Reconstructing ancestral character states: a critical reappraisal

Using parsimony to reconstruct ancestral character states on a phylogenetic tree has become a popular method for testing ecological and evolutionary hypotheses. Despite its popularity, the assumptions and uncertainties of reconstructing the ancestral states of a single character have received less attention than the much less challenging endeavor of reconstructing phylogenetic trees from many characters. Recent research suggests that parsimony reconstructions are often sensitive to violations of the almost universal assumption of equal probabilities of gains and losses. In addition, maximum likelihood has been developed as an alternative to parsimony reconstruction, and has also revealed a surprising amount of uncertainty in ancestral reconstructions.     

Likelihood analysis of phylogenetic networks using directed graphical models

A method for computing the likelihood of a set of sequences assuming a phylogenetic network as an evolutionary hypothesis is presented. The approach applies directed graphical models to sequence evolution on networks and is a natural generalization of earlier work by Felsenstein on evolutionary trees, including it as a special case. The likelihood computation involves several steps. First, the phylogenetic network is rooted to form a directed acyclic graph (DAG). Then, applying standard models for nucleotide/amino acid substitution, the DAG is converted into a Bayesian network from which the joint probability distribution involving all nodes of the network can be directly read. The joint probability is explicitly dependent on branch lengths and on recombination parameters (prior probability of a parent sequence). The likelihood of the data assuming no knowledge of hidden nodes is obtained by marginalization, i.e., by summing over all combinations of unknown states. As the number of terms increases exponentially with the number of hidden nodes, a Markov chain Monte Carlo procedure (Gibbs sampling) is used to accurately approximate the likelihood by summing over the most important states only. Investigating a human T-cell lymphotropic virus (HTLV) data set and optimizing both branch lengths and recombination parameters, we find that the likelihood of a corresponding phylogenetic network outperforms a set of competing evolutionary trees. In general, except for the case of a tree, the likelihood of a network will be dependent on the choice of the root, even if a reversible model of substitution is applied. Thus, the method also provides a way in which to root a phylogenetic network by choosing a node that produces a most likely network.     

A formula for maximum possible steps in multistate characters: isolating matrix parameter effects on measures of evolutionary convergence

To identify a biological signal in the distribution of homoplasy, it is first necessary to isolate non-biological factors affecting its measurement. The number of states per character in a phylogenetic data matrix may indicate evolutionary flexibility and, consequently, the likelihood of recurrent evolution. However, we show here that the number of states per character limits the maximum number of steps that may be inferred using parsimony. A formula is provided for the maximum number of steps that may be taken by a character with a given number of states and taxa. We show that as more character states are included the maximum proportion of steps that can be attributed to homoplasy falls, and the greatest amount of homoplasy measurable with the consistency index declines.
© The Willi Hennig Society 2009.     

The measurement of test severity, significance tests for resolution, and a unified philosophy of phylogenetic inference

The philosopher Karl Popper described a concept termed degree of corroboration , C , for evaluating and comparing hypotheses according to the results of their tests. C is, fundamentally, a comparison of two likelihoods: p ( e|hb ), the likelihood of the hypothesis ( h ) in conjunction with the background knowledge ( b ), and p ( e|b ), the likelihood of b alone. C is closely related to the likelihood ratio of nested hypotheses. When phylogenetic analysis is interpreted as an attempt to assess C for a phylogenetic tree (the hypothesis, h ), several interpretations have been given for p ( e|b ). Here I describe a new interpretation that equates p ( e|b ) with the probability of the data in the absence of a hypothesis of phylogenetic resolution, that is with the likelihood of an unresolved or polytomous tree. Under this interpretation, C for a fully or partially resolved phylogenetic tree is the likelihood of that tree minus the likelihood of the corresponding unresolved tree. These same two likelihoods can be used in a likelihood ratio test (LRT) to assess the significance of the degree of corroboration of the hypothesis of phylogenetic resolution. This LRT for resolution is closely related to permutation tests for phylogenetic structure in the data, because data that evolved on a true polytomous tree are expected to be phylogenetically randomized. It therefore reconciles the interpretation of the evidence ( e ) as the distribution of character states among taxa (rather than the score of the optimal tree) with the interpretation of permutation tests as methods for assessing C. Likelihood methods are (contrary to the views of some commentators) central to understanding how Popper's C applies to phylogenetic hypotheses, and they form the foundation of a unified and inclusive philosophy of phylogenetic inference.     

Failed refutations: further comments on parsimony and likelihood methods and their relationship to Popper's degree of corroboration

Kluge's (2001, Syst. Biol. 50:322-330) continued arguments that phylogenetic methods based on the statistical principle of likelihood are incompatible with the philosophy of science described by Karl Popper are based on false premises related to Kluge's misrepresentations of Popper's philosophy. Contrary to Kluge's conjectures, likelihood methods are not inherently verificationist; they do not treat every instance of a hypothesis as confirmation of that hypothesis. The historical nature of phylogeny does not preclude phylogenetic hypotheses from being evaluated using the probability of evidence. The low absolute probabilities of hypotheses are irrelevant to the correct interpretation of Popper's concept termed degree of corroboration, which is defined entirely in terms of relative probabilities. Popper did not advocate minimizing background knowledge; in any case, the background knowledge of both parsimony and likelihood methods consists of the general assumption of descent with modification and additional assumptions that are deterministic, concerning which tree is considered most highly corroborated. Although parsimony methods do not assume (in the sense of entailing) that homoplasy is rare, they do assume (in the sense of requiring to obtain a correct phylogenetic inference) certain things about patterns of homoplasy. Both parsimony and likelihood methods assume (in the sense of implying by the manner in which they operate) various things about evolutionary processes, although violation of those assumptions does not always cause the methods to yield incorrect phylogenetic inferences. Test severity is increased by sampling additional relevant characters rather than by character reanalysis, although either interpretation is compatible with the use of phylogenetic likelihood methods. Neither parsimony nor likelihood methods assess test severity (critical evidence) when used to identify a most highly corroborated tree(s) based on a single method or model and a single body of data; however, both classes of methods can be used to perform severe tests. The assumption of descent with modification is insufficient background knowledge to justify cladistic parsimony as a method for assessing degree of corroboration. Invoking equivalency between parsimony methods and likelihood models that assume no common mechanism emphasizes the necessity of additional assumptions, at least some of which are probabilistic in nature. Incongruent characters do not qualify as falsifiers of phylogenetic hypotheses except under extremely unrealistic evolutionary models; therefore, justifications of parsimony methods as falsificationist based on the idea that they minimize the ad hoc dismissal of falsifiers are questionable. Probabilistic concepts such as degree of corroboration and likelihood provide a more appropriate framework for understanding how phylogenetics conforms with Popper's philosophy of science. Likelihood ratio tests do not assume what is at issue but instead are methods for testing hypotheses according to an accepted standard of statistical significance and for incorporating considerations about test severity. These tests are fundamentally similar to Popper's degree of corroboration in being based on the relationship between the probability of the evidence e in the presence versus absence of the hypothesis h, i.e., between p(e|hb) and p(e|b), where b is the background knowledge. Both parsimony and likelihood methods are inductive in that their inferences (particular trees) contain more information than (and therefore do not follow necessarily from) the observations upon which they are based; however, both are deductive in that their conclusions (tree lengths and likelihoods) follow necessarily from their premises (particular trees, observed character state distributions, and evolutionary models). For these and other reasons, phylogenetic likelihood methods are highly compatible with Karl Popper's philosophy of science and offer several advantages over parsimony methods in this context.     

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.     

Parsimony, likelihood, and simplicity

The latest charge against parsimony in phylogenetic inference is that it involves estimating too many parameters. The charge is derived from the fact that, when each character is allowed a branch length vector of its own (instead of the homogeneous branch lengths assumed in current likelihood models), the results for likelihood and parsimony are identical. Parsimony, however, can also be derived from simpler models, involving fewer parameters. Therefore, parsimony provides (as many authors had argued before) the simplest explanation of the data, or the most realistic, depending on one's views. If (as argued by likelihoodists) phylogenetic inference is to use the simplest model that provides sufficient explanation of the data, the starting point of phylogenetic analyses should be parsimony, not maximum likelihood. If the addition of new parameters (which increase the likelihood) to a parsimony estimation is seen as desirable, this may lead to a preference for results based on current likelihood models. If the addition of parameters is continued, however, the results will eventually come back to the same place where they had started, since allowing each character a branch length of its own also produces parsimony. Parsimony can be justified by very different types of models—either very complex or very simple. This suggests that parsimony does have a unique place among methods of phylogenetic estimation.     

Vagaries in the delimitation of character states in quantitative variation--an experimental study

An experimental study on the delimitation of character states in continuous variation indicates that (1) the way data are presented influences the assignment of character states and (2) states in the same data set are delimited in various ways by different individuals. Forty-nine individuals were given a set of graphs denoting variation of 10 characters in the genus Kalmia (Ericaceae) and outgroups, all identification having been removed from the graphs. The variation was represented in one of three ways: as 95% confidence intervals on a linear scale, as 95% confidence intervals on a log10 scale, or with bars showing SD x 2 on a linear scale. No two individuals scored a set of graphs in the same way, and only one character in one representation was scored identically by all individuals; the scoring for this character was completely different when the ordinate was changed from linear to logarithmic. Together, the 49 individuals delimited states within each character between 9 and 16 different ways. In general, variation represented by 2 x SD bars elicited the largest numbers of different scorings, yet with a relatively low number of states; the complexity of the patterns in the graphs in this representation was greatest. Expert knowledge appears to be of dubious value in delimiting states in such variation, and if such characters are to be used in phylogenetic analyses, states could be delimited by people who know nothing of the details of the study being scored; in any case, presentation of data and an explicit protocol to follow when delimiting states are essential. In converting data of this type into character states, psychological factors are particularly likely to come into play. Other implications of our experiments include the severe underdetermination of some phylogenetic hypotheses by observation and the heterogeneous nature of morphological data.     

Corroboration versus "Strongest Evidence"

Background knowledge comprises accepted (well-corroborated) theories and results. Such theories are taken to be true for the purpose of interpreting evidence when assessing the corroboration of a hypothesis currently in question. Accordingly, background knowledge does not properly include rejected theories, false assumptions, or null models. In particular, regarding a model of random character distribution as "background knowledge" would rule out corroboration of phylogenetic hypotheses, since it would make character data irrelevant to inferring phylogeny. The presence of homoplasy is not grounds for treating characters as if they were randomly distributed, since characters can show strong phylogenetic structure even when they show homoplasy. This means that clique (compatibility) analysis is unjustified, since that method depends crucially on the assumption that characters showing any homoplasy at all are unrelated to phylogeny. Although likelihood does not measure corroboration, corroboration is closely connected to likelihood: for given evidence and background, the most likely trees are also best corroborated. Most parsimonious trees are best corroborated; the apparent clash between parsimony and likelihood is an artifact of the use of unrealistic models in most "maximum likelihood" methods.     

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.     

Estimating a binary character's effect on speciation and extinction

Determining whether speciation and extinction rates depend on the state of a particular character has been of long-standing interest to evolutionary biologists. To assess the effect of a character on diversification rates using likelihood methods requires that we be able to calculate the probability that a group of extant species would have evolved as observed, given a particular model of the character's effect. Here we describe how to calculate this probability for a phylogenetic tree and a two-state (binary) character under a simple model of evolution (the "BiSSE" model, binary-state speciation and extinction). The model involves six parameters, specifying two speciation rates (rate when the lineage is in state 0; rate when in state 1), two extinction rates (when in state 0; when in state 1), and two rates of character state change (from 0 to 1, and from 1 to 0). Using these probability calculations, we can do maximum likelihood inference to estimate the model's parameters and perform hypothesis tests (e.g., is the rate of speciation elevated for one character state over the other?). We demonstrate the application of the method using simulated data with known parameter values.     

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

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

A likelihood approach to estimating phylogeny from discrete morphological character data

Evolutionary biologists have adopted simple likelihood models for purposes of estimating ancestral states and evaluating character independence on specified phylogenies; however, for purposes of estimating phylogenies by using discrete morphological data, maximum parsimony remains the only option. This paper explores the possibility of using standard, well-behaved Markov models for estimating morphological phylogenies (including branch lengths) under the likelihood criterion. An important modification of standard Markov models involves making the likelihood conditional on characters being variable, because constant characters are absent in morphological data sets. Without this modification, branch lengths are often overestimated, resulting in potentially serious biases in tree topology selection. Several new avenues of research are opened by an explicitly model-based approach to phylogenetic analysis of discrete morphological data, including combined-data likelihood analyses (morphology + sequence data), likelihood ratio tests, and Bayesian analyses.     

Comparative and phylogenetic analysis of developmental sequences

Event pairing has been proposed for the optimization of developmental sequences (event sequences) on a given phylogenetic hypothesis (cladogram) to determine instances of sequence heterochrony. Here, we show that event pairing is faulty, leading to the optimization of impossible hypothetical ancestors, the underestimation of the lengths of the developmental sequences on the tree, and the proposition of synapomorphies that are not supported by the data. When used for phylogenetic analysis, event pairing can even produce cladograms that are inconsistent with the data. These errors are caused by the fact that event pairing treats dependent features as if they were independent. We present a new method for comparative and phylogenetic analysis of developmental sequences that does not exhibit these errors. Our method applies Search-based character optimization and treats the entire developmental sequence as a single character that is then analyzed by using an edit cost function, which specifies the transformation cost between pairs of observed and unobserved character states, and dynamic programming. In other words, the developmental sequence is directly optimized on the tree. We used event pairing as an edit cost function, but others are possible.     

Relative apparent synapomorphy analysis (RASA). I: The statistical measurement of phylogenetic signal

We have developed a new approach to the measurement of phylogenetic signal in character state matrices called relative apparent synapomorphy analysis (RASA). RASA provides a deterministic, statistical measure of natural cladistic hierarchy (phylogenetic signal) in character state matrices. The method works by determining whether a measure of the rate of increase of cladistic similarity among pairs of taxa as a function of phenetic similarity is greater than a null equiprobable rate of increase. Our investigation of the utility and limitations of RASA using simulated and bacteriophage T7 data sets indicates that the method has numerous advantages over existing measures of signal. A first advantage is computational efficiency. A second advantage is that RASA employs known methods of statistical inference, providing measurable sensitivity and power. The performance of RASA is examined under various conditions of branching evolution as the number of characters, character states per character, and mutations per branch length are varied. RASA appears to provide an unbiased and reliable measure of phylogenetic signal, and the general approach promises to be useful in the development of new techniques that should increase the rigor and reliability of phylogenetic estimates.      

The phylogenetic position of the Clitellata and the Echiura - on the problematic assessment of absent characters*

Absent characters (negative characters) are difficult to assess and their correct interpretation as symplesiomorphies, synapomorphies or convergencies (homoplasies) is one of the greatest challenges in phylogenetic systematics. Different phylogenetic assessments often result in contradictory phylogenetic hypotheses, in which the direction of evolutionary changes is diametrically opposed. Especially in deciding between primary (plesiomorphic) and secondary (apomorphic) absence, false conclusions may be reached if only the outgroup comparison and the principle of parsimony are employed without attempting any biological evaluation or interpretation of characters. For example, in the higher‐level systematization of the Annelida and related taxa different assessments of absent characters have led to conflicting hypotheses about the phylogenetic relationships and the ground pattern of the annelid stem species. Varying phylogenetic interpretations regarding the absence of the chemosensory nuchal organs in the clitellates and their presence in polychaetes initiated a controversy that produced two alternative phylogenetic hypotheses: (1) the Clitellata are highly derived Annelida related to a subtaxon within the, in this case, paraphyletic ‘Polychaeta’ or (2) the Clitellata are comparatively primitive Annelida representing the sister group of a monophyletic taxon Polychaeta. In the former, the absence of nuchal organs in the Clitellata is regarded as a secondary character, in the latter as primary. As most Clitellata are either limnetic or terrestrial, we must ask which characters are plesiomorphies, taken from their marine stem species without changes. In addition to a thorough investigation and evaluation of clitellate characters, a promising approach to these questions is to look for such characters in limnetic and terrestrial annelids clearly not belonging to the Clitellata. A similar problem applies to the evaluation of the position of the Echiura, which lack both segmentation and nuchal organs. Evidence is presented that in both taxa these absent characters represent derived, apomorphic character states. The consequences for their phylogenetic position and the questionable monophyly of the Polychaeta are discussed. The conclusion drawn from morphological character assessments is in accordance with recently published hypotheses based on molecular data.     

Perfectly misleading distances from ternary characters

D. Huson and M. Steel showed that for any two binary phylogenetic trees on the same set of n taxa, there exists a sequence of multistate characters that is homoplasy-free only on the first tree but perfectly additive only on the second one. The original construction of such a sequence required n - 1 character states and it remained an open question whether a sequence using fewer character states can always be found. In the present note we will answer this question by showing that three character states suffice to construct such misleading sequences--even if we insist that they conform to an ultrametric (i.e., fit a molecular clock).     

The evolution of pelvic osteology and soft tissues on the line to extant birds (Neornithes)

Substantial differences in pelvic osteology and soft tissues separate crown group crocodylians (Crocodylia) and birds (Neornithes). A phylogenetic perspective including fossils reveals that these disparities arose in a stepwise pattern along the line to extant birds, with major changes occurring both within and outside Aves. Some character states that preceded the origin of Neornithes are only observable or inferable in extinct taxa. These transitional states are important for recognizing the derived traits of neornithines. Palaeontological and neontological data are vital for reconstructing the sequence of pelvic changes along the line to Neornithes. Soft tissue correlation with osteological structures allows changes in soft tissue anatomy to be traced along a phylogenetic framework, and adds anatomical significance to systematic characters from osteology. Explicitly addressing homologies of bone surfaces reveals many subtleties in pelvic evolution that were previously unrecognized or implicit. I advocate that many anatomical features often treated as independent characters should be interpreted as different character states of the same character. Relatively few pelvic character states are unique to Neornithes. Indeed, many features evolved quite early along the line to Neornithes, blurring the distinction between 'avian' and 'non-avian' anatomy.