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.     

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.     

CENTRAL MOMENTS AND PROBABILITY DISTRIBUTION OF COLLESS'S COEFFICIENT OF TREE IMBALANCE

The great increase in the number of phylogenetic studies of a wide variety of organisms in recent decades has focused considerable attention on the balance of phylogenetic trees—the degree to which sister clades within a tree tend to be of equal size—for at least two reasons: (1) the degree of balance of a tree may affect the accuracy of estimates of it; (2) the degree of balance, or imbalance, of a tree may reveal something about the macroevolutionary processes that produced it. In particular, variation among lineages in rates of speciation or extinction is expected to produce trees that are less balanced than those that result from phylogenetic evolution in which each extant species of a group has the same probability of speciation or extinction. Several coefficients for measuring the balance or imbalance of phylogenetic trees have been proposed. I focused on Colless's coefficient of imbalance (7) for its mathematical tractability and ease of interpretation. Earlier work on this statistic produced exact methods only for calculating the expected value. In those studies, the variance and confidence limits, which are necessary for testing the departure of observed values of I from the expected, were estimated by Monte Carlo simulation. I developed recursion equations that allow exact calculation of the mean, variance, skewness, and complete probability distribution of I for two different probability-generating models for bifurcating tree shapes. The Equal-Rates Markov (ERM) model assumes that trees grow by the random speciation and extinction of extant species, with all species that are extant at a given time having the same probability of speciation or extinction. The Equal Probability (EP) model assumes that all possible labeled trees for a given number of terminal taxa have the same probability of occurring. Examples illustrate how these theoretically derived probabilities and parameters may be used to test whether the evolution of a monophyletic group or set of monophyletic groups has proceeded according to a Markov model with equal rates of speciation and extinction among species, that is, whether there has been significant variation among lineages in expected rates of speciation or extinction.     

The conditioned reconstructed process

We investigate a neutral model for speciation and extinction, the constant rate birth-death process. The process is conditioned to have n extant species today, we look at the tree distribution of the reconstructed trees—i.e. the trees without the extinct species. Whereas the tree shape distribution is well-known and actually the same as under the pure birth process, no analytic results for the speciation times were known. We provide the distribution for the speciation times and calculate the expectations analytically. This characterizes the reconstructed trees completely. We will show how the results can be used to date phylogenies.     

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.     

Recognizing the forest for the trees: testing temporal patterns of cladogenesis using a null model of stochastic diversification

Computer simulations are developed and employed to examine the expected temporal distributions of nodes under a null model of stochastic lineage bifurcation and extinction. These Markovian models of phylogenetic process were constructed so as to permit direct comparisons against empirical phylogenetic trees generated from molecular or other information available solely from extant species. For replicate simulated phylads with n extant species, cumulative distribution functions (cdf's) of branching times were calculated, and compared (using the Kolmogorov-Smirnov test statistic D) to those from three published empirical trees. Molecular phylogenies for columbine plants and avian cranes showed statistically significant departures from the null expectations, in directions indicating recent and ancient species' radiations, respectively, whereas a molecular phylogeny for the Drosophila virilis species group showed no apparent historical clustering of branching events. Effects of outgroup choice and phylogenetic frame of reference were investigated for the columbines and found to have a predictable influence on the types of conclusions to be drawn from such analyses. To enable other investigators to statistically test for nonrandomness in temporal cladogenetic pattern in empirical trees generated from data on extant species, we present tables of mean cdf's and associated probabilities under the null model for expected branching times in phylads of varying size. The approaches developed in this report complement and extend those of other recent methods for employing null models to assess the statistical significance of pattern in evolutionary trees.      

NULL MODELS FOR THE NUMBER OF EVOLUTIONARY STEPS IN A CHARACTER ON A PHYLOGENETIC TREE

Random trees and random characters can be used in null models for testing phylogenetic hypothesis. We consider three interpretations of random trees: first, that trees are selected from the set of all possible trees with equal probability; second, that trees are formed by random speciation or coalescence (equivalent); and third, that trees are formed by a series of random partitions of the taxa. We consider two interpretations of random characters: first, that the number of taxa with each state is held constant, but the states are randomly reshuffled among the taxa; and second, that the probability each taxon is assigned a particular state is constant from one taxon to the next. Under null models representing various combinations of randomizations of trees and characters, exact recursion equations are given to calculate the probability distribution of the number of character state changes required by a phylogenetic tree. Possible applications of these probability distributions are discussed. They can be used, for example, to test for a panmictic population structure within a species or to test phylogenetic inertia in a character's evolution. Whether and how a null model incorporates tree randomness makes little difference to the probability distribution in many but not all circumstances. The null model's sense of character randomness appears more critical. The difficult issue of choosing a null model is discussed.     

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.     

The disparity of priapulid, archaeopriapulid and palaeoscolecid worms in the light of new data

Priapulids and their extinct relatives, the archaeopriapulids and palaeoscolecids, are vermiform, carnivorous ecdysozoans with an armoured, extensible proboscis. These worms were an important component of marine communities during the Palaeozoic, but were especially abundant and diverse in the Cambrian. Today, they comprise just seven genera in four families. Priapulids were among the first groups used to test hypotheses concerning the morphological disparity of Cambrian fossils relative to the extant fauna. A previous study sampled at the generic level, concluding that Cambrian genera embodied marginally less morphological diversity than their extant counterparts. Here, we sample predominantly at the species level and include numerous fossils and some extant forms described in the last fifteen years. Empirical morphospaces for priapulids, archaeopriapulids and palaeoscolecids are relatively insensitive to changes in the taxon or character sample: their overall form has altered little, despite the markedly improved sampling. Cambrian and post-Cambrian genera occupy adjacent rather than broadly overlapping regions of these spaces, and Cambrian species still show lower morphological disparity than their post-Cambrian counterparts. Crucially, the significance of this difference has increased with improved taxon sampling over research time. In contrast with empirical morphospaces, the phylogeny of priapulids, archaeopriapulids and palaeoscolecids derived from morphological characters is extremely sensitive to details of taxon sampling and the manner in which characters are weighted. However, the extant Priapulidae and Halicryptidae invariably resolve as sister families, with this entire clade subsequently being sister group to the Maccabeidae. In our most inclusive trees, the extant Tubiluchidae are separated from these other living taxa by a number of small, intervening fossil clades.     

Speciation and extinction drive the appearance of directional range size evolution in phylogenies and the fossil record

While the geographic range of a species is a fundamental unit of macroecology and a leading predictor of extinction risk, the evolutionary dynamics of species' ranges remain poorly understood. Based on statistical associations between range size and species age, many studies have claimed support for general models of range evolution in which the area occupied by a species varies predictably over the course of its life. Such claims have been made using both paleontological data and molecular estimates of the age of extant species. However, using a stochastic model, we show that the appearance of trends in range size with species' age can arise even when range sizes have evolved at random through time. This occurs because the samples of species used in existing studies are likely to be biased with respect to range size: for example, only those species that happened to have large or expanding ranges are likely to survive to the present, while extinct species will tend to be those whose ranges, by chance, declined through time. We compared the relationship between the age and range size of species arising under our stochastic model to those observed across 1,269 species of extant birds and mammals and 140 species of extinct Cenozoic marine mollusks. We find that the stochastic model is able to generate the full spectrum of empirical age-area relationships, implying that such trends cannot be simply interpreted as evidence for models of directional range size evolution. Our results therefore challenge the theory that species undergo predictable phases of geographic expansion and contraction through time.     

Genetic distance and species formation in evolving populations

Summary We compare the behavior of the genetic distance between individuals in evolving populations for three stochastic models.In the first model reproduction is asexual and the distribution of genetic distances reflects the genealogical tree of the population. This distribution fluctuates greatly in time, even for very large populations.In the second model reproduction is sexual with random mating allowed between any pair of individuals. In this case, the population becomes homogeneous and the genetic distance between pairs of individuals has small fluctuations which vanish in the limit of an infinitely large population.In the third model reproduction is still sexual but instead of random mating, mating only occurs between individuals which are genetically similar to each other. In that case, the population splits spontaneously into species which are in reproductive isolation from one another and one observes a steady state with a continual appearance and extinction of species in the population. We discuss this model in relation to the biological theory of speciation and isolating mechanisms.We also point out similarities between these three models of evolving populations and the theory of disordered systems in physics. Offprint requests to: P.G. Higgs     

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.     

Properties of phylogenetic trees generated by Yule-type speciation models

We investigate some discrete structural properties of evolutionary trees generated under simple null models of speciation, such as the Yule model. These models have been used as priors in Bayesian approaches to phylogenetic analysis, and also to test hypotheses concerning the speciation process. In this paper we describe new results for three properties of trees generated under such models. Firstly, for a rooted tree generated by the Yule model we describe the probability distribution on the depth (number of edges from the root) of the most recent common ancestor of a random subset of k species. Next we show that, for trees generated under the Yule model, the approximate position of the root can be estimated from the associated unrooted tree, even for trees with a large number of leaves. Finally, we analyse a biologically motivated extension of the Yule model and describe its distribution on tree shapes when speciation occurs in rapid bursts.     

Increased taxon sampling greatly reduces phylogenetic error

Several authors have argued recently that extensive taxon sampling has a positive and important effect on the accuracy of phylogenetic estimates. However, other authors have argued that there is little benefit of extensive taxon sampling, and so phylogenetic problems can or should be reduced to a few exemplar taxa as a means of reducing the computational complexity of the phylogenetic analysis. In this paper we examined five aspects of study design that may have led to these different perspectives. First, we considered the measurement of phylogenetic error across a wide range of taxon sample sizes, and conclude that the expected error based on randomly selecting trees (which varies by taxon sample size) must be considered in evaluating error in studies of the effects of taxon sampling. Second, we addressed the scope of the phylogenetic problems defined by different samples of taxa, and argue that phylogenetic scope needs to be considered in evaluating the importance of taxon-sampling strategies. Third, we examined the claim that fast and simple tree searches are as effective as more thorough searches at finding near-optimal trees that minimize error. We show that a more complete search of tree space reduces phylogenetic error, especially as the taxon sample size increases. Fourth, we examined the effects of simple versus complex simulation models on taxonomic sampling studies. Although benefits of taxon sampling are apparent for all models, data generated under more complex models of evolution produce higher overall levels of error and show greater positive effects of increased taxon sampling. Fifth, we asked if different phylogenetic optimality criteria show different effects of taxon sampling. Although we found strong differences in effectiveness of different optimality criteria as a function of taxon sample size, increased taxon sampling improved the results from all the common optimality criteria. Nonetheless, the method that showed the lowest overall performance (minimum evolution) also showed the least improvement from increased taxon sampling. Taking each of these results into account re-enforces the conclusion that increased sampling of taxa is one of the most important ways to increase overall phylogenetic accuracy.     

Positive correlation between diversification rates and phenotypic evolvability can mimic punctuated equilibrium on molecular phylogenies

The hypothesis of punctuated equilibrium proposes that most phenotypic evolution occurs in rapid bursts associated with speciation events. Several methods have been developed that can infer punctuated equilibrium from molecular phylogenies in the absence of paleontological data. These methods essentially test whether the variance in phenotypes among extant species is better explained by evolutionary time since common ancestry or by the number of estimated speciation events separating taxa. However, apparent "punctuational" trait change can be recovered on molecular phylogenies if the rate of phenotypic evolution is correlated with the rate of speciation. Strong support for punctuational models can arise even if the underlying mode of trait evolution is strictly gradual, so long as rates of speciation and trait evolution covary across the branches of phylogenetic trees, and provided that lineages vary in their rate of speciation. Species selection for accelerated rates of ecological or phenotypic divergence can potentially lead to the perception that most trait divergence occurs in association with speciation events.     

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.     

Stochastic models for phylogenetic trees on higher-order taxa

Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of higher-order taxa. A coherent model for trees on (say) genera should involve both a species-level model and a model for the classification scheme by which species are assigned to genera. We present a general framework for such models, and describe three alternate classification schemes. Combining with the species-level model of Aldous and Popovic (Adv Appl Probab 37:1094–1115, 2005), one gets models for higher-order trees, and we initiate analytic study of such models. In particular we derive formulas for the lifetime of genera, for the distribution of number of species per genus, and for the offspring structure of the tree on genera. David Aldous’s research was supported by NSF Grant DMS-0704159.     

Neutral Models with Generalised Speciation

Hubbell’s neutral theory claims that ecological patterns such as species abundance distributions can be explained by a stochastic model based on simple assumptions. One of these assumptions, the point mutation assumption, states that every individual has the same probability to speciate. Etienne et al. have argued that other assumptions on the speciation process could be more realistic, for example, that every species has the same probability to speciate (Etienne, et al. in Oikos 116:241–258, 2007). They introduced a number of neutral community models with a different speciation process, and conjectured formulas for their stationary species abundance distribution. Here we study a generalised neutral community model, encompassing these modified models, and derive its stationary distribution, thus proving the conjectured formulas.     

Recent oceanic long-distance dispersal and divergence in the amphi-Atlantic rain forest genus Renealmia L.f. (Zingiberaceae)

Renealmia L.f. (Zingiberaceae) is one of the few tropical plant genera with numerous species in both Africa and South America but not in Asia. Based on phylogenetic analysis of nuclear ribosomal internal transcribed spacer (ITS) and chloroplast trnL-F DNA, Renealmia is shown to be monophyletic with high branch support. Low sequence divergence found in the two genome regions (ITS: 0-2.4%; trnL-F: 0-1.9%) suggests recent diversification within the genus. Molecular divergence age estimates give further support to the recent origin of the genus and show that Renealmia has attained its amphi-Atlantic distribution by an oceanic long-distance dispersal event from Africa to South America during the Miocene or Pliocene (15.8-2.7 My ago). Some support is found for the hypothesis that speciation in neotropical Renealmia was influenced by the Andean orogeny. Speciation has been approximately simultaneous on both sides of the Atlantic, but increased taxon sampling is required to compare the speciation rates between the New World and Old World tropics.