Bayesian inference of character evolution

Much recent progress in evolutionary biology is based on the inference of ancestral states and past transformations in important traits on phylogenetic trees. These exercises often assume that the tree is known without error and that ancestral states and character change can be mapped onto it exactly. In reality, there is often considerable uncertainty about both the tree and the character mapping. Recently introduced Bayesian statistical methods enable the study of character evolution while simultaneously accounting for both phylogenetic and mapping uncertainty, adding much needed credibility to the reconstruction of evolutionary history.     

Reconstructing ancestral ranges in historical biogeography: properties and prospects

Recent years have witnessed a proliferation of quantitative methods for biogeographic inference. In particular, novel parametric approaches represent exciting new opportunities for the study of range evolution. Here, we review a selection of current methods for biogeographic analysis and discuss their respective properties. These methods include generalized parsimony approaches, weighted ancestral area analysis, dispersal-vicariance analysis, the dispersal--extinction--cladogenesis model and other maximum likelihood approaches, and Bayesian stochastic mapping of ancestral ranges, including a novel approach to inferring range evolution in the context of island biogeography. Some of these methods were developed specifically for problems of ancestral range reconstruction, whereas others were designed for more general problems of character state reconstruction and subsequently applied to the study of ancestral ranges. Methods for reconstructing ancestral history on a phylogenetic tree differ not only in the types of ancestral range states that are allowed, but also in the various historical events that may change the ancestral ranges. We explore how the form of allowed ancestral ranges and allowed transitions can both affect the outcome of ancestral range estimation. Finally, we mention some promising avenues for future work in the development of model-based approaches to biogeographic analysis.     

Something for nothing? Reconstruction of ancestral character states in asterinid sea star development

SUMMARY Traits from early development mapped onto phylogenetic trees can potentially offer insight into the evolutionary history of development by inferring the states of those characters among ancestors at nodes in the phylogeny. A key and often-overlooked aspect of such mapping is the underlying model of character evolution. Without a well-supported and realistic model ("nothing"), character mapping of ancestral traits onto phylogenetic trees might often return results ("something") that lack a sound basis. Here we reconsider a challenging case study in this area of evolutionary developmental biology: the inference of ancestral states for ecological and morphological characters in the reproduction and larval development of asterinid sea stars. We apply improved analytical methods to an expanded set of asterinid phylogenetic data and developmental character states. This analysis shows that the new methods might generally offer some independent insight into choice of a model of character evolution, but that in the specific case of asterinid sea stars the quantitative features of the model (especially the relative probabilities of different directions of change) have an important effect on the results. We suggest caution in applying ancestral state reconstructions in the absence of an independently corroborated model of character evolution, and highlight the need for such modeling in evolutionary developmental biology.     

Systematics and morphological evolution within the moss family Bryaceae: a comparison between parsimony and Bayesian methods for reconstruction of ancestral character states

The Bryaceae are a large cosmopolitan moss family including genera of significant morphological and taxonomic complexity. Phylogenetic relationships within the Bryaceae were reconstructed based on DNA sequence data from all three genomic compartments. In addition, maximum parsimony and Bayesian inference were employed to reconstruct ancestral character states of 38 morphological plus four habitat characters and eight insertion/deletion events. The recovered phylogenetic patterns are generally in accord with previous phylogenies based on chloroplast DNA sequence data and three major clades are identified. The first clade comprises Bryum bornholmense, B. rubens, B. caespiticium, and Plagiobryum. This corroborates the hypothesis suggested by previous studies that several Bryum species are more closely related to Plagiobryum than to the core Bryum species. The second clade includes Acidodontium, Anomobryum, and Haplodontium, while the third clade contains the core Bryum species plus Imbribryum. Within the latter clade, B. subapiculatum and B. tenuisetum form the sister clade to Imbribryum. Reconstructions of ancestral character states under maximum parsimony and Bayesian inference suggest fourteen morphological synapomorphies for the ingroup and synapomorphies are detected for most clades within the ingroup. Maximum parsimony and Bayesian reconstructions of ancestral character states are mostly congruent although Bayesian inference shows that the posterior probability of ancestral character states may decrease dramatically when node support is taken into account. Bayesian inference also indicates that reconstructions may be ambiguous at internal nodes for highly polymorphic characters.     

Mapping uncertainty and phylogenetic uncertainty in ancestral character state reconstruction: an example in the moss genus Brachytheciastrum

The evolution of species traits along a phylogeny can be examined through an increasing number of possible, but not necessarily complementary, approaches. In this paper, we assess whether deriving ancestral states of discrete morphological characters from a model whose parameters are (i) optimized by ML on a most likely tree; (II) optimized by ML onto each of a Bayesian sample of trees; and (III) sampled by a MCMC visiting the space of a Bayesian sample of trees affects the reconstruction of ancestral states in the moss genus Brachytheciastrum. In the first two methods, the choice of a single- or two-rate model and of a genetic distance (wherein branch lengths are used to determine the probabilities of change) or speciational (wherein changes are only driven by speciation events) model based upon a likelihood-ratio test strongly depended on the sampled trees. Despite these differences in model selection, reconstructions of ancestral character states were strongly correlated to each others across nodes, often at r > 0.9, for all the characters. The Bayesian approach of ancestral character state reconstruction offers, however, a series of advantages over the single-tree approach or the ML model optimization on a Bayesian sample of trees because it does not involve restricting model parameters prior to reconstructing ancestral states, but rather allows a range of model parameters and ancestral character states to be sampled according to their posterior probabilities. From the distribution of the latter, conclusions on trait evolution can be made in a more satisfactorily way than when a substantial part of the uncertainty of the results is obscured by the focus on a single set of model parameters and associated ancestral states. The reconstructions of ancestral character states in Brachytheciastrum reveal rampant parallel morphological evolution. Most species previously described based on phenetic grounds are thus resolved of polyphyletic origin. Species polyphylly has been increasingly reported among mosses, raising severe reservations regarding current species definition.     

Independent contrasts succeed where ancestor reconstruction fails in a known bacteriophage phylogeny

Abstract.— Methods of ancestor reconstruction are important tools for evolutionary inference that are difficult to test empirically because ancestral states are rarely known with certainty. We evaluated reconstruction methods for continuous phenotypic characters using taxa from an experimentally generated bacteriophage phylogeny. Except for one slowly evolving character, the estimated ancestral states of continuous phenotypic characters were highly inaccurate and biased, even when including a known ancestor at the root. This error was caused by a directional trend in character evolution and by rapid rates of character evolution. Computer simulations confirmed that such factors affect reconstruction of continuous characters in general. We also used phenotypic viral characters to evaluate two methods that attempt to estimate the correlation between characters during evolution. Whereas a nonphylogenetic regression was relatively inaccurate and biased, independent contrasts accurately estimated the correlation between characters with little bias.     

Molecular phylogenetic approach for studying life-history evolution: the ambiguous example of the genus Medicago L.

We present a molecular phylogeny including most species of the genus Medicago L. (Fabaceae). Based on the consensus of the 48 most parsimonious trees, life-history and mating-system characters are mapped, and a putative history of the genus is suggested. The most parsimonious reconstruction suggests an ancestral annual and selfing state, and recurrent evolution towards perenniality and outcrossing. Based on theoretical predictions and classical hypotheses of the history of the genus, different assumptions about the ancestral state and different weighting schemes of evolution between the character states are made. Assuming an outcrossing, perennial ancestral state (partly supported by morphological features) does not fundamentally change the reconstruction. To meet theoretical expectations, various weighting schemes favouring evolution towards annuality and selfing are applied. Influence and validity of such weighting schemes are discussed with regard to other studies.     

EXAMINING TWO STANDARD ASSUMPTIONS OF ANCESTRAL RECONSTRUCTIONS: REPEATED LOSS OF DICHROMATISM IN DABBLING DUCKS (ANATINI)

Although phylogenetic reconstruction of ancestral character states is becoming an increasingly common technique for studying evolution, few researchers have assessed the reliability of these reconstructions. Here I test for congruence between a phylogenetic reconstruction and a widely accepted scenario based on independent lines of evidence. I used Livezey's (1991) phylogeny to reconstruct ancestral states of plumage dichromatism in dabbling ducks (Anatini). Character state mapping reconstructs monochromatic ancestors for the genus Anas as well as most of its main clades. This reconstruction differs strongly from the widely accepted scenario of speciation and plumage evolution in the group (e.g., Delacour and Mayr 1945; Sibley 1957). This incongruence may occur because two standard assumptions of character state reconstruction are probably not met in this case. Violating either of these two assumptions would be a source of error sufficient to create misleading reconstructions. The first assumption that probably does not apply to ducks is that terminal taxa, in this case species, are monophyletic. Many of the widespread dichromatic species of ducks may be paraphyletic and ancestral to isolated monochromatic species. Three lines of evidence support this scenario: population-level phylogenies, biogeography, and vestigial plumage patterns. The second assumption that probably does not apply to duck plumage color is that gains and losses of character states are equally likely. Four lines of evidence suggest that dichromatic plumage might be lost more easily than gained: weak female preferences for bright male plumage, biases toward the loss of sexually dichromatic characters, biases toward the loss of complex characters, and repeated loss of dichromatism in other groups of birds. These seven lines of evidence support the accepted scenario that widespread dichromatic species repeatedly budded off isolated monochromatic species. Drift and genetic biases probably caused the easy loss of dichromatism in ducks and other birds during peripatric speciation. In order to recover the accepted scenario using Livezey's tree, losses of dichromatism must be five times more likely than gains. The results of this study caution against the uncritical use of unordered parsimony as the sole criterion for inferring ancestral states. Detailed population-level sampling is needed and altered transformation weighting may be warranted in ducks and in many other groups and character types with similar attributes.     

Character-state space versus rate of evolution in phylogenetic inference

With only four alternative character states, parallelisms and reversals are expected to occur frequently when using nucleotide characters for phylogenetic inference. Greater available character‐state space has been described as one of the advantages of third codon positions relative to first and second codon positions, as well as amino acids relative to nucleotides. We used simulations to quantify how character‐state space and rate of evolution relate to one another, and how this relationship is affected by differences in: tree topology, branch lengths, rate heterogeneity among sites, probability of change among states, and frequency of character states. Specifically, we examined how inferred tree lengths, consistency and retention indices, and accuracy of phylogenetic inference are affected. Our results indicate that the relatively small increases in the character‐state space evident in empirical data matrices can provide enormous benefits for the accuracy of phylogenetic inference. This advantage may become more pronounced with unequal probabilities of change among states. Although increased character‐state space greatly improved the accuracy of topology inference, improvements in the estimation of the correct tree length were less apparent. Accuracy and inferred tree length improved most when character‐state space increased initially; further increases provided more modest improvements. © The Willi Hennig Society 2004.     

ANCESTRAL CHARACTER ESTIMATION UNDER THE THRESHOLD MODEL FROM QUANTITATIVE GENETICS

Evolutionary biology is a study of life's history on Earth. In researching this history, biologists are often interested in attempting to reconstruct phenotypes for the long extinct ancestors of living species. Various methods have been developed to do this on a phylogeny from the data for extant taxa. In the present article, I introduce a new approach for ancestral character estimation for discretely valued traits. This approach is based on the threshold model from evolutionary quantitative genetics. Under the threshold model, the value exhibited by an individual or species for a discrete character is determined by an underlying, unobserved continuous trait called “liability.” In this new method for ancestral state reconstruction, I use Bayesian Markov chain Monte Carlo (MCMC) to sample the liabilities of ancestral and tip species, and the relative positions of two or more thresholds, from their joint posterior probability distribution. Using data simulated under the model, I find that the method has very good performance in ancestral character estimation. Use of the threshold model for ancestral state reconstruction relies on a priori specification of the order of the discrete character states along the liability axis. I test the use of a Bayesian MCMC information theoretic criterion based approach to choose among different hypothesized orderings for the discrete character. Finally, I apply the method to the evolution of feeding mode in centrarchid fishes.     

MEASURING EVOLUTIONARY CONSTRAINTS: A MARKOV MODEL FOR PHYLOGENETIC TRANSITIONS AMONG SEED DISPERSAL SYNDROMES

I introduce a Markov probabilistic model of transitions among discrete morphological states as a method for describing and testing nonrandom patterns of evolutionary change. The Markov model assumes one-generational dependency, i.e., that the future direction of evolutionary change depends on the current morphology of a species, not on any history of changes. This model is very flexible, allowing for any number of discrete states to describe morphology, yet permit rigorous testing of even complex evolutionary hypotheses. I apply this model to changes in seed dispersal mechanisms within 571 genera of Neotropical plants, using cladistic methods to infer the ancestral and derived states within each genus. I then test a series of progressively more complex hypotheses about the constraints that might shape the patterns of observed evolutionary transitions: 1) no transition constraints; 2) all dispersal mechanisms are equally labile evolutionarily; 3) the probability of particular evolutionary transitions among dispersal mechanisms depends on the descendant state but not on the ancestral state; 4) transition probabilities differ among pairs of dispersal mechanisms, but are reciprocal within such pairs. More complex hypotheses matched the data significantly better than did simpler hypotheses. However, only one of the hypotheses (reciprocal transitions) fit the observed data and then only for the most cautious interpretation of the frequencies of transitions within genera. These results suggest that evolutionary transitions among major adaptive syndromes are indeed ordered, and the observed patterns of transitions suggest possible reasons for such macroevolutionary structure.     

Evolutionary history of vegetative reproduction in Porpidia s.L. (Lichen-forming ascomycota)

The evolutionary history of gains and losses of vegetative reproductive propagules (soredia) in Porpidia s.l., a group of lichen-forming ascomycetes, was clarified using Bayesian Markov chain Monte Carlo (MCMC) approaches to monophyly tests and a combined MCMC and maximum likelihood approach to ancestral character state reconstructions. The MCMC framework provided confidence estimates for the reconstructions of relationships and ancestral character states, which formed the basis for tests of evolutionary hypotheses. Monophyly tests rejected all hypotheses that predicted any clustering of reproductive modes in extant taxa. In addition, a nearest-neighbor statistic could not reject the hypothesis that the vegetative reproductive mode is randomly distributed throughout the group. These results show that transitions between presence and absence of the vegetative reproductive mode within Porpidia s.l. occurred several times and independently of each other. Likelihood reconstructions of ancestral character states at selected nodes suggest that--contrary to previous thought--the ancestor to Porpidia s.l. already possessed the vegetative reproductive mode. Furthermore, transition rates are reconstructed asymmetrically with the vegetative reproductive mode being gained at a much lower rate than it is lost. A cautious note has to be added, because a simulation study showed that the ancestral character state reconstructions were highly dependent on taxon sampling. However, our central conclusions, particularly the higher rate of change from vegetative reproductive mode present to absent than vice versa within Porpidia s.l., were found to be broadly independent of taxon sampling.     

Plausibility of inferred ancestral phenotypes and the evaluation of alternative models of limb evolution in scincid lizards

Phylogenetic approaches to inferring ancestral character states are becoming increasingly sophisticated; however, the potential remains for available methods to yield strongly supported but inaccurate ancestral state estimates. The consistency of ancestral states inferred for two or more characters affords a useful criterion for evaluating ancestral trait reconstructions. Ancestral state estimates for multiple characters that entail plausible phenotypes when considered together may reasonably be assumed to be reliable. However, the accuracy of inferred ancestral states for one or more characters may be questionable where combined reconstructions imply implausible phenotypes for a proportion of internal nodes. This criterion for assessing reconstructed ancestral states is applied here in evaluating inferences of ancestral limb morphology in the scincid lizard clade Lerista. Ancestral numbers of digits for the manus and pes inferred assuming the models that best fit the data entail ancestral digit configurations for many nodes that differ fundamentally from configurations observed among known species. However, when an alternative model is assumed for the pes, inferred ancestral digit configurations are invariably represented among observed phenotypes. This indicates that a suboptimal model for the pes (and not the model providing the best fit to the data) yields accurate ancestral state estimates.     

Maximum likelihood inference of geographic range evolution by dispersal, local extinction, and cladogenesis

In historical biogeography, model-based inference methods for reconstructing the evolution of geographic ranges on phylogenetic trees are poorly developed relative to the diversity of analogous methods available for inferring character evolution. We attempt to rectify this deficiency by constructing a dispersal-extinction-cladogenesis (DEC) model for geographic range evolution that specifies instantaneous transition rates between discrete states (ranges) along phylogenetic branches and apply it to estimating likelihoods of ancestral states (range inheritance scenarios) at cladogenesis events. Unlike an earlier version of this approach, the present model allows for an analytical solution to probabilities of range transitions as a function of time, enabling free parameters in the model, rates of dispersal, and local extinction to be estimated by maximum likelihood. Simulation results indicate that accurate parameter estimates may be difficult to obtain in practice but also show that ancestral range inheritance scenarios nevertheless can be correctly recovered with high success if rates of range evolution are low relative to the rate of cladogenesis. We apply the DEC model to a previously published, exemplary case study of island biogeography involving Hawaiian endemic angiosperms in Psychotria (Rubiaceae), showing how the DEC model can be iteratively refined from inspecting inferences of range evolution and also how geological constraints involving times of island origin may be imposed on the likelihood function. The DEC model is sufficiently similar to character models that it might serve as a gateway through which many existing comparative methods for characters could be imported into the realm of historical biogeography; moreover, it might also inspire the conceptual expansion of character models toward inclusion of evolutionary change as directly coincident, either as cause or consequence, with cladogenesis events. The DEC model is thus an incremental advance that highlights considerable potential in the nascent field of model-based historical biogeographic inference.     

The threefold parallelism of Agassiz and Haeckel,and polarity determination in phylogenetic systematics

A parallel exists between the threefold parallelism of Agassiz and Haeckel and the three valid methods of polarity determination in phylogenetic systematics. The structural gradation among taxa within a linear hierarchy, ontogenetic recapitulation, and geological succession of the threefold parallelism resemble outgroup comparison, the ontogenetic method, and the paleontological method, respectively, which are methods of polarity determination in phylogenetic systematics. The parallel involves expected congruence among similar components of the distribution of character states among organisms. The threefold parallelism is a manifestation of a world view based on linear hierarchies, whereas polarity determination is part of the methodology of phylogenetic systematics which assumes that organisms are grouped into a nested hierarchy. The threefold parallelism facilitated the ranking of previously established taxa into linear hierarchies consisting mostly of paraphyletic groups. In contrast, methods of polarity determination identify apomorphies that determine and diagnose monophyletic taxa (clades) in the nested genealogical hierarchy. Taxa in linear hierarchies are defined by sets of character states, whereas clades are defined by common ancestry. Although the threefold parallelism was ostensibly abandoned with the rejection of Haeckel's biogenetic law, some of its components continue to facilitate the progressive scenarios that are common in evolutionary thought. Although a general view of progression in organismal history may be invalid, the progressive or directional sequence of character state changes that results in the characterization of a particular clade has considerable heuristic value. Agassiz's ostensibly nested hierarchy and other pre-Darwinian classifications do not provide support for the view that the natural system can be discovered without recourse to the principle of common descent.     

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

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

Empirical and hierarchical Bayesian estimation of ancestral states

Several methods have been proposed to infer the states at the ancestral nodes on a phylogeny. These methods assume a specific tree and set of branch lengths when estimating the ancestral character state. Inferences of the ancestral states, then, are conditioned on the tree and branch lengths being true. We develop a hierarchical Bayes method for inferring the ancestral states on a tree. The method integrates over uncertainty in the tree, branch lengths, and substitution model parameters by using Markov chain Monte Carlo. We compare the hierarchical Bayes inferences of ancestral states with inferences of ancestral states made under the assumption that a specific tree is correct. We find that the methods are correlated, but that accommodating uncertainty in parameters of the phylogenetic model can make inferences of ancestral states even more uncertain than they would be in an empirical Bayes analysis.     

Phylogenetic Relationships Among Treeshrews (Scandentia): A Review and Critique of the Morphological Evidence

Although the supraordinal relationships of Scandentia (treeshrews) have been studied in great detail from both morphological and molecular perspectives, the phylogenetic relationships among treeshrews have been largely ignored. Here we review several published studies of qualitative morphological variation among living treeshrews and their contribution to our understanding of intraordinal phylogenetic relationships. Reanalysis of the data from each of these studies demonstrates that none of the trees in the original publications represents the most parsimonious interpretation. In addition to performing new analyses, we argue that all such studies to date suffer from one or more fundamental shortcomings, notably the failure to include reference to nonscandentian outgroups and the a priori assumption of generic monophyly of the relatively speciose genus Tupaia. Parsimony analyses of these data sets fail to resolve either intergeneric or interspecific relationships. Finally, several inconsistencies and conflicts with respect to character coding both within and between published studies are discussed. We conclude that a more rigorous investigation of morphological character state variation is sorely needed, one that explicitly identifies voucher specimens and does not make any assumptions of generic monophyly. This is necessary not only for the purpose of resolving phylogenetic relationships, but also for inference of ancestral states in a group that continues to figure prominently in studies of placental mammal diversification.     

Reconstructing ancestral ecologies: challenges and possible solutions

There are several ways to extract information about the evolutionary ecology of clades from their phylogenies. Of these, character state optimization and 'ancestor reconstruction' are perhaps the most widely used despite their being fraught with assumptions and potential pitfalls. Requirements for robust inferences of ancestral traits in general (i.e. those applicable to all types of characters) include accurate and robust phylogenetic hypotheses, complete species-level sampling and the appropriate choice of optimality criterion. Ecological characters, however, also require careful consideration of methods for accounting for intraspecific variability. Such methods include 'Presence Coding' and 'Polymorphism Coding' for discrete ecological characters, and 'Range Coding' and 'MaxMin Coding' for continuously variable characters. Ultimately, however, historical inferences such as these are, as with phylogenetic inference itself, associated with a degree of uncertainty. Statistically based uncertainty estimates are available within the context of model-based inference (e.g. maximum likelihood and Bayesian); however, these measures are only as reliable as the chosen model is appropriate. Although generally thought to preclude the possibility of measuring relative uncertainty or support for alternative possible reconstructions, certain useful non-statistical support measures (i.e. 'Sharkey support' and 'Parsimony support') are applicable to parsimony reconstructions.