The superficial resemblance of phylogenetic trees to other branching structures allows searching for macroevolutionary patterns. However, such trees are just statistical inferences of particular historical events. Recent meta-analyses report finding regularities in the branching pattern of phylogenetic trees. But is this supported by evidence, or are such regularities just methodological artifacts? If so, is there any signal in a phylogeny?
In order to evaluate the impact of polytomies and imbalance on tree shape, the distribution of all binary and polytomic trees of up to 7 taxa was assessed in tree-shape space. The relationship between the proportion of outgroups and the amount of imbalance introduced with them was assessed applying four different tree-building methods to 100 combinations from a set of 10 ingroup and 9 outgroup species, and performing covariance analyses. The relevance of this analysis was explored taking 61 published phylogenies, based on nucleic acid sequences and involving various taxa, taxonomic levels, and tree-building methods.
All methods of phylogenetic inference are quite sensitive to the artifacts introduced by outgroups. However, published phylogenies appear to be subject to a rather effective, albeit rather intuitive control against such artifacts. The data and methods used to build phylogenetic trees are varied, so any meta-analysis is subject to pitfalls due to their uneven intrinsic merits, which translate into artifacts in tree shape. The binary branching pattern is an imposition of methods, and seldom reflects true relationships in intraspecific analyses, yielding artifactual polytomies in short trees. Above the species level, the departure of real trees from simplistic random models is caused at least by two natural factors –uneven speciation and extinction rates; and artifacts such as choice of taxa included in the analysis, and imbalance introduced by outgroups and basal paraphyletic taxa. This artifactual imbalance accounts for tree shape convergence of large trees.
There is no evidence for any universal scaling in the tree of life. Instead, there is a need for improved methods of tree analysis that can be used to discriminate the noise due to outgroups from the phylogenetic signal within the taxon of interest, and to evaluate realistic models of evolution, correcting the retrospective perspective and explicitly recognizing extinction as a driving force. Artifacts are pervasive, and can only be overcome through understanding the structure and biological meaning of phylogenetic trees.
Catalan Abstract in Translation S1.
Citation: Altaba CR (2009) Universal Artifacts Affect the Branching of Phylogenetic Trees, Not Universal Scaling Laws. PLoS ONE4(2): e4611. https://doi.org/10.1371/journal.pone.0004611
Editor: Robert DeSalle, American Museum of Natural History, United States of America
Received: September 17, 2008; Accepted: January 21, 2009; Published: February 26, 2009
Copyright: © 2009 Altaba. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The author has no support or funding to report.
Competing interests: The author has declared that no competing interests exist.
The quest for the Holy Grail inspired great deeds of all sorts, with little use in the end. A current parallel is the search for the Tree of Life, which written in capitals appears to have a Biblical dimension. Indeed, its mythology includes the notion that in such tree one could reach an understanding of life's diversification in the planet. It is thus not too surprising that its search has fired long, acrimonious polemics on the “right” path to truth, eventually looking more like religious wars in the quest of an unattainable dream than scientific arguments in search of the best approximation to reality. Nowadays the field of phylogenetics is healthily moving away from such confrontations, focusing instead in far more fertile avenues of research. However, the temptation of finding in phylogenetic trees the essence of life remains in the eyes of converts.
The superficial resemblance of phylogenetic trees to real branching structures, such as real trees  and rivers , is at the origin of the quest for general patterns in the shape of phylogenies. Such possibility is indeed intriguing –if this idea had any validity, it should be possible to look for a grand unifying theme in the history of life. Along this line of thought, three recent meta-analyses report to have found regularities in the shape of phylogenetic trees –, leading to claims that random models of evolution may explain life's diversification , as suggested by early studies , or even that there is a “universal scaling in the branching of the Tree of Life”, which would imply that “similar evolutionary forces drive diversification across the broad range of scales” . If this was true, it would indeed be a remarkable finding.
Evolution surely involves linear relationships from parents to offspring, and thus from ancestor to descendant. In order to depict such relationships in print, two-dimensional diagrams are customarily employed, called phylogenetic trees. Thus it seems logical to analyze these trees in order to address macroevolutionary questions , –. It is also possible to search for correlates of hierarchical dendritic structures and their properties, such as the relationship between fractal river basins and neutral models of the fish communities inhabiting them . Thus, the geometry of phylogenetic trees deserves indeed a detailed study , .
However, phylogenetic trees are not real structures. They are almost certainly flawed reconstructions of historical events . Moreover, these trees are just statistical inferences . And most critically, they are calculated without seeking for universal laws and regularities, but instead with the goal of reconstructing particular historical events . It is therefore essential to understand that not all phylogenetic trees have the same value, because they are complex hypotheses. The information content of a such a tree critically depends on at least three points: 1) the quality and quantity of information upon which it is based; 2) the validity of the method used to infer historical relationships; and 3) the fit of the inferred tree to the data. Thus, the worth of a particular phylogenetic tree may range from trivial to substantial, and its accuracy from mere guess to robust hypothesis. A straightforward conclusion is that any meta-analysis of phylogenetic trees performed with no control over their intrinsic merit is subject to severe pitfalls.
In this context, the reported finding of a universal regularity in phylogenetic trees stems from a radical confusion of reality and diagram. Herewith I refute such claims, on the basis that they are based solely on artifact. The idea of universal scaling in phylogenies is completely unwarranted, being instead a consequence of bias in principles and methods. Further developments in the analysis of phylogenetic tree shape should avoid the artifact pitfalls, correcting distortions and reading the paramount signature of biological processes.
The distribution of all possible trees in the space defined by A and C is not random (Fig. 1). All possible trees occur between the bounds imposed by the least and most structured possibilities –fully unresolved and pectinate, respectively. This is an intuitive result, but is relevant because only a small sector of the graph is actually occupied by trees (the remaining regions of the space represent network graphs that are not trees). Trees including polytomies (non-binary, or unresolved) occur throughout this sector. In contrast, all binary trees are bound by a lower limit representing symmetrical trees –i.e., all fully resolved trees lye between two limits: an upper, most structured limit, and a lower one representing average random trees. Thus, any tree located below the symmetrical tree expectation must include at least one polytomy.
All trees of up to 7 terminal taxa are shown. Solid symbols indicate binary trees, empty symbols stand for non-binary trees. Ellipses encompass all trees with the same number of terminal taxa (n). The lines are the interpolated expectation for three kinds of trees (the 4-taxa examples shown at right): totally symmetrical, random average (middle); pectinate, most imbalanced (top); and totally unresolved, trivial (bottom). The space actually occupied by all trees is limited by the upper and lower bounds. All binary (fully resolved) trees occur at or above the limit imposed by symmetrical trees. Only trees including at least one polytomy (non-binary, or unresolved) occur below this limit.
The relationship between branch size (A) and cumulative branch size (C) for two analyzed phylogenetic trees (Fig. 2) is shown in Figure 3. At small branch sizes (A<101), the data can hardly be distinguished from this expectation, largely due to the narrow band available for small trees. Within a large intermediate section (roughly, 101<A<102) the real data are mostly above the symmetrical tree line and span through most of the binary-tree area, indicating that imbalance ranges from null to extreme throughout these real trees. This surely occurs in virtually all real cases, because extinction and unequal rates of speciation occur in the real world and will prevent build-up of perfectly balanced trees. The symmetrical tree (or random model) is thus a baseline useful to measure the degree of imbalance, but cannot be taken as a null model because it represents an unreasonable scenario.
Fig. 2). Each data point represents a node. Notice the logarithmic scale on both axes. Open circles show data for tree A, solid dots stand for tree B. The diagonal line is the interpolated expectation from a random average, totally symmetrical tree. Arrows point at below-expectation values belonging to multifurcations. The dotted circle encloses rapidly diverging values belonging to outgroup and basal paraphyletic taxa.
The few data points below the diagonal (indicated by arrows) represent trifurcations in both trees. These non-bifurcating nodes indicate unresolved nodes, the tree-building algorithm being unable to select one of two or more competing hypothesis about binary branching pattern for the three lineages involved. These three-stem nodes are not hypotheses of real multifurcation, being instead purely artifactual.
Near the basal stem of the real trees (roughly, A≥102) the values of C conspicuously take off, showing that initial branching is most unbalanced in both trees. These deviating, extreme values represent outgroup and non-monophyletic basal taxa. Outgroups are non-arachnid chelicerates (Pycnogonida and Xiphosura) in tree A, and non-pectinids (Limidae, Propeamusiidae and Spondylidae) in tree B. Basal taxa that turn out to be non-monophyletic are the polyphyletic Acari in tree A (highlighted in pink), and the paraphyletic Limidae (blue), Propeamusiidae (green) and Aequipectinini (purple) in tree B. Given that the outgroups were chosen from distantly related taxa, and that poorly defined basal taxa are a heritage of pre-cladistic taxonomy, the deviating values near the root of both phylogenetic trees are just a consequence of method, and are thus purely artifactual.
The resolution provided by the combined use of A and C is not optimal. The value of C is sensitive to the level at which imbalance and polytomies occur. Also, different trees often have the same pair of values. Moreover, both analyzed real trees yield similar scatter plots, in spite of being quite different.
The 100 combinations of ingroup and outgroup taxa analyzed with four different tree-building methods yielded a non-random relationship between outgroups and the imbalance introduced by these (Fig. 4). The regression of tree imbalance (as measured by log ingroup imbalance) on the proportion of outgroups is highly significant for all four methods, as well as for the whole set of trees (Table 1). However, the regression coefficient ranges from low to moderate, given the wide dispersion of data points. Likewise, the regression slope also varies widely among subsets. The lowest values of r2 and slope are provided by the Bayesian trees, a reflection of their sensitivity to outgroup selection and their tendency to have high node support. At the opposite end, maximum parsimony yields the highest scores for r2 and slope, showing the comparative robustness of this method against variations in the outgroups chosen –parsimony uses outgroups basically to determine character-state polarity. Maximum likelihood and distance methods stand at mid range, probably due to the more algorithm-dependent ways in which they work. Taking all 400 trees together also yields intermediate values, as a result of averaging over the four methods. Pairwise covariance analyses among the four methods show that maximum likelihood and distance regressions are not significantly different, while maximum parsimony and Bayesian are distinct (Table 2).
Linear regressions are shown for each tree-building method, and for the whole set of 400 trees (thick black line). BA = Bayesian, ML = maximum likelihood, MP = maximum parsimony, NJ = BIONJ distance method.
The imbalance attributable to outgroups in published phylogenetic trees shows a wide dispersion (Fig. 5). Linear regressions are not significant for maximum parsimony, maximum likelihood and distance-based trees, due to the extreme dispersion of data points. For Bayesian trees, a moderate relationship exists (y = −0.0634x+0.0437, r2 = 0.396, P<0.05), but this is probably a spurious result stemming from two artifacts –this method's sensitivity even when few outgroups are included, and the lack in this subset of trees with a high proportion of outgroups. Taking the whole set of published trees, a weak linear regression was found (y = −0.0186x+0.0259, r2 = 0.077, P<0.05). However, all values of log outgroup imbalance are normally distributed (mean = 0.0148, s.d. = 0.0436, AD = 0.543, P = 0.157), suggesting the existence of a constraining factor that keeps real trees close to a situation of null impact of outgroups on tree balance. Although most analyses have few outgroups and these appear to have a low, mostly positive impact on tree balance, values are mostly negative roughly between outgroup proportions around 1 and 2, and above 2 the few data points are close to zero. This suggests a non-linear relationship. Indeed, a quadratic regression (y = 0.0144x2−0.0554x+0.0366, r2 = 0.115, P<0.05) appears to be slightly better for all published trees. This curvilinear regression suggests that the constraining factor is particularly intense when outgroups clearly outnumber ingroup taxa.
The distressing point from the comparison of different methods of phylogenetic inference is that all of them are quite sensitive to the artifacts introduced by outgroups. The differences among trees obtained with different methods are minor, and appear to be largely related just to the idiosincracy of algorithms. The good news, however, is that published phylogenetic trees appear to be under a remarkable, unexpected constraint. The constraining factor is most likely the fact that practicing taxonomists appear to be generally (and rather intuitively) aware of these artifacts, so they tend to choose carefully the array of outgroup taxa. A corollary of this is that there is no hope for any brute-force meta-analysis performed without consideration of what phylogenetic trees really mean and how they are obtained. A second consequence of this finding is that there is a wide open field for designing formal ways to discriminate the noise due to outgroups from the phylogenetic signal within the taxon of interest. The methods presented here and the following discussion may provide some guide.
Not all phylogenetic trees are equally valid –in fact, there are huge differences in their robustness or support. This variable extent and reliability of phylogenetic hypotheses translates into artifacts in tree shape. For example, poor quality data introduce noise that results in increased imbalance –. Likewise, tree size does have an impact, because real large trees tend to approach a predictable, moderate level of imbalance . These problems can be circumvented in part because tree shape and fit to the data appear to be unrelated , and there is at least one measure of imbalance that is independent of tree size . Without being aware of these problems and how to treat them, one may gather a bewildering array of grossly dissimilar trees. Thus, having no control over what different trees mean surely will reduce any possibility of finding common rules.
The three meta-analyses – were based on TreeBASE (http://www.treebase.org), a searchable, archival repository of data and scientific references , which can be explored by statistical packages designed to perform large-scale analyses of tree shape . Only binary trees were included in , while polytomies were resolved under a random model in . In order to ensure “testing the universality of the results derived across scales”, thousands of cladograms and a few dozen “intraspecific phylogenies” were compiled in . This sampling was totally uncritical, aimed at amassing a bulk of different trees. Moreover, it was partially manual, although simply taking numerous trees with no selection criterion from the literature or from a repository database should yield virtually identical results. Basically, the problem is that it is unclear whether adding numerous hypotheses with an unknown degree of uncertainty may yield a credible global answer.
Resolving phylogenetic trees into perfectly dichotomous branching patterns is a general goal in phylogenetics . However, as any approach that imposes structure on the data, bifurcations are an imposition of method, not necessarily a reality –. All tree-building methods will force a binary tree on the data, but it has seldom been tested at what point of the analysis the conclusions might stretch beyond the assumptions, and thus at what level of detail it would be warranted to stop . One such limitation involves short interior branches (i.e., fast evolutionary radiations), which may be even more prone to error in reality than predicted by theoretical studies . Actually, it may not be really necessary to resolve a multifurcation “bush” (i.e., non-binary splits, or polytomies) in rapidly branching parts of a tree, because the temporal information encoded in that unresolved topology may be more relevant than the detailed sequence of bifurcations . Another overstretching of methods occurs because above species level multifurcations that surely exist in evolution will always tend to be split. A justification may be that it is easier to work on a strictly binary set of nodes, although it is already possible to deal with polytomies in trees . Ideally, the assumptions of systematists should be in agreement with those underlying tree-building algorithms . However, even if there is a real dichotomous structure in the data, unresolved nodes will often occur mostly at or near the terminal branches, because the data analyzed are usually gathered with the goal of resolving mostly the intermediate taxonomic levels considered, and thus may not allow discriminating among very similar terminal taxa. Thus, the best resolution is generally in the middle of published trees. One must bear in mind that awfully unresolved trees are seldom published. Also, it is in the central area that the researcher's interest was in the first place. This explains departures from expected values in the left part of Fig. 3. It is also a good reason to prefer analyses in the tree space defined by A and C, given that it includes polytomous trees.
The artifactual nature of binary trees is most relevant at or below the species level. Species may be incompletely isolated due to recent or incomplete speciation, the pattern of speciation may not be a simple cladogenetic event but may be instead paraphyletic, hybridization may cause reticulate evolution, and sorting of ancestral polymorphisms may render gene trees incongruent with species trees , –. Toward the contemporary tips of a phylogenetic tree, resolution is subject to the delimitation of species, a complex and often arbitrary issue that is not part of the phylogenetic inference process; eventually, recognizing the distinctiveness of individual taxa becomes problematic, because recent and incipient speciation may be difficult to identify , . Even more problematic is portraying intraspecific variation as a branching tree. Within a species there is gene flow, so gene trees will most rarely be amenable to be translated directly into a history of population subdivision. It would be more meaningful to ask in the first place if there is an inherent hierarchical structure in data . Actually, the clustering of subpopulations and the comparison of trees for different genes are by no means simple tasks, and dichotomous branching ordinations are just a small part of the methods available . However, being aware of their meaning, they can be powerful tools in combination with other approaches to deal with intraspecific data , . It is obvious that trees of intraspecific variation are actually simplified sketches, and thus have a radically different nature than interspecific trees. Thus, the mixing of intraspecific and interspecific trees in  has no justification, and their claims of uniform branching pattern above and below the species level are simply an artifact of applying similar binary-tree-building methods to different biological questions. At any rate, the high prevalence of multifurcations that exists among intraspecific trees reflects the inadequacy of tree-building methods for reticulate data, and their finding of lower-than expected values of C at short branch lengths is solely an artifact.
The selection of trees is also a source of noise. In fact, different tree-building methods produce significantly different arrays of trees , . This precaution was not taken into account by , , who mixed trees obtained from various kinds of tree-building algorithms –some distance-based (neighbor-joining), some based on parsimony, and still others on maximum likelihood. The differences between these methods can be shown to be rather of “degrees of freedom” , , yet they are based on different assumptions and often yield different outcomes for the same data matrix (as shown in Fig. 4). Moreover, real-world deviations from theoretical simple models of evolution may easily produce artifactual phylogenetic reconstructions under the commonly used models of sequence evolution, and it is still unclear how to capture the historical signal with a minimum of parameters to be estimated from the data –. Also, trees may differ if calculated with a naïve one-step process, or are derived from an approach that seeks to compare trees and find an average final model ,  –even in simple 3-taxon cases, the outcome may differ strikingly, with substantial evolutionary implications . Thus it remains unclear why trees obtained with different methods from a variety of taxa should be mixed up with no control.
The value of a null model lies not in its mathematical elegance, but in its relevance to the question posed. On average, a totally balanced tree is also expected from Yule's equal-rates Markov model , , , but this kind of tree would be most unusual for any large set of real taxa. In the case of phylogenetic trees, null models based on random, increasing, balanced diversification ,  were only a reasonable early start. More elaborate stochastic models exhibit an enhanced approach to real trees , , but it is unclear whether there is any reason to prefer any such model beyond a rough fit to the data and the rejection of the overly simplistic Yule model. Clearly, more realistic models are needed that place randomness right where relevant variables impact the model's behavior , , –. From this viewpoint, it should come as no surprise the finding in all three meta-analyses – that the average imbalance of phylogenetic trees inferred from real data falls neatly in between extreme possibilities (i.e., the symmetric and pectinate trees in ; the random and uniform models in ; and random and pectinate trees in ).
The departure of real trees from random models can be caused at least by two major natural factors, and two artifacts. The first natural factor is simply that extinction does occur, so not all lineages can continue to divide at the specified rate. As lineages go extinct along a tree, its imbalance will almost inevitably increase. This is a consequence of extinction being the outcome of complex dynamics, so it is not reasonable to expect that it should remain stable across the tree. The second natural deviating factor is that diversification rates will surely vary across the different branches of the tree over time, because it is a complex function of a plethora of intrinsic and environmental factors operating on living organisms. Several methods have been devised to estimate absolute rates of speciation and extinction, showing that large variation in those parameters is the rule –. Indeed, balanced random processes are too slow to account for most patterns of observed diversity, yet diversification is subject to complex environmental constraints , . A reflection of such complexity is likely to result in autocorrelation of diversification rate along lineages . Thus, real phylogenies should be expected to range throughout all possible topologies, with no reasonable way of a priori delimiting tree space.
Aside from real-world issues, the two major artifacts that increase imbalance are related to the taxa included in the analysis. On one hand, all known taxa from a given group are rarely included, so some choice has to be made. Often this may be imposed by the availability of samples. However, it may be difficult to know whether species have been removed from the analysis deliberately and selectively . And including selected species from high-rank taxa may cause problems of two sorts. Actually, real trees are quite imbalanced, and more so if the taxa are above the species level . In addition, such large branches will inevitably result in underestimation of real change, and thus of long branch lengths. This is the pervasive node-density artifact, whose impact on tree shape is still unclear . At any rate, non-random taxon sampling will cause errors in estimates of speciation and extinction rates, more so than just incomplete taxon sampling , . Indeed, the inclusion of evolutionarily isolated species may affect synthetic measures of phylogenetic trees .
On the other hand, outgroups (used to place the root of the tree) are a definite source of imbalance. At the highest taxonomic levels considered, C has higher-than-expected values, indicating that long branches tend to be more pectinate. But this is due to the inclusion of selected taxa from progressively more distantly related lineages. This is routinely done in order to provide various outgroups. This is justified because, based on sampling theory, the more dense the sampling of outgroup taxa, the more stable the internal topology will be and the stronger the test for the monophyly of the ingroup , . Being clear that outgroup taxa significantly contribute to an excess of imbalance , , , there is a motive for removing outgroups from tree analysis , . Unfortunately, the outgroup taxa are often not displayed in the published trees, and it is frequent that more outgroups are included than those explicitly identified as such. Actually, outgroups often involve more than just the first low-diversity branch, or the usual basal one or two single-species branches. In some instances, such as in tree A (Fig. 2), a priori outgroups turn out not to be the branches closest to the root, making any automated identification and deletion of outgroups highly suspect. This problem is exacerbated if the basal taxa turn out to be paraphyletic , because they will appear as pectinate long branches. The two trees analysed in detail (Fig. 3) show several basal branches that belong to outgroups that are revealed to be paraphyletic. Actually, higher taxa that have traditionally been considered as basal to other higher-order taxa often turn out to be paraphyletic when subject to cladistic evaluation –the Acari, Limidae, Propeamussiidae and Aequipectinini are likely candidates to join the club of outfashioned, unnatural groups such as the Protobranchia, Reptilia, and Pongidae. Without a proper identification of outgroup taxa, coupled to a taxonomic assessment of any basal paraphyletic taxa, it is very hard to control for the pervasive artifact of imbalance increasing at the highest taxonomic levels of published trees. Therefore, the reported findings of imbalance increasing at large tree sizes stems from this control being insufficient in  and just missing in , and thus appears to be totally caused by the outgroup and basal paraphyly artifacts.
Various tree-shape statistics have been divised, whose merits vary widely. Most of these methods extract a single summary index from the distribution of nodes, so it's not too surprising that the majority of such measures of tree shape are sensitive to the level, or depth in the phylogeny at which imbalance is concentrated ,  and to the presence of polytomies . As summarized in Fig. 1, C suffers from these same shortcomings. Focusing instead on the dispersion of node traits in a bidimensional plot aims at capturing more of the tree's features , although interpretation of such analysis is also difficult , . Likewise, estimates of the alpha model fail to adjust extreme tree shapes and often yield a zero value , thus being also hard to interpret. As shown above, the relationship between A and C can be used to locate and explain imbalance in the different regions of a given tree, even if there are polytomies. The drawbacks of this method are that it does not have optimal resolution because different trees yield identical values, and all trees are constrained within a small sector of geometric space, so even quite distinct trees will yield similar plots. Nevertheless, it is clear that the two phylogenies in Fig. 2 have quite different shape, yet are translated into overall similar plots in Fig. 3. It is also relevant to notice that these two parameters can be used to design meaningful measures (such as log outgroup imbalance) of the impact of outgroups (and possibly other artifacts) in tree space. Thus, the uniform relationship among branch size A and cumulative branch size C is due to a narrow design of methods, not a quality of results.
A third avenue is to compare trees strictly in terms of what they are –high-dimensional parameters amenable to geometrical depictions in ultrametric space . Actually, ultrametrics have been successfully applied to a variety of questions where data have a hierarchical structure , , . This perspective allows the exploration of geometric space , , , without relying on simulations, and leading to the application of statistical methods . It is thus possible to develop a measure of resolution for different tree-shape statistics, and thus select those statistics that have similar values only for similar trees . The analysis shown in Fig. 1 is a step in this direction, pointing at further developments in generalized tree shape distribution.
However, there is a critical caveat to any analysis of the shape of phylogenetic trees. Our perspective being inevitably from the present, extant diversity always appears to come out of a burst from a distant single stem . Virtually all real trees will have a rather “conical” shape, due to the fact that the recent splits considered are many more than old surviving lineages. Including extinct taxa should help in correcting this retrospective illusion, but the incompleteness of the fossil record will always play against such correction. But this leads to a second obstacle, which is related but more difficult to tackle –what exactly are fossil taxa that are basal to later diversification. In an orthodox cladistic framework, such an extinct species will always be treated as the sister group of all later branches, provided the traits of later taxa can be inequivocally identified in their earliest stages. Now, this methodological shortcut may not always provide an accurate description of reality, our placing of those early stems, or “species germinalis”, being strongly dependent on later evolution that is only apparent from our contemporary point of view . Clearly there is a challenge to develop methods for correcting our “convex from the present” view of phylogenetic trees prior to analysis of their actual shape and information content.
In spite of grand declarations, the Darwinian goal of classifying organisms in terms of their relationships of common descent has powered evolutionary research and is at the root of the field of phylogenetics. There is really nothing like universal scaling in phylogenetic trees –and no good reason why it should exist. We are dealing with attempts to understand history , thus a phylogenetic tree is only a diagram of a complex irreversible process. In this sense, the linking of TreeBASE to databases providing information on the taxa actually included in each analysis  is a valuable addition that should help in assessing the significance and merits of each tree before including it in any meta-analysis. Beyond failures based on unreasonable assumptions and oversimplistic paradigms, the wealth of information encoded in phylogenetic trees is there to be deciphered. However, this will not happen with any uncontrolled meta-analysis, but only through an integration of population genetics, ecology, paleontology, and graph theory. Artifacts pave the way, and they can only be overcome with an understanding of the structure and biological meaning of phylogenetic trees.
Exploring the geometry of unlabeled trees with constant internodal distances represents only an initial approach. It is critical to notice that taking tree topologies alone explicitly disregarding any time scale has the implicit problem of obviating extinction. Actually, time on a phylogeny does matter, at least because individual branch lengths actually are estimates of different processes depending on where they are located within the tree. Towards the terminal taxa, individual branch lengths estimate the inverse of the speciation rate, but at the basal regions they rather estimate the inverse of the diversification rate, being the difference between the speciation and extinction rates –. It may even be possible to distinguish decreasing speciation from increasing extinction in early evolutionary radiations . This is relevant to methods such as the lineage-through-time approach , , which ignores extinct lineages and is thus sensitive to the effects of poor sampling of taxonomic diversity, as well as to its intrinsic inability to distinguish reduced extinction and enhanced speciation . Although the variability of branch lengths in real trees can be used to test hypothesis about evolutionary rates , , precise estimation of these rates requires large phylogenetic trees , and it is still unclear how to assess in general the impact of disappearing lineages on the shape of phylogenetic trees. Although it is episthemologically impossible to read directly the empty space left by vanished taxa, the contribution of missing branches to the observed patterns remains as a signature to be deciphered. Eventually, it is the biological phenomenon of extinction that imposes an ultrametric structure on phylogenetic trees, because the unavoidable disappearance of interfertile individuals and intermediate taxa throughout life's history sets apart the surviving lineages and promotes the growth of biodiversity.
Materials and Methods
All rooted, unlabeled trees consisting of up to 7 terminal branches (unnamed taxa) were enumerated, separating binary (fully resolved) trees from those having at least one polytomy (i.e., having one unresolved node). Among the variety of indices devised to sumarize tree shape, the values of branch size (the number of subtaxa from a given node, A) and cumulative branch size (the sum of the sizes of all branches from a given node, C), the two variables measured in , were manually calculated for each tree. In order to explore the distribution of all trees in an A vs. C plot (Fig. 1), these values were calculated also for three series of trees: perfectly symmetrical trees, which are expected on average from a purely random branching process; pectinate trees, which are most imbalanced; and totally unresolved trees, being the trivial bottom-line with one single node. Each series was drawn as a line; this is a continuous interpolation that allows drawing a simple limit in this tree space .
Two data-rich phylogenetic trees were selected from recent literature: Fig. 7 in , and Fig. 1 in . They belong to different phyla (Arthropoda and Mollusca) and different environments (terrestrial and marine, respectively). Both include only distinct species (i.e., there are only undisputed individual terminal branches), are relatively large (≥60 terminal taxa), include several outgroups and non-monophyletic basal taxa, are the product of excellent scholarship on DNA sequences, and are considered by their authors as working hypotheses likely to change with the inclusion of further evidence. They are shown in Figure 2, redrawn in order to depict only their topology. Tree A is more balanced near the terminal taxa, while tree B is more balanced near the root. The values of A and C were calculated for all subtrees in both trees. A log-log plot of A vs. C was drawn in order to show deviations from the symmetrical tree expectation (Fig. 3).
In order to explore the variation in the relationship between A and C in relation to the proportion of outgroups included in phylogenetic analyses, different tree-building methods were applied to various combinations of a given set of ingroups and outgroup taxa. The aminoacid sequences included in this analysis belong to the AAA (ATPases Associated with a wide variety of cellular Activities) protein (either replication factor C small subunit, or DNA polymerase III gamma subunit), introduced as example in the Phylogeny.fr  data window (viruses excluded): 10 eukaryots considered as ingroup taxa, and 9 prokaryots (4 Eubacteria and 5 Archaea) taken as outgroups. The species considered are (followed by accession number in the Entrez database: http://www.ncbi.nlm.nih.gov/sites/entrez?dbprotein): Plasmodium chambaudi (XP_745209), Trypanosoma brucei (XP_829019), Dictyostelium discoideum (XP_629875), Schizosaccaromyces pombe (NP_593121), Ustilago maydis (XP_756876), Arabidopsis thaliana (NP_176504), Caenorhabditis elegans (NP_500069), Anopheles gambiae (XM_308395.4), Strongylocentrotus purpuratus (XP_790650), Homo sapiens (NP_002905), Aquifex aeolicus (NP_214275), Polaribacter irgensii (ZP_01118896), Ehrlichia ruminantium (YP_196867), Neisseria meningitidis (NP_284372), Methanosarcina acetivorans (NP_615630), Haloarcula marismortui (YP_137064), Halobacterium species NRC-1 (NP_280914), Methanosphaera stadtmanae (YP_447457), and Methanospirillum hungatei (YP_502463). A total of 100 combinations of ingroup and outgroup taxa were selected, spanning throughout all possible values of the ingroup/outgroup ratio. For each combination of taxa, an independent analysis was performed using the Phylogeny.fr platform (http://www.phylogeny.fr). Sequences were aligned with MUSCLE , and phylogenetic trees were estimated through four different methods: Bayesian approach using MrBayes (ver. 3.1.2)  with GTR option for substitution types, invariable and gamma rate variation across sites; maximum likelihood using PhyML (ver. 3.0 aLRT) , ; maximum parsimony as implemented in TNT (ver. 1.1) with sectorial search and tree fusing , ; and distance analysis using BIONJ . The Bayesian analyses included a Monte Carlo Markov Chain with 10,000 generations, sampling a tree every 10 generations, and discarding the first 250 trees sampled as burn-in. The other three methods involved 100 bootstrap replicates, yielding strict consensus trees. Nodes with support values below 50% were collapsed. The root was placed between the Archaea and the Eubacteria (or in rare cases the group formed by these and one archaeon). Values of A and C were calculated manually for each of the 400 resulting trees and their ingroup set. The difference in the C/A ratio (taking logarithmic values) between the whole tree and after deleting the outgroups is called log outgroup imbalance, and is a measure of the change in relative position within the tree space defined by these two variables (shown in Fig. 2). Thus, a positive value means a steeper position of the whole tree relative to the ingroup set for the position in that tree space, due to a positive contribution of the outgroups to tree imbalance. A negative value means a drop in relative position when outgroups are considered, meaning that outgroups actually decrease tree imbalance. The values of log outgroup imbalance were plotted against the relative proportion of outgroups in the dataset (Fig. 4). Linear regressions were calculated for the whole set of 400 trees, and separately for those obtained by each tree-building method. These regressions were compared pairwise through analyses of covariance.
In order to test whether the relationship found occurs in other datasets, a total of 61 published phylogenies (including the two already analyzed) were selected (Table 3) –. This is an explicitly ecclectic selection of studies, based on the variety of my interests and readings. It is no more arbitrary than a random download from a database of phylogenetic trees, and no less rigorous than a well-posed query to it –actually it is more reliable because trees were selected only after scrutiny of the actual papers where they have been published. The species involved span throughout a wide variety of eukaryots, and the supraspecific ingroup taxa range from a single genus to a whole class. The data are only nucleic acid sequences, and the period of publication is the last 11 years. Most papers provided one tree, although in several instances the same dataset was analyzed with different methods, and different methods are sometimes applied to different datasets. Thus, every tree sampled is taken as independent. Only species-level taxa were considered; thus whenever populations belonging to the same (sub)species represented different branches these were united. Nodes with support values below 50% were collapsed. In all cases, the outgroups were those actually included in the analysis –this is often clear in the illustrated phylogenetic trees, but in a few papers it is only evident in the text. Values of A and C were calculated manually for each of the 400 resulting trees and their ingroup set, and log outgroup imbalance was plotted against the relative proportion of outgroups in the dataset (Fig. 5). The fit of all these log outgroup imbalance values to a normal distribution was tested with the Anderson-Darling goodness-of-fit statistic. Linear and quadratic regressions were calculated for the whole set of published trees, as well as for subsets of trees obtained with different methods.
The Phylogeny.fr platform (including the TNT program) was used thanks to its availability in the web through CNRS and the Willi Hennig Society. Robert DeSalle and an anonymous reviewer provided most useful comments on the manuscript.
Conceived and designed the experiments: CRA. Performed the experiments: CRA. Analyzed the data: CRA. Contributed reagents/materials/analysis tools: CRA. Wrote the paper: CRA.
- 1. Pluciński M, Pluciński S, Rodríguez-Iturbe I (2008) Consequences of the fractal architecture of trees on their structural measures. Journ Theoret Biol 251: 82–92.M. PlucińskiS. PlucińskiI. Rodríguez-Iturbe2008Consequences of the fractal architecture of trees on their structural measures.Journ Theoret Biol2518292
- 2. Rodriguez-Iturbe I, Rinaldo A (1997) Fractal river basins: chance and self organization. New York: Cambridge University Press. I. Rodriguez-IturbeA. Rinaldo1997Fractal river basins: chance and self organizationNew YorkCambridge University Press564
- 3. Ford DJ (2005) Probabilities on cladograms: introduction to the alpha model. DJ Ford2005Probabilities on cladograms: introduction to the alpha model.arXiv:math/0511246v1. arXiv:math/0511246v1.
- 4. Blum MG, François O (2006) Which random processes describe the Tree of Life? A large-scale study of phylogenetic tree imbalance. Syst Biol 55: 685–691.MG BlumO. François2006Which random processes describe the Tree of Life? A large-scale study of phylogenetic tree imbalance.Syst Biol55685691
- 5. Herrada EA, Tessone CJ, Klemm K, Eguíluz VM, Hernández-García E, et al. (2008) Universal Scaling in the Branching of the Tree of Life. PLoS ONE 3(7): e2757.EA HerradaCJ TessoneK. KlemmVM EguíluzE. Hernández-García2008Universal Scaling in the Branching of the Tree of Life.PLoS ONE3(7)e2757DOI:10.1371/journal.pone.0002757. DOI:10.1371/journal.pone.0002757.
- 6. Gould SJ, Raup DM, Sepkoski JJ, Schopf TJM, Simberloff D (1977) The shape of evolution: comparison of real and random clades. Paleobiology 3: 23–40.SJ GouldDM RaupJJ SepkoskiTJM SchopfD. Simberloff1977The shape of evolution: comparison of real and random clades.Paleobiology32340
- 7. Sanderson MJ, Donoghue MJ (1996) Reconstructing shifts in diversification rates on phylogenetic trees. Trends Ecol Evol 11: 15–20.MJ SandersonMJ Donoghue1996Reconstructing shifts in diversification rates on phylogenetic trees.Trends Ecol Evol111520
- 8. Mooers AØ, Heard SB (1997) Inferring evolutionary process from phylogenetic tree shape. Quart Rev Biol 72: 31–54.AØ MooersSB Heard1997Inferring evolutionary process from phylogenetic tree shape.Quart Rev Biol723154
- 9. Chan KMA, Moore BR (2002) Whole-tree methods for detecting differential diversification rates. Syst Biol 51: 855–865.KMA ChanBR Moore2002Whole-tree methods for detecting differential diversification rates.Syst Biol51855865
- 10. Felsenstein J (2003) Inferring phylogenies. Sunderland, Massachusetts: Sinauer Press. J. Felsenstein2003Inferring phylogeniesSunderland, MassachusettsSinauer Press664
- 11. Chan KMA, Moore BR (2005) SymmeTREE: whole-tree analysis of differential diversification rates. Bioinformatics 21: 1709–1710.KMA ChanBR Moore2005SymmeTREE: whole-tree analysis of differential diversification rates.Bioinformatics2117091710
- 12. Simon C, Page R (2005) The past and future of systematic biology. Syst Biol 54: 1–3.C. SimonR. Page2005The past and future of systematic biology.Syst Biol5413
- 13. Harvey PH, Holmes EC, Nee S (2005) Model phylogenies to explain the real world. BioEssays 16: 767–770.PH HarveyEC HolmesS. Nee2005Model phylogenies to explain the real world.BioEssays16767770
- 14. Matsen FA (2006) A geometric approach to tree shape statistics. Syst Biol 55: 652–661.FA Matsen2006A geometric approach to tree shape statistics.Syst Biol55652661
- 15. Bortolussi N, Durand E, Blum M, François O (2006) apTreeshape: statistical analysis of phylogenetic tree shape. Bioinformatics 22: 363–364.N. BortolussiE. DurandM. BlumO. François2006apTreeshape: statistical analysis of phylogenetic tree shape.Bioinformatics22363364
- 16. Drummond AJ, Ho SYW, Phillips MJ, Rambaut A (2006) Relaxed phylogenetics and dating with confidence. PLoS Biol 4(5): e88.AJ DrummondSYW HoMJ PhillipsA. Rambaut2006Relaxed phylogenetics and dating with confidence.PLoS Biol4(5)e88DOI: 10.1371/journal.pbio.0040088. DOI: 10.1371/journal.pbio.0040088.
- 17. Ricklefs RE (2007) Estimating diversification rates from phylogenetic information. Trends Ecol Evol 22: 601–610.RE Ricklefs2007Estimating diversification rates from phylogenetic information.Trends Ecol Evol22601610
- 18. Phillimore AB, Price TD (2008) Density-dependent cladogenesis in birds. PLoS Biol 6(3): e71.AB PhillimoreTD Price2008Density-dependent cladogenesis in birds.PLoS Biol6(3)e71DOI:10.1371/journal.pbio.0060071. DOI:10.1371/journal.pbio.0060071.
- 19. Muneepeerakul M, Bertuzzo E, Lynch HJ, Fagan WF, Rinaldo A, et al. (2008) Neutral metacommunity models predict fish diversity patterns in Mississippi–Missouri basin. Nature 453: 220–222.M. MuneepeerakulE. BertuzzoHJ LynchWF FaganA. Rinaldo2008Neutral metacommunity models predict fish diversity patterns in Mississippi–Missouri basin.Nature453220222
- 20. Billera LJ, Holmes SP, Vogtmann K (2001) Geometry of the Space of Phylogenetic Trees. Adv Appl Math 27: 733–767.LJ BilleraSP HolmesK. Vogtmann2001Geometry of the Space of Phylogenetic Trees.Adv Appl Math27733767
- 21. Holmes S (2003) Statistics for phylogenetic trees. Theoret Pop Biol 63: 17–32.S. Holmes2003Statistics for phylogenetic trees.Theoret Pop Biol631732
- 22. Vogt L (2008) The unfalsifiability of cladograms and its consequences. Cladistics 24: 62–73.L. Vogt2008The unfalsifiability of cladograms and its consequences.Cladistics246273
- 23. Steel M, Dress A, Bockner S (2000) Some simple but fundamental limits for supertree and consensus tree methods. Syst Biol 42: 363–368.M. SteelA. DressS. Bockner2000Some simple but fundamental limits for supertree and consensus tree methods.Syst Biol42363368
- 24. Giribet G, Edgecombe GD, Wheeler WC, Babbitt C (2002) Phylogeny and systematic position of Opiliones: a combined analysis of Chelicerate relationships using morphological and molecular data. Cladistics 18: 5–70.G. GiribetGD EdgecombeWC WheelerC. Babbitt2002Phylogeny and systematic position of Opiliones: a combined analysis of Chelicerate relationships using morphological and molecular data.Cladistics18570
- 25. Puslednik L, Serb JM (2008) Molecular phylogenetics of the Pectinidae (Mollusca: Bivalvia) and effect of increased taxon sampling and outgroup selection on tree topology. Molec Phylogenet Evol 48: 1178–88.L. PuslednikJM Serb2008Molecular phylogenetics of the Pectinidae (Mollusca: Bivalvia) and effect of increased taxon sampling and outgroup selection on tree topology.Molec Phylogenet Evol48117888
- 26. Mooers AØ (1995) Tree balance and tree completeness. Evolution 49: 379–384.AØ Mooers1995Tree balance and tree completeness.Evolution49379384
- 27. Huelsenbeck JP, Kirkpatrick M (1996) Do phylogenetic methods produce trees with biased shapes? Evolution 50: 1418–1424.JP HuelsenbeckM. Kirkpatrick1996Do phylogenetic methods produce trees with biased shapes?Evolution5014181424
- 28. Salisbury BA (1999) Misinformative characters and phylogeny shape. Syst Biol 48: 153–169.BA Salisbury1999Misinformative characters and phylogeny shape.Syst Biol48153169
- 29. Stam E (2002) Does imbalance in phylogenies reflect only bias? Evolution 56: 1292–1295.E. Stam2002Does imbalance in phylogenies reflect only bias?Evolution5612921295
- 30. Sanderson MJ, Donoghue MJ, Piel W, Eriksson T (1994) Tree-BASE: A prototype database of phylogenetic analyses and an interactive tool for browsing the phylogeny of life. Am Journ Bot 81: 183–189.MJ SandersonMJ DonoghueW. PielT. Eriksson1994Tree-BASE: A prototype database of phylogenetic analyses and an interactive tool for browsing the phylogeny of life.Am Journ Bot81183189
- 31. Rokas A, Carroll SB (2006) Bushes in the tree of life. PLoS Biol 4(11): e352.A. RokasSB Carroll2006Bushes in the tree of life.PLoS Biol4(11)e352DOI: 10.1371/journal. pbio.0040352. DOI: 10.1371/journal. pbio.0040352.
- 32. Maddison WP (1989) Reconstructing character evolution on polytomous cladograms. Cladistics 5: 365–377.WP Maddison1989Reconstructing character evolution on polytomous cladograms.Cladistics5365377
- 33. Hoelzer GA, Melnick DJ (1994) Patterns of speciation and limits to phylogenetic resolution. Trends Ecol Evol 9: 104–107.GA HoelzerDJ Melnick1994Patterns of speciation and limits to phylogenetic resolution.Trends Ecol Evol9104107
- 34. Murtagh F (2006) Identifying and exploiting ultrametricity. In: Decker R, Lenz HJ, editors. Advances in Data Analysis. Berlin: Springer. pp. 263–272.F. Murtagh2006Identifying and exploiting ultrametricity.R. DeckerHJ LenzAdvances in Data AnalysisBerlinSpringer263272
- 35. Whitfield JB, Lockhart PJ (2007) Deciphering ancient rapid radiations. Trends Ecol Evol 22: 258–265.JB WhitfieldPJ Lockhart2007Deciphering ancient rapid radiations.Trends Ecol Evol22258265
- 36. Sousa A, Zé-Zé L, Silva P, Tenreiro R (2008) Exploring tree-building methods and distinct molecular data to recover a known asymmetric phage phylogeny. Molec Phylogenet Evol 48: 563–573.A. SousaL. Zé-ZéP. SilvaR. Tenreiro2008Exploring tree-building methods and distinct molecular data to recover a known asymmetric phage phylogeny.Molec Phylogenet Evol48563573
- 37. Coddington JA, Scharff N (2005) Problems with “soft” polytomies. Cladistics 12: 139–145.JA CoddingtonN. Scharff2005Problems with “soft” polytomies.Cladistics12139145
- 38. Barraclough TG, Nee S (2001) Phylogenetics and speciation. Trends Ecol Evol 16: 391–399.TG BarracloughS. Nee2001Phylogenetics and speciation.Trends Ecol Evol16391399
- 39. Purvis A, Agapow P (2002) Phylogeny imbalance: taxonomic level matters. Syst Biol 51: 844–854.A. PurvisP. Agapow2002Phylogeny imbalance: taxonomic level matters.Syst Biol51844854
- 40. Wiemers M, Fiedler K (2007) Does the DNA barcoding gap exist? – a case study in blue butterflies (Lepidoptera: Lycaenidae). Frontiers Zool 4: 8.M. WiemersK. Fiedler2007Does the DNA barcoding gap exist? – a case study in blue butterflies (Lepidoptera: Lycaenidae).Frontiers Zool48DOI:10.1186/1742-9994-4-8. DOI:10.1186/1742-9994-4-8.
- 41. Weir JT (2006) Divergent timing and patterns of species accumulation in lowland and highland neotropical birds. Evolution 60: 842–855.JT Weir2006Divergent timing and patterns of species accumulation in lowland and highland neotropical birds.Evolution60842855
- 42. Sridhar S (2007) Algorithms for Analyzing Intraspecific Sequence Variation. Pittsburgh: PhD Thesis, Carnegie Mellon University. S. Sridhar2007Algorithms for Analyzing Intraspecific Sequence VariationPittsburghPhD Thesis, Carnegie Mellon Universityxvi+159
- 43. Wallace RG, Fitch WM (2008) Influenza A H5N1 Immigration Is Filtered Out at Some International Borders. PLoS ONE 3(2): e1697.RG WallaceWM Fitch2008Influenza A H5N1 Immigration Is Filtered Out at Some International Borders.PLoS ONE3(2)e1697DOI:10.1371/journal.pone.0001697. DOI:10.1371/journal.pone.0001697.
- 44. Heard SB, Mooers AØ (1996) Imperfect information and the balance of cladograms and phenograms. Syst Biol 45: 115–118.SB HeardAØ Mooers1996Imperfect information and the balance of cladograms and phenograms.Syst Biol45115118
- 45. Tuffley C, Steel M (1997) Links between maximum likelihood and maximum parsimony under a simple model of site substitution. Bull Math Biol 59: 581–607.C. TuffleyM. Steel1997Links between maximum likelihood and maximum parsimony under a simple model of site substitution.Bull Math Biol59581607
- 46. Steel M (2005) Should phylogenetic models be trying to ‘fit an elephant’? Trends Genet 21: 307–309.M. Steel2005Should phylogenetic models be trying to ‘fit an elephant’?Trends Genet21307309
- 47. Zhou Y, Rodrigue N, Lartillot L, Philippe H (2007) Evaluation of the models handling heterotachy in phylogenetic inference. BMC Evolutionary Biology 7: 206.Y. ZhouN. RodrigueL. LartillotH. Philippe2007Evaluation of the models handling heterotachy in phylogenetic inference.BMC Evolutionary Biology7206DOI: 10.1186/1471-2148-7-206. DOI: 10.1186/1471-2148-7-206.
- 48. Sumner JG, Charleston MA, Jermiin LS, Jarvis PD (2008) Markov invariants, plethysms, and phylogenetics. Journ Theoret Biol 253: 601–615.JG SumnerMA CharlestonLS JermiinPD Jarvis2008Markov invariants, plethysms, and phylogenetics.Journ Theoret Biol253601615
- 49. Altaba CR (1997) Phylogeny and biogeography of midwife toads (Alytes, Discoglossidae): a reappraisal. Contr Zool 66: 257–262.CR Altaba1997Phylogeny and biogeography of midwife toads (Alytes, Discoglossidae): a reappraisal.Contr Zool66257262
- 50. Harding EF (1971) The probabilities of rooted tree-shapes generated by random bifurcation. Adv Appl Probab 3: 44–77.EF Harding1971The probabilities of rooted tree-shapes generated by random bifurcation.Adv Appl Probab34477
- 51. Steel M, McKenzie A (2001) Properties of phylogenetic trees generated by Yule-type speciation models. Math Biosci 170: 91–112.M. SteelA. McKenzie2001Properties of phylogenetic trees generated by Yule-type speciation models.Math Biosci17091112
- 52. Mooers AØ, Harmon LJ, Blum MGB, Wong DHJ, Heard SB (2007) Some models of phylogenetic tree shape. In: Gascuel O, Steel M, editors. Reconstructing evolution: new mathematical and computational advances. New York: Oxford University Press. pp. 149–170.AØ MooersLJ HarmonMGB BlumDHJ WongSB Heard2007Some models of phylogenetic tree shape.O. GascuelM. SteelReconstructing evolution: new mathematical and computational advancesNew YorkOxford University Press149170
- 53. Ricklefs RE (2006) The unified neutral theory of biodiversity: do the numbers add up? Ecology 87: 1424–1431.RE Ricklefs2006The unified neutral theory of biodiversity: do the numbers add up?Ecology8714241431
- 54. Ricklefs RE (2006) Global variation in the diversification rate of passerine birds. Ecology 87: 2468–2478.RE Ricklefs2006Global variation in the diversification rate of passerine birds.Ecology8724682478
- 55. Hey J (1992) Using phylogenetic trees to study speciation and extinction. Evolution 46: 627–640.J. Hey1992Using phylogenetic trees to study speciation and extinction.Evolution46627640
- 56. Nee S, Mooers AO, Harvey PH (1992) Tempo and mode of evolution revealed from molecular phylogenies. Proc Natl Acad Sci U S A 89: 8322–8326.S. NeeAO MooersPH Harvey1992Tempo and mode of evolution revealed from molecular phylogenies.Proc Natl Acad Sci U S A8983228326
- 57. Heard SB (1996) Patterns in phylogenetic tree balance with variable and evolving speciation rates. Evolution 50: 2141–2148.SB Heard1996Patterns in phylogenetic tree balance with variable and evolving speciation rates.Evolution5021412148
- 58. Magallón S, Sanderson MJ (2001) Absolute diversification rates in angiosperm clades. Evolution 55: 1762–1780.S. MagallónMJ Sanderson2001Absolute diversification rates in angiosperm clades.Evolution5517621780
- 59. Bokma F (2003) Testing for equal rates of cladogenesis in diverse taxa. Evolution 57: 2469–2474.F. Bokma2003Testing for equal rates of cladogenesis in diverse taxa.Evolution5724692474
- 60. Paradis E (2003) Analysis of diversification: combining phylogenetic and taxonomic data. Proc R Soc Lond B Biol Sci 270: 2499–2505.E. Paradis2003Analysis of diversification: combining phylogenetic and taxonomic data.Proc R Soc Lond B Biol Sci27024992505
- 61. Nee S (2006) Birth-death models in macroevolution. Annu Rev Ecol Evol Syst 37: 1–17.S. Nee2006Birth-death models in macroevolution.Annu Rev Ecol Evol Syst37117
- 62. Rabosky DL (2006) Likelihood methods for detecting temporal shifts in diversification rates. Evolution 60: 1152–1164.DL Rabosky2006Likelihood methods for detecting temporal shifts in diversification rates.Evolution6011521164
- 63. Rabosky DL, Lovette IJ (2008) Explosive evolutionary radiations: decreasing speciation or increasing extinction through time? Evolution 62: 1866–1875.DL RaboskyIJ Lovette2008Explosive evolutionary radiations: decreasing speciation or increasing extinction through time?Evolution6218661875
- 64. Venditti C, Meade A, Pagel M (2006) Detecting the node-density artifact in phylogeny reconstruction. Syst Biol 55: 637–643.C. VendittiA. MeadeM. Pagel2006Detecting the node-density artifact in phylogeny reconstruction.Syst Biol55637643
- 65. Pybus G, Harvey PH (2000) Testing macro-evolutionary models using incomplete molecular phylogenies. Proc R Soc Lond B Biol Sci 267: 2267–2272.G. PybusPH Harvey2000Testing macro-evolutionary models using incomplete molecular phylogenies.Proc R Soc Lond B Biol Sci26722672272
- 66. Bokma F (2008) Bayesian estimation of speciation and extinction probabilities from (in)complete phylogenies. Evolution. F. Bokma2008Bayesian estimation of speciation and extinction probabilities from (in)complete phylogenies.EvolutionIn press. In press.
- 67. Redding DW, Hartmann K, Mimoto A, Bokal D, DeVos M, et al. (2008) Evolutionarily distinctive species often capture more phylogenetic diversity than expected. Journ Theoret Biol 251: 606–615.DW ReddingK. HartmannA. MimotoD. BokalM. DeVos2008Evolutionarily distinctive species often capture more phylogenetic diversity than expected.Journ Theoret Biol251606615
- 68. Nixon KC, Carpenter JM (1993) On outgroups. Cladistics 9: 413–426.KC NixonJM Carpenter1993On outgroups.Cladistics9413426
- 69. Barriel V, Tassy P (1998) Rooting with multiple outgroups: consensus versus parsimony. Cladistics 14: 193–200.V. BarrielP. Tassy1998Rooting with multiple outgroups: consensus versus parsimony.Cladistics14193200
- 70. Heard SB (1992) Patterns in tree balanceamongcladistic, phenetic, and randomly generated phylogenetic trees. Evolution 46: 1818–1826.SB Heard1992Patterns in tree balanceamongcladistic, phenetic, and randomly generated phylogenetic trees.Evolution4618181826
- 71. Agapow PM, Purvis A (2002) Power of eight tree shape statistics to detect nonrandom diversification: a comparison by simulation of two models of cladogenesis. Syst Biol 51: 866–872.PM AgapowA. Purvis2002Power of eight tree shape statistics to detect nonrandom diversification: a comparison by simulation of two models of cladogenesis.Syst Biol51866872
- 72. Aldous D (2001) Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. Stat Sci 16: 23–34.D. Aldous2001Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today.Stat Sci162334
- 73. Rammal R, Toulouse G, Virasoro MA (1986) Ultrametricity for physicists. Rev Mod Phys 58: 765–788.R. RammalG. ToulouseMA Virasoro1986Ultrametricity for physicists.Rev Mod Phys58765788
- 74. Murtagh F Khrennikov AY, Rakić Z, Volovich IV, editors. (2006) From data to the physics using ultrametrics: new results in high dimensional data analysis.p-Adic Mathematical Physics. Amer Inst Phys Conf Proc 826: 151–161.F. Murtagh2006From data to the physics using ultrametrics: new results in high dimensional data analysis.p-Adic Mathematical Physics.AY KhrennikovZ. RakićIV VolovichAmer Inst Phys Conf Proc826151161
- 75. Roberts MD (2008) Ultrametric distance in syntax. MD Roberts2008Ultrametric distance in syntax.arXiv:cs/9810012v4. arXiv:cs/9810012v4.
- 76. Penny D, Hendy MD (1985) The use of tree comparison metrics. Syst Zool 34: 75–82.D. PennyMD Hendy1985The use of tree comparison metrics.Syst Zool347582
- 77. Cela-Conde C, Altaba CR (2002) Multiplying genera versus moving species: a new taxonomic proposal for the family Hominidae. South Afr Journ Sci 98: 1–4.C. Cela-CondeCR Altaba2002Multiplying genera versus moving species: a new taxonomic proposal for the family Hominidae.South Afr Journ Sci9814
- 78. Page RDM (2007) TBMap: a taxonomic perspective on the phylogenetic database TreeBASE. BMC Bioinformatics 8: 158.RDM Page2007TBMap: a taxonomic perspective on the phylogenetic database TreeBASE.BMC Bioinformatics8158DOI:10.1186/1471-2105-8-158. DOI:10.1186/1471-2105-8-158.
- 79. Bokma F (2006) Artificial neural networks can learn to estimate extinction rates from molecular phylogenies. J Theor Biol 243: 449–454.F. Bokma2006Artificial neural networks can learn to estimate extinction rates from molecular phylogenies.J Theor Biol243449454
- 80. Weir JT, Schluter D (2007) The latitudinal gradient in recent speciation and extinction rates of birds and mammals. Science 315: 1574–157.JT WeirD. Schluter2007The latitudinal gradient in recent speciation and extinction rates of birds and mammals.Science3151574157
- 81. Bininda-Emonds ORP, Cardillo M, Jones KE, MacPhee RDE, Beck RMD, et al. (2007) The delayed rise of present-day mammals. Nature 446: 507–512.ORP Bininda-EmondsM. CardilloKE JonesRDE MacPheeRMD Beck2007The delayed rise of present-day mammals.Nature446507512
- 82. Harvey PH, May RM, Nee S (1994) Phylogenies without fossils. Evolution 48: 523–529.PH HarveyRM MayS. Nee1994Phylogenies without fossils.Evolution48523529
- 83. Nee S, May RM, Harvey PH (1994) The reconstructed evolutionary process. Philos Trans R Soc Lond B Biol Sci 344: 305–311.S. NeeRM MayPH Harvey1994The reconstructed evolutionary process.Philos Trans R Soc Lond B Biol Sci344305311
- 84. François O, Mioland C (2007) Gaussian approximation for phylogenetic branch length statistics under stochastic models of biodiversity. Math Biosci 209: 108–123.O. FrançoisC. Mioland2007Gaussian approximation for phylogenetic branch length statistics under stochastic models of biodiversity.Math Biosci209108123
- 85. Bokma F (2008) Detection of “punctuated equilibrium” by Bayesian estimation of speciation and extinction rates, ancestral character states, and rates of anagenetic and cladogenetic evolution on a molecular phylogeny. Evolution. F. Bokma2008Detection of “punctuated equilibrium” by Bayesian estimation of speciation and extinction rates, ancestral character states, and rates of anagenetic and cladogenetic evolution on a molecular phylogeny.EvolutionIn press. In press.
- 86. Dereeper A, Guignon V, Blanc G, Audic S, Buffet S, et al. (2008) Phylogeny.fr: robust phylogenetic analysis for the non-specialist. Nucleic Acids Res 36(Web Server issue): W465–469.A. DereeperV. GuignonG. BlancS. AudicS. Buffet2008Phylogeny.fr: robust phylogenetic analysis for the non-specialist.Nucleic Acids Res36(Web Server issue)W465469
- 87. Edgar RC (2004) MUSCLE: multiple sequence alignment with high accuracy and high throughput. Nucl Ac Res 32: 1792–97.RC Edgar2004MUSCLE: multiple sequence alignment with high accuracy and high throughput.Nucl Ac Res32179297
- 88. Ronquist F, Huelsenbeck JP (2003) MrBayes 3: Bayesian phylogenetic inference under mixed models. Bioinformatics 19: 1572–1574.F. RonquistJP Huelsenbeck2003MrBayes 3: Bayesian phylogenetic inference under mixed models.Bioinformatics1915721574
- 89. Guindon S, Gascuel O (2003) PhyML - A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood. Syst Biol 52: 696–704.S. GuindonO. Gascuel2003PhyML - A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood.Syst Biol52696704
- 90. Guindon S, Lethiec F, Duroux P, Gascuel O (2005) PHYML Online–a web server for fast maximum likelihood-based phylogenetic inference. Nucl Ac Res 33(Web Server issue): W557–559.S. GuindonF. LethiecP. DurouxO. Gascuel2005PHYML Online–a web server for fast maximum likelihood-based phylogenetic inference.Nucl Ac Res33(Web Server issue)W557559
- 91. Goloboff PA (1999) Analyzing large data sets in reasonable times: solutions for composite optima. Cladistics 15: 415–428.PA Goloboff1999Analyzing large data sets in reasonable times: solutions for composite optima.Cladistics15415428
- 92. Goloboff P, Farris S, Nixon K (2000) TNT (Tree analysis using New Technology) (BETA) ver. 1.1. Tucumán, Argentina: Published by the authors. P. GoloboffS. FarrisK. Nixon2000TNT (Tree analysis using New Technology) (BETA) ver. 1.1Tucumán, ArgentinaPublished by the authors
- 93. Gascuel O (1997) BIONJ: an improved version of the NJ algorithm based on a simple model of sequence data. Molec Biol Evol 14: 685–695.O. Gascuel1997BIONJ: an improved version of the NJ algorithm based on a simple model of sequence data.Molec Biol Evol14685695
- 94. Hyman IT, Ho SYW, Jermiin LS (2007) Molecular phylogeny of Australian Helicarionidae, Euconulidae and related groups (Gastropoda: Pulmonata: Stylommatophora) based on mitochondrial DNA. Molec Phylogenet Evol 45: 792–812.IT HymanSYW HoLS Jermiin2007Molecular phylogeny of Australian Helicarionidae, Euconulidae and related groups (Gastropoda: Pulmonata: Stylommatophora) based on mitochondrial DNA.Molec Phylogenet Evol45792812
- 95. Dietzen C, Garcia-del-Rey E, Delgado Castro G, Wink M (2008) Phylogeography of the blue tit (Parus teneriffae-group) on the Canary Islands based on mitochondrial DNA sequence data and morphometrics. J Ornithol 149: 1–12.C. DietzenE. Garcia-del-ReyG. Delgado CastroM. Wink2008Phylogeography of the blue tit (Parus teneriffae-group) on the Canary Islands based on mitochondrial DNA sequence data and morphometrics.J Ornithol149112
- 96. Terry MD, Whiting MF (2005) Mantophasmatodea and phylogeny of the lower neopterous insects. Cladistics 21: 240–257.MD TerryMF Whiting2005Mantophasmatodea and phylogeny of the lower neopterous insects.Cladistics21240257
- 97. Véla E, Magnin F, Pavon D, Pfenninger M (2008) Phylogénie moléculaire et données paléobiogéographiques sur le gastéropode terrestre Tudorella sulcata (Draparnaud, 1805) en France et en Algérie orientale. Geodiversitas 30: 233–246.E. VélaF. MagninD. PavonM. Pfenninger2008Phylogénie moléculaire et données paléobiogéographiques sur le gastéropode terrestre Tudorella sulcata (Draparnaud, 1805) en France et en Algérie orientale.Geodiversitas30233246
- 98. Koblmüller S, Egger B, Sturmbauer C, Sefc KM (2007) Evolutionary history of Lake Tanganyika's scale-eating cichlid fishes. Molec Phylogenet Evol 44: 1295–1305.S. KoblmüllerB. EggerC. SturmbauerKM Sefc2007Evolutionary history of Lake Tanganyika's scale-eating cichlid fishes.Molec Phylogenet Evol4412951305
- 99. Hidalgo O, Garcia-Jacas N, Garnatje T, Susanna A (2006) Phylogeny of Rhaponticum (Asteraceae, Cardueae-Centaurinae) and related genera inferred from nuclear and chloroplast DNA sequence data: taxonomic and biogeographic implications. Ann Bot 97: 705–714.O. HidalgoN. Garcia-JacasT. GarnatjeA. Susanna2006Phylogeny of Rhaponticum (Asteraceae, Cardueae-Centaurinae) and related genera inferred from nuclear and chloroplast DNA sequence data: taxonomic and biogeographic implications.Ann Bot97705714
- 100. Brambilla M, Vitulano S, Spina F, Baccetti N, Gargallo G, et al. (2008) A molecular phylogeny of the Sylvia cantillans complex: cryptic species within the Mediterranean basin. Molec Phylogenet Evol 48: 461–472.M. BrambillaS. VitulanoF. SpinaN. BaccettiG. Gargallo2008A molecular phylogeny of the Sylvia cantillans complex: cryptic species within the Mediterranean basin.Molec Phylogenet Evol48461472
- 101. Flynn JJ, Finarelli JA, Zehr S, Hsu J, Nedbal MA (2005) Molecular phylogeny of the Carnivora (Mammalia): assessing the impact of increased sampling on resolving enigmatic relationships. Syst Biol 54: 317–337.JJ FlynnJA FinarelliS. ZehrJ. HsuMA Nedbal2005Molecular phylogeny of the Carnivora (Mammalia): assessing the impact of increased sampling on resolving enigmatic relationships.Syst Biol54317337
- 102. Regier JC, Shultz JW, Kambic RE (2005) Pancrustacean phylogeny: hexapods are terrestrial crustaceans and maxillopods are not monophyletic. Proc R Soc Lond B 272: 395–401.JC RegierJW ShultzRE Kambic2005Pancrustacean phylogeny: hexapods are terrestrial crustaceans and maxillopods are not monophyletic.Proc R Soc Lond B272395401
- 103. Wethington AR, Lydeard C (2007) A molecular phylogeny of Physidae (Gastropoda: Basommatophora) based on mitochondrial DNA sequences. J Moll Stud 73: 241–257.AR WethingtonC. Lydeard2007A molecular phylogeny of Physidae (Gastropoda: Basommatophora) based on mitochondrial DNA sequences.J Moll Stud73241257
- 104. Bonnett RM, Chippendale PT (2004) Speciation, phylogeography and evolution of life history and morphology in plethodontid salamanders of the Eurycea multiplicata complex. Molec Ecol 13: 1189–1203.RM BonnettPT Chippendale2004Speciation, phylogeography and evolution of life history and morphology in plethodontid salamanders of the Eurycea multiplicata complex.Molec Ecol1311891203
- 105. Nikolaev S, Montoya-Burgos JI, Margulies EH, Program NCS, Rougemont J, et al. (2007) Early history of hammals is elucidated with the ENCODE multiple species sequencing data. PLoS Genet 3(1): e2.S. NikolaevJI Montoya-BurgosEH MarguliesNCS ProgramJ. Rougemont2007Early history of hammals is elucidated with the ENCODE multiple species sequencing data.PLoS Genet3(1)e2
- 106. Alonso MR, Goodacre SL, Emerson BC, Ibáñez M, Hutterer R, Groh K (2006) Canarian land snail diversity: conflict between anatomical and molecular data on the phylogenetic placement of five new species of Napaeus (Gastropoda, Pulmonata, Enidae). Biol J Linn Soc 89: 169–187.MR AlonsoSL GoodacreBC EmersonM. IbáñezR. HuttererK. Groh2006Canarian land snail diversity: conflict between anatomical and molecular data on the phylogenetic placement of five new species of Napaeus (Gastropoda, Pulmonata, Enidae).Biol J Linn Soc89169187
- 107. Wilke T, Davis GM, Gong X, Liu H-X (2000) Erhaia (Gastrpoda: Rissooidea): phylogenetic relationships and the question of Paragonimus coevolution in Asia. Am J Trop Med Hyg 62: 453–459.T. WilkeGM DavisX. GongH-X Liu2000Erhaia (Gastrpoda: Rissooidea): phylogenetic relationships and the question of Paragonimus coevolution in Asia.Am J Trop Med Hyg62453459
- 108. Prasad AB, Allard MW (2008) Confirming the phylogeny of mammals by use of large comparative sequence data sets. Molec Biol Evol 25: 1795–1808.AB PrasadMW Allard2008Confirming the phylogeny of mammals by use of large comparative sequence data sets.Molec Biol Evol2517951808
- 109. Bretagnolle V, Attié C, Pasquet E (1998) Cytochrome-B evidence for validity and phylogenetic relationships of Pseudobulweria and Bulweria (Procellariidae). Auk 115: 188–195.V. BretagnolleC. AttiéE. Pasquet1998Cytochrome-B evidence for validity and phylogenetic relationships of Pseudobulweria and Bulweria (Procellariidae).Auk115188195
- 110. Sundberg P, Turbeville JM, Lindh S (2001) Phylogenetic relationships among higher nemertean (Nemertea) taxa inferred from 18S rDNA sequences. Molec Phylogenet Evol 20: 327–334.P. SundbergJM TurbevilleS. Lindh2001Phylogenetic relationships among higher nemertean (Nemertea) taxa inferred from 18S rDNA sequences.Molec Phylogenet Evol20327334
- 111. Piaggio AJ, Spicer GS (2001) Molecular phylogeny of the chipmunks inferred from mitochondrial cytochrome b and cytochrome oxidase II gene sequences. Molec Phylogenet Evol 20: 335–350.AJ PiaggioGS Spicer2001Molecular phylogeny of the chipmunks inferred from mitochondrial cytochrome b and cytochrome oxidase II gene sequences.Molec Phylogenet Evol20335350
- 112. Westerman M, Springer MS, Dixon J, Krajewski C (1999) Molecular relationships of the extinct pig-footed bandicoot Chaeropus ecaudatus (Marsupialia: Perameloidea) using 12S rRNA sequences. J Mamm Evol 6: 271–288.M. WestermanMS SpringerJ. DixonC. Krajewski1999Molecular relationships of the extinct pig-footed bandicoot Chaeropus ecaudatus (Marsupialia: Perameloidea) using 12S rRNA sequences.J Mamm Evol6271288
- 113. Dubey S, Koyasu K, Parapanov R, Ribi M, Hutterer R, Vogel P (2008) Molecular phylogenetics reveals Messinian, Pliocene, and Pleistocene colonizations of islands by North African shrews. Molec Phylogenet Evol 47: 877–882.S. DubeyK. KoyasuR. ParapanovM. RibiR. HuttererP. Vogel2008Molecular phylogenetics reveals Messinian, Pliocene, and Pleistocene colonizations of islands by North African shrews.Molec Phylogenet Evol47877882
- 114. Ahyong ST, O'Meally D (2004) Phylogeny of the Decapoda Reptantia: resolution using three molecular loci and morphology. Raffles Bull Zool 52: 673–693.ST AhyongD. O'Meally2004Phylogeny of the Decapoda Reptantia: resolution using three molecular loci and morphology.Raffles Bull Zool52673693
- 115. Geiger DL, Thacker CR (2005) Molecular phylogeny of Vetigastropoda reveals non-monophyletic Scissurellidae, Trochoidea, and Fissurelloidea. Moll Res 25: 47–55.DL GeigerCR Thacker2005Molecular phylogeny of Vetigastropoda reveals non-monophyletic Scissurellidae, Trochoidea, and Fissurelloidea.Moll Res254755
- 116. Macey JR, Schulte JA, Larson A, Tuniyev BS, Orlov N, et al. (1999) Molecular phylogenetics, tRNA evolution, and historical biogeography in anguid lizards and related taxonomic families. Molec Phylogenet Evol 12: 250–72.JR MaceyJA SchulteA. LarsonBS TuniyevN. Orlov1999Molecular phylogenetics, tRNA evolution, and historical biogeography in anguid lizards and related taxonomic families.Molec Phylogenet Evol1225072
- 117. Guan F, Niu AO, Attwood SW, Li YL, Zhang B, et al. (2008) Molecular phylogenetics of Triculine snails (Gastropoda: Pomatiopsidae). Molec Phylogenet Evol 48: 702–707.F. GuanAO NiuSW AttwoodYL LiB. Zhang2008Molecular phylogenetics of Triculine snails (Gastropoda: Pomatiopsidae).Molec Phylogenet Evol48702707
- 118. Syring J, Farrell K, Businský R, Cronn R, Liston A (2007) Widespread genealogical nonmonophyly in species of Pinus subgenus Strobus. Syst Biol 56: 163–181.J. SyringK. FarrellR. BusinskýR. CronnA. Liston2007Widespread genealogical nonmonophyly in species of Pinus subgenus Strobus.Syst Biol56163181
- 119. Sasaki T, Yasukawa Y, Takahashi K, Miura S, Shedlock AM, Okada N (2006) Extensive morphological convergence and rapid radiation in the evolutionary history of the family Geoemydidae (Old World pond turtles) revealed by SINE insertion analysis. Syst Biol 55: 912–927.T. SasakiY. YasukawaK. TakahashiS. MiuraAM ShedlockN. Okada2006Extensive morphological convergence and rapid radiation in the evolutionary history of the family Geoemydidae (Old World pond turtles) revealed by SINE insertion analysis.Syst Biol55912927
- 120. Cicero C, Johnson NK (2001) Higher-level phylogeny of new world vireos (Aves: Vireonidae) based on sequences of multiple mitochondrial DNA genes. Molec Phylogenet Evol 20: 27–40.C. CiceroNK Johnson2001Higher-level phylogeny of new world vireos (Aves: Vireonidae) based on sequences of multiple mitochondrial DNA genes.Molec Phylogenet Evol202740
- 121. Marjanović D, Laurin M (2007) Fossils, molecules, divergence times, and the origin of Lissamphibians. Syst Biol 56: 369–388.D. MarjanovićM. Laurin2007Fossils, molecules, divergence times, and the origin of Lissamphibians.Syst Biol56369388
- 122. Manos PS, Soltis PS, Soltis DE, Manchester SR, Oh SH, et al. (2007) Phylogeny of extant and fossil Juglandaceae inferred from the integration of molecular and morphological data sets. Syst Biol 56: 412–430.PS ManosPS SoltisDE SoltisSR ManchesterSH Oh2007Phylogeny of extant and fossil Juglandaceae inferred from the integration of molecular and morphological data sets.Syst Biol56412430
- 123. Paxinos EE, James HF, Olson SL, Sorenson MD, Jackson J, et al. (2002) mtDNA from fossils reveals a radiation of Hawaiian geese recently derived from the Canada goose (Branta canadensis). Proc Nat Acad Sci USA 99: 1399–1404.EE PaxinosHF JamesSL OlsonMD SorensonJ. Jackson2002mtDNA from fossils reveals a radiation of Hawaiian geese recently derived from the Canada goose (Branta canadensis).Proc Nat Acad Sci USA9913991404
- 124. Huff SW, Campbell D, Gustafson DL, Lydeard C, Altaba CR, et al. (2004) Investigations into the phylogenetic relationships of freshwater pearl mussels (Bivalvia: Margaritiferidae) based on molecular data: implications for their taxonomy and biogeography. J Moll Stud 70: 379–388.SW HuffD. CampbellDL GustafsonC. LydeardCR Altaba2004Investigations into the phylogenetic relationships of freshwater pearl mussels (Bivalvia: Margaritiferidae) based on molecular data: implications for their taxonomy and biogeography.J Moll Stud70379388
- 125. Zeng L, Swalla BJ (2005) Molecular phylogeny of the protochordates: chordate evolution. Can J Zool 83: 24–33.L. ZengBJ Swalla2005Molecular phylogeny of the protochordates: chordate evolution.Can J Zool832433