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

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

PATTERNS IN TREE BALANCE AMONG CLADISTIC,PHENETIC, AND RANDOMLY GENERATED PHYLOGENETIC TREES

I examine patterns in tree balance for a sample of 208 cladograms and phenograms from the recent literature. I provide an expression for expected imbalance under a simple, uniform-rate random speciation model, and I estimate variances by simulation for the same model. Imbalance decreases with tree size (number of included taxa) in both theoretical and literature trees. In contrast to previous suggestions, I find cladistic trees to be no more imbalanced than phenetic trees when confounding variables are appropriately controlled. The degree of imbalance found in literature trees is inconsistent with the uniform-rate speciation model; this is most likely a result of variability in speciation and extinction rates among real lineages. The existence of such variation is a necessary (but not sufficient) condition for the operation of the macroevolutionary processes of species sorting and species selection.     

Selective extinction and rapid loss of evolutionary history in the bird fauna

The extinction of species results in a permanent loss of evolutionary history. Recent theoretical studies show that this loss may be proportionally much smaller than the loss of species, but under some conditions can exceed it. Such conditions occur when the phylogenetic tree that describes the evolutionary relationships among species is highly imbalanced due to differences between lineages in past speciation and/or extinction rates. I used the taxonomy by C. G. Sibley and B. L. Monroe Jr to estimate the global loss of bird evolutionary history from historical and predicted extinctions, and to quantify the ensuing changes in balance of the bird phylogenetic tree. In the global bird fauna, evolutionary history is being lost at a high rate, similar to the rate of species extinction. The bird phylogenetic tree is highly imbalanced, and the imbalance is increased significantly by anthropogenic extinction. Historically, the elevated loss of bird evolutionary history has been fuelled mostly by phylogenetic non-randomness in the extinction of species, but the direct effect of tree imbalance is substantial and could dominate in the future.     

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.     

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.     

Recovering speciation and extinction dynamics based on phylogenies

Phylogenetic trees of only extant species contain information about the underlying speciation and extinction pattern. In this review, I provide an overview over the different methodologies that recover the speciation and extinction dynamics from phylogenetic trees. Broadly, the methods can be divided into two classes: (i) methods using the phylogenetic tree shapes (i.e. trees without branch length information) allowing us to test for speciation rate variation and (ii) methods using the phylogenetic trees with branch length information allowing us to quantify speciation and extinction rates. I end the article with an overview on limitations, open questions and challenges of the reviewed methodology.     

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.      

ACCURACY OF ESTIMATED PHYLOGENIES: EFFECTS OF TREE TOPOLOGY AND EVOLUTIONARY MODEL

A simulation study was carried out to investigate the relative importance of tree topology (both balance and stemminess), evolutionary rates (constant, varying among characters, and varying among lineages), and evolutionary models in determining the accuracy with which phylogenetic trees can be estimated. The three evolutionary context models were phyletic (characters can change at each simulated time step), speciational (changes are possible only at the time of speciation into two daughter lineages), and punctuational (changes occur at the time of speciation but only in one of the daughter lineages). UPGMA clustering and maximum parsimony (“Wagner trees”) methods for estimating phylogenies were compared. All trees were based on eight recent OTUs. The three evolutionary context models were found to have the largest influence on accuracy of estimates by both methods. The next most important effect was that of the stemminess × context interaction. Maximum parsimony and UPGMA performed worst under the punctuational models. Under the phyletic model, trees with high stemminess values could be estimated more accurately and balanced trees were slightly easier to estimate than unbalanced ones. Overall, maximum parsimony yielded more accurate trees than UPGMA—but that was expected for these simulations since many more characters than OTUs were used. Our results suggest that the great majority of estimated phylogenetic trees are likely to be quite inaccurate; they underscore the inappropriateness of characterizing current phylogenetic methods as being for reconstruction rather than for estimation.     

New Analytic Results for Speciation Times in Neutral Models

In this paper, we investigate the standard Yule model, and a recently studied model of speciation and extinction, the “critical branching process.” We develop an analytic way—as opposed to the common simulation approach—for calculating the speciation times in a reconstructed phylogenetic tree. Simple expressions for the density and the moments of the speciation times are obtained. Methods for dating a speciation event become valuable, if for the reconstructed phylogenetic trees, no time scale is available. A missing time scale could be due to supertree methods, morphological data, or molecular data which violates the molecular clock. Our analytic approach is, in particular, useful for the model with extinction, since simulations of birth-death processes which are conditioned on obtaining n extant species today are quite delicate. Further, simulations are very time consuming for big n under both models.     

Distribution of branch lengths and phylogenetic diversity under homogeneous speciation models

The constant rate birth–death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces ‘reconstructed trees’ which describe the relationship between extant lineages. We derive the probability density of the length of a randomly chosen pendant edge in a reconstructed tree. For the special case of a pure-birth process with complete sampling, we also provide the probability density of the length of an interior edge, of the length of an edge descending from the root, and of the diversity (which is the sum of all edge lengths). We show that the results depend on whether the reconstructed trees are conditioned on the number of leaves, the age, or both.     

Tree balance,time slices,and evolutionary turnover in cretaceous planktonic foraminifera

Studies of phylogenetic tree shape often concentrate on the balance of phylogenies of extant taxa. Paleontological phylogenies (which include extinct taxa) can contain additional useful information and can directly document changes in tree shape through evolutionary time. Unfortunately, the inclusion of extinct taxa lowers the power of direct examinations of tree balance because it increases the range of tree shapes expected under null models of evolution (with equal rates of speciation and extinction across lineages). A promising approach for the analysis of tree shape in paleontological phylogenies is to break the phylogeny down into time slices, examining the shape of the phylogeny of taxa alive at each time slice and changes in that shape between successive time slices. This method was illustrated with 57 time slices through a stratophenetic phylogeny of the Cretaceous planktonic foraminiferal superfamily Globotruncanacea. At 3 of 56 intervals between time slices, 93-92.5 million years ago (MYA), 89-88.5 MYA, and 85.5-84 MYA, the group showed steep increases in imbalance. Although none of these increases were significant after Bonferroni correction, these points in the history of the Globotruncanacea were nevertheless identified as deserving of further macroevolutionary investigation. The 84 MYA time slice coincides with a peak in species turnover for the superfamily. Time slices through phylogenies may prove useful for identifying periods of time when evolution was proceeding in a nonstochastic manner.     

SPECIATIONAL HISTORY IN A DIVERSE CLADE OF HABITAT-SPECIALIZED SPIDERS (ARANEAE: NESTICIDAE: NESTICUS): INFERENCES FROM GEOGRAPHIC-BASED SAMPLING

This paper summarizes the results of an initial effort to reconstruct the speciational history of cave spiders (Nesticus) from the southern Appalachian Mountains of eastern North America. The Appalachian Nesticus fauna includes a large series of about 30 species distributed across islandlike cave and montane habitats. Many of the species are geographically restricted; all of the species are found in allopatry. Observed patterns of morphological variation and biogeographic evidence suggest that species diversification in this lineage may have occurred recently, perhaps in response to Pleistocene climatic fluctuations. To address questions about the spatial and temporal dynamics of Nesticus speciation, while accounting for potential phylogenetic difficulties, I have gathered nuclear and mitochondrial DNA sequences for a sample of individuals from 81 populations representing 28 Nesticus species. Analyses of these data indicate that considerable genetic divergence exists within and among currently recognized morphological species. Consistent with relatively deep species divergences, most of which likely predate the Pleistocene, is a prevailing pattern of phylogenetic concordance between taxonomic species and monophyletic gene tree lineages. The few deviations from monophyly detected can be tentatively attributed to a peripatric mode of speciation. Although species limits as inferred by the molecular data are generally concordant with patterns of morphological continuity and discontinuity in genitalia, there is evidence to suggest that cryptic phylogenetic lineages exist within some morphologically continuous units. This observation, in combination with the general depth of species lineages, makes any argument about rapid evolution in Nesticus genitalic characteristics unnecessary.     

USING PHYLOGENETIC TREES TO STUDY SPECIATION AND EXTINCTION

One tool in the study of the forces that determine species diversity is the null, or simple, model. The fit of predictions to observations, good or bad, leads to a useful paradigm or to knowledge of forces not accounted for, respectively. It is shown how simple models of speciation and extinction lead directly to predictions of the structure of phylogenetic trees. These predictions include both essential attributes of phylogenetic trees: lengths, in the form of internode distances; and topology, in the form of internode links. These models also lead directly to statistical tests which can be used to compare predictions with phylogenetic trees that are estimated from data. Two different models and eight data sets are considered. A model without species extinction consistently yielded predictions closer to observations than did a model that included extinction. It is proposed that it may be useful to think of the diversification of recently formed monophyletic groups as a random speciation process without extinction.     

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     

Coalescent time distributions in trees of arbitrary size

The relationship between speciation times and the corresponding times of gene divergence is of interest in phylogenetic inference as a means of understanding the past evolutionary dynamics of populations and of estimating the timing of speciation events. It has long been recognized that gene divergence times might substantially pre-date speciation events. Although the distribution of the difference between these has previously been studied for the case of two populations, this distribution has not been explicitly computed for larger species phylogenies. Here we derive a simple method for computing this distribution for trees of arbitrary size. A two-stage procedure is proposed which (i) considers the probability distribution of the time from the speciation event at the root of the species tree to the gene coalescent time conditionally on the number of gene lineages available at the root; and (ii) calculates the probability mass function for the number of gene lineages at the root. This two-stage approach dramatically simplifies numerical analysis, because in the first step the conditional distribution does not depend on an underlying species tree, while in the second step the pattern of gene coalescence prior to the species tree root is irrelevant. In addition, the algorithm provides intuition concerning the properties of the distribution with respect to the various features of the underlying species tree. The methodology is complemented by developing probabilistic formulae and software, written in R. The method and software are tested on five-taxon species trees with varying levels of symmetry. The examples demonstrate that more symmetric species trees tend to have larger mean coalescent times and are more likely to have a unimodal gamma-like distribution with a long right tail, while asymmetric trees tend to have smaller mean coalescent times with an exponential-like distribution. In addition, species trees with longer branches generally have shorter mean coalescent times, with branches closest to the root of the tree being most influential.     

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.     

Allopatry increases the balance of phylogenetic trees during radiation under neutral speciation

The shape of a phylogenetic tree is defined by the sequence of speciation events, represented by its branching points, and extinctions, represented by branch interruptions. In a neutral scenario of parapatry and isolation by distance, species tend to branch off the original population one after the other, leading to highly unbalanced trees. In this case the degree of imbalance, measured by the normalized Sackin index, grows linearly with species richness. Here we claim that moderate values of imbalance for trees with large number of species can occur if the geographic distribution involves more than one deme (allopatry) and speciation is parapatric within demes. The combined values of balance (normalized Sackin index) and species richness provide an estimate of how many demes were involved in the process if it happened in such neutral scenario. We also show that the spatial division in demes moderately slows down the diversification process, portraying a neutral mechanism for structuring the branch length distribution of phylogenetic trees.     

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.     

SEARCHING FOR EVOLUTIONARY PATTERNS IN THE SHAPE OF A PHYLOGENETIC TREE

If all species in a clade are equally likely to speciate or become extinct, then highly symmetric and highly asymmetric phylogenetic trees are unlikely to result. Variation between species in speciation and extinction rates can cause excessive asymmetry. We developed six non-parametric statistical tests that test for nonrandom patterns of branching in any bifurcating tree. The tests are demonstrated by applying them to two published phylogenies for genera of beetles. Comparison of the power of the six statistics under a simple model of biased speciation suggests which of them may be most useful for detecting nonrandom tree shapes.