able to distinguish along-lineage and speciational change and accurately estimate the parameters associated with character change and diversification rates. We applied BiSSE-ness to an empirical primate data set and found evidence for along-lineage changes in primate mating systems and social behaviors, whereas shifts in habitat were associated with speciation. In cases where trait changes may be linked to the speciation process itself (e.g., niche-related traits), BiSSE-ness provides a suitable framework with which to simultaneously address questions regarding species diversification and character change.     

Simulating trees with a fixed number of extant species

In this paper, I develop efficient tools to simulate trees with a fixed number of extant species. The tools are provided in my open source R-package TreeSim available on CRAN. The new model presented here is a constant rate birth-death process with mass extinction and/or rate shift events at arbitrarily fixed times 1) before the present or 2) after the origin. The simulation approach for case (2) can also be used to simulate under more general models with fixed events after the origin. I use the developed simulation tools for showing that a mass extinction event cannot be distinguished from a model with constant speciation and extinction rates interrupted by a phase of stasis based on trees consisting of only extant species. However, once we distinguish between mass extinction and period of stasis based on paleontological data, fast simulations of trees with a fixed number of species allow inference of speciation and extinction rates using approximate Bayesian computation and allow for robustness analysis once maximum likelihood parameter estimations are available.