Mapping Uncertainty and Phylogenetic Uncertainty in Ancestral Character State Reconstruction: An Example in the Moss Genus Brachytheciastrum

A. Vanderpoorten; B. Goffinet

doi:10.1080/10635150601088995

Mapping Uncertainty and Phylogenetic Uncertainty in Ancestral Character State Reconstruction: An Example in the Moss Genus Brachytheciastrum

Vanderpoorten, A.;Goffinet, B. 2006-12-01 00:00:00 Abstract 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. Ancestral character-state reconstruction, Bayesian inference, comparative methods, moss, uncertainty The study of trait evolution and diversification has traditionally relied on fossil records, comparisons between fossils and extant forms, and among groups of extant species and estimated divergence times (Mooers et al., 1999). The exponential development of molecular techniques and statistical tools has more recently enabled the exploration of diversification and adaptation of traits in a phylogenetic context (Pagel, 1998; Martins, 2000). Phylogenetic reconstruction of ancestral character states offers a unique framework in evolutionary studies when fossil evidence is not available, either due to the nature of the investigated traits (e.g., behavioral or molecular evolution) or in groups of taxa, wherein fossil evidence is absent or exceedingly scarce. This endeavor involves the reconstruction of ancestral character states on phylogenetic trees according to some evolutionary model or set of assumptions (Pagel, 1999a) globally termed ‘comparative methods.’ Comparative methods can be used to discover, in a manner that might be described as ‘statistical paleontology,’ the diversity of biological traits exhibited by ancestral species, but also the nature of the underlying evolutionary process, i.e., the mode, tempo, and phylogenetic component of the evolution (Pagel, 1998). Maximum parsimony has been the most widely used principle for inferring character-state transformations onto a phylogenetic tree. The parsimony criterion singles out the solution requiring the minimum amount of changes on a tree. A range of alternative reconstructions on the same tree however exists, creating a source of error known as ‘mapping uncertainty’ (Ronquist, 2004) or ‘within-tree uncertainty’ (Pagel et al., 2004). By contrast, maximum likelihood estimators have enabled an assessment of the accuracy of reconstructions (Cunningham et al., 1998; Cunningham, 1999). Under the likelihood criterion, branch lengths are used to determine the probability of change. Furthermore, and perhaps more importantly, ML methods implement explicit models of evolution and therefore enable one to make and test hypotheses regarding evolutionary processes by contrasting the fit of different models to the data. The characterization of the phylogenetic ‘signal’ or component of evolution, i.e., the fact that phylogenetically related organisms tend to resemble each other more than distantly related ones (Blomberg and Garland, 2002), has for example important consequences for the understanding of trait evolution itself (Mooers et al., 1999). Non-phylogenetic models indeed assume that no change occurred in the internal branches and that all changes are restricted to terminal branches, as if the historical signal had been erased in the course of the evolutionary history (Mooers et al., 1999; Oakley et al., 2005). In turn, phylogenetic models assume that the branching pattern of the phylogeny predicts phenotypic evolution. The fit of alternative phylogenetic and nonphylogenetic models, which can be tested by standard likelihood-ratio tests (Oakley et al., 2005), can have important consequences in comparative studies involving across-species trait correlations that are not appropriately described by conventional statistical methods disregarding phylogenetic dependence in the data (Freckleton et al., 2002; Pagel, 2002; Blomberg et al., 2003). Comparative studies have traditionally been performed onto one or a few trees. Phylogenies are, however, rarely known without error. Different estimates of the phylogenetic tree can return different answers to the comparative question (Miller and Venable, 2003; Ober, 2003; Thompson and Oldroyd, 2004), causing a second source of uncertainty known as ‘phylogenetic uncertainty’ (Pagel and Lutzoni, 2002; Ronquist, 2004; Pagel et al., 2004). In this context, Markov chain Monte Carlo methods offer a formal framework to sample phylogenies according to their posterior probabilities. A straightforward way of taking phylogenetic uncertainty into account when reconstructing ancestral character states is to find the best-fit model on each tree and derive the corresponding ancestral character states as proposed, for example, by the program package Mesquite (Maddison and Maddison, 2005). This procedure enables an assessment of among-tree variation in ancestral character state reconstruction but does not account for the uncertainty associated with the estimation of the rate parameters themselves on each individual tree. Most recently, a Bayesian Markov chain Monte Carlo procedure was proposed to derive the posterior probability distribution of rate coefficients and ancestral character states (Pagel and Lutzoni, 2002; Pagel et al., 2004). At each iteration, the chain proposes a new combination of rate parameters and randomly selects a new tree from the Bayesian sample. The likelihood of the new combination is calculated and this new state of the chain is accepted or rejected following evaluation by the Metropolis-Hastings term. In an attempt to examine trait evolution along a phylogeny, one is thus left with a series of possible, not necessarily complementary approaches. If the limitations of the MP criterion for character state reconstruction have already been emphasized (Cunningham et al., 1998; Cunningham, 1999), the Bayesian approach of phylogenetic uncertainty is fairly recent and has therefore been applied only in a few cases to comparative studies (e.g., Lutzoni et al., 2001; Pagel et al., 2004). In mosses, the second most diverse phylum of land plants after the Angiosperms, fossil evidence is exceedingly rare (Goffinet, 2000) and comparative methods constitute a tool of prime importance to test hypotheses on the phylogenetic component of morphological evolution and the soundness of characters traditionally used in taxonomy. Although molecular phylogenies are becoming increasingly available to test previous taxonomic concepts (see [Goffinet and Buck 2004] for a review), morphological evolution has rarely been explicitly revisited by formally reconstructing ancestral shifts in character states (Vanderpoorten et al., 2002). In this paper, we test species concepts in the moss genus Brachytheciastrum by retracing the evolution of traditional taxonomic characters in a phylogenetic context. We seek for an appropriate model of evolution for reconstructing ancestral character states within the genus, contrasting results from (1) a ML optimization of rate parameters on a single, ML tree; (2) a ML optimization of rate parameters applied to a Bayesian sample of trees; and (3) a Bayesian sample of rate parameters used to produce the posterior probability distribution of ancestral character states. Methods Taxon Sampling, Molecular and Morphological Data Brachytheciastrum is one of 41 genera of the highly diverse pleurocarpous moss family Brachytheciaceae (Hypnales), which, with slightly less than 600 species, represent one of the most diverse families of pleurocarpous mosses (Ignatov and Huttunen, 2002). Brachytheciastrum currently includes nine species that form a strongly supported clade sister to Homalothecium (Vanderpoorten et al., 2005). One species of the latter, H. megaptilum, was selected as outgroup. Within the ingroup, multiple specimens belonging to eight of the nine species were sampled depending on the availability of sufficiently recent collections (Table 1). Each species was therefore represented by one (e.g., B. bellicum, currently only known from the type locality [Buck et al., 2001]) to several accessions. A set of 19 variable morphological characters, including the ones that have been used in the original species descriptions and a series of others that have recently been used in species-level taxonomy of the Brachytheciaceae (Ignatov and Huttunen, 2002), was scored for each of these specimens ( Appendices 1 and 2). Table 1 Taxon sampling, voucher information, and GenBank accession numbers for the ITS region and the atpB-rbcL intergenic spacer. Taxon ITS atpB-rbcL Voucher (herbarium where deposited) Locality (country; province, region, or state) bellicum AY737458 AY663293 Cano & Ros 9510 (MUR) Morocco, Rif collinum a AY737478 AY663296 Sotiaux 14574 (LG) France, Hautes Alpes collinum b AY737459 AY663297 Buck 23168 (NY) USA, OR collinum c AY736258 AY736265 Ignatov 31/55 (MHA) Russia, Altai collinum d AY736257 AY736264 Euragina 5. V 2002 (MHA) Russia, Astrakhan collinum e AY736256 AY736263 Czernyadievk £53 (MHA) Russia, Kamchatka dieckei a AY737460 AY663298 Sergio sn (LISU) Portugal, Beira Alta dieckei b AY737475 AY663319 Sergio & Seneca 8163 (NY) Portugal, Beira Alta dieckei c AY737476 AY663313 Canos & Ros 9512 (NY) Morocco, Rif dieckei d AY737477 AY663316 Cano & Ros 9513 (NY) Morocco, Rif fendleri AY737461 AY663302 Weber & Wittmann B112193 (NY) USA, CO leibergii AY737462 AY663301 Buck 37564 (NY) USA, OR olympicum a AY737474 AY736271 Düll exs 268 (LG) USA, CA olympicum b AY737472 AY736270 Düll exs 359 (LG) USA, CA olympicum c AY952446 AY952447 Seregin et al. M-255 (MW) Cyprus, Troodos Range trachypodium a AY736260 AY736267 Ignatov 31/229 1992 (MHA) Russia, Altai trachypodium b AY736261 AY736268 Ignatov 00-1055 6.IX. 2000 (MHA) Russia, Yakytia trachypodium c AY736259 AY736266 23. VII 1976 H. Roivainen (MHA) Russia, Caucasus velutinum a AY737473 AY663299 Sotiaux 27346 (LG) Belgium, Luxembourg velutinum b AY737464 AY663300 Vanderpoorten B51 (LG) Belgium, Liège velutinum c AY736262 AY736269 Ignatov 15.9.1996 (MHA) Russia, Kursk Homalothecium megaptilum AY737455 AY663307 Vanderpoorten 4691 (LG) Canada, BC Taxon ITS atpB-rbcL Voucher (herbarium where deposited) Locality (country; province, region, or state) bellicum AY737458 AY663293 Cano & Ros 9510 (MUR) Morocco, Rif collinum a AY737478 AY663296 Sotiaux 14574 (LG) France, Hautes Alpes collinum b AY737459 AY663297 Buck 23168 (NY) USA, OR collinum c AY736258 AY736265 Ignatov 31/55 (MHA) Russia, Altai collinum d AY736257 AY736264 Euragina 5. V 2002 (MHA) Russia, Astrakhan collinum e AY736256 AY736263 Czernyadievk £53 (MHA) Russia, Kamchatka dieckei a AY737460 AY663298 Sergio sn (LISU) Portugal, Beira Alta dieckei b AY737475 AY663319 Sergio & Seneca 8163 (NY) Portugal, Beira Alta dieckei c AY737476 AY663313 Canos & Ros 9512 (NY) Morocco, Rif dieckei d AY737477 AY663316 Cano & Ros 9513 (NY) Morocco, Rif fendleri AY737461 AY663302 Weber & Wittmann B112193 (NY) USA, CO leibergii AY737462 AY663301 Buck 37564 (NY) USA, OR olympicum a AY737474 AY736271 Düll exs 268 (LG) USA, CA olympicum b AY737472 AY736270 Düll exs 359 (LG) USA, CA olympicum c AY952446 AY952447 Seregin et al. M-255 (MW) Cyprus, Troodos Range trachypodium a AY736260 AY736267 Ignatov 31/229 1992 (MHA) Russia, Altai trachypodium b AY736261 AY736268 Ignatov 00-1055 6.IX. 2000 (MHA) Russia, Yakytia trachypodium c AY736259 AY736266 23. VII 1976 H. Roivainen (MHA) Russia, Caucasus velutinum a AY737473 AY663299 Sotiaux 27346 (LG) Belgium, Luxembourg velutinum b AY737464 AY663300 Vanderpoorten B51 (LG) Belgium, Liège velutinum c AY736262 AY736269 Ignatov 15.9.1996 (MHA) Russia, Kursk Homalothecium megaptilum AY737455 AY663307 Vanderpoorten 4691 (LG) Canada, BC View Large Preliminary investigation (Vanderpoorten et al., 2005) suggested that the atpB-rbcL intergenic spacer (cpDNA) and the ITS region (nrDNA) may exhibit the appropriate level of variation to discriminate species in the genus. These two loci were amplified and sequenced for each accession according to the protocols described in Vanderpoorten et al. (2002). Due to the difficulties encountered with the amplification of the chloroplast locus in several accessions, a specific set of primers was designed within conserved regions at the 5’ and 3' ends of the molecule from the available sequences of the genus: atpB : GGGACCAATAATTTGAGTAATACGTCC (Tm = 65.8°C); rbcL : GGTGACATAGGTCCCTCCC (Tm = 63.2°C). Phylogenetic Analyses Phylogenetic analyses of DNA sequences were conducted by maximizing the likelihood under the assumptions of a model of nucleotide substitution. The hierarchical likelihood-ratio test (hLRT) has been the most popular method to select, among increasingly complex models, the one that best fits the data with a minimum of estimated parameters. hLRTs do, however, not allow for non-nested comparisons or simultaneous comparison of multiple models. Their use for model selection has therefore been recently questioned. In this context, other selection techniques, including the Bayesian information criterion (BIC) and Akaike information criterion, have been proposed (see Huelsenbeck et al. [2004] and Posada and Buckley [2004] for reviews). Here, we selected the model in the decision theory framework developed by Minin et al. (2003), which is based on the BIC but incorporates branch length error as a performance measure. Simulations suggested that models selected with this criterion result in slightly more accurate branch length estimates, an essential feature of the phylogeny in a character-state reconstruction context. Model selection was done using the program DT-ModSel (Minin et al., 2003). The selected model was implemented in heuristic searches with 300 random addition replicates with TBR branch swapping to find the most likely tree in PAUP* (Swofford, 2002). Branches of zero length were collapsed during the search. No taxon was resolved as part of two distinct clades supported each by > 70% Bayesian proportions (BP, see below) in analyses of the nuclear and chloroplast data sets and these partitions were therefore combined into a single matrix (TreeBase accession number M2985). The score of the candidate trees that resulted from the heuristic search was reassessed by specifically modeling base composition, substitution rates, and rate heterogeneity for the chloroplast locus and each of the different partitions of the ITS region, namely ITS1, the 5.8S rRNA gene, and ITS2, using the algorithms implemented by PAML (Yang, 1997). Within each partition, rate heterogeneity was modeled using a discrete gamma distribution with eight categories. A phylogram of the final tree selected for its highest likelihood was eventually constructed with TreeView (Page, 1996). Significant departure of alternative topologies involving a morphological taxon concept from the optimal molecular topologies was tested by constraining the accessions of the same morphospecies to monophyly. Optimal constrained topologies were sought under maximum likelihood. Significant departure from the unconstrained optimal topology was tested using the procedure described by Shimodaira and Hasagawa (1999) with 1000 replicates of full optimization. Support for clades was assessed using a Bayesian procedure employing a mixture model that simultaneously implements several rate matrices without a priori partitioning of the data (Pagel and Meade, 2004). Four chains of 1,000,000 iterations were run and trees were sampled every 10,000 generations to ensure independence of successive trees. The number of generations needed to reach stationarity in the Markov chain Monte Carlo algorithm was estimated by visual inspection of the plot of the ML score at each sampling point. The trees of the ‘burn-in’ for each run were excluded from the tree set, and the 100 remaining trees from each run were combined to form the full sample of trees assumed to be representative of the posterior probability distribution. The sampling size, comparable to that used in other studies (e.g., Pagel et al., 2004), allowed the chains to visit most of the frequently occurring topologies, as shown by the similarity of the posteriors returned by each of the four runs. We contrasted the performances of increasingly complex models employing one to three rate matrices, and with or without gamma distributions, to model within-matrix rate heterogeneity, by plotting the log-likelihood values against the standard deviation of the rate matrix parameters, looking for a cut-off point that corresponds to a slowing in the improvement to the overall log-likelihood and a sharp increase in the standard deviation of the model parameters. Morphological Evolution Model Optimization and Test of Hypotheses The phylogeny was used to study the evolution for each individual morphological character. The probabilities of change in a branch were calculated by estimating the instantaneous rates of transitions among all possible pairs of states by implementing the Markov model of the software Multistate. We used the ‘global’ approach, wherein model parameters are first fixed and then used to derive the set of most likely ancestral character states (Pagel, 1999b). ‘Local’ estimators, by contrast, allow for alternative hypotheses of ancestral states to be tested at each individual node, but do not represent the most likely estimates because different rates are fitted after the node under scrutiny has been set to its two possible states (Mooers, 2004). Global reconstructions, which, for reasons that are still unclear, are more accurate than local ones (Mooers, 2004), provide true posterior probabilities of states across nodes, and thus yield the single best description of the past (Pagel, 1999b; Mooers, 2004). The model includes two parameters: the instantaneous transition rate q and a parameter (κ) used to perform branch length transformations in order to improve the fit of the model to the data. κ differentially stretches or compresses individual branches. κ > 1 stretches long branches more than shorter ones, indicating that longer branches contribute more to trait evolution (as if the rate of evolution accelerates within a long branch). κ < 1 compresses longer branches more than shorter ones. At the extreme, κ = 0 is consistent with a mode of evolution, in which trait evolution is independent of the length of the branch (Pagel, 1994). We tested whether models directly employing genetic distances (or a transformation thereof) to determine the probability of change, i.e., models allowing for continuous changes along the branches, described the evolution of the traits significantly better than ‘speciational’ models employing branches of equal lengths. To this end, we contrasted the fit of a model, wherein κ was restricted to 0 (all branches of equal length), with the fit of a model, wherein κ was free to take its most likely value. The two models differ in one parameter and can thus be compared by a likelihood-ratio test, according to which the more complicated model provides a significantly better representation of the data if twice the difference in log-likelihood returned by the respective models is higher than a chi-square variate with one degree of freedom (Pagel, 1994). Finally, we used a likelihood ratio to test whether applying a model including a forward and backward transition rate significantly improved the likelihood as compared to a single rate model. All the parameters were then fixed to calculate the probabilities of ancestral character states across all nodes. In binary characters, evidence for phylogenetic signal in the data is found anytime the probabilities of ancestral states differ from 0.5 and signal intensity is proportional to departure of ancestral state probabilities from 0.5 (A. Meade and M. Pagel, personal communication). Indeed, the probabilities of change along each branch are weighted by the prior probability of state at the beginning of the branch (Pagel, 1999b). Thus, when all ancestral state probabilities equal 0.5, the state at a node is independent of the state at the previous node, as if there was no history in the tree. In this case, our experience is that transition rates acquire very large values, so that the transitions probabilities pii(t) and pij(t) do not depart from the 0.5 stationary frequencies assumed by the model (see Lewis, 2001:915). The significance of the phylogenetic signal was tested by comparing the fit of phylogenetic vs nonphylogenetic models to the data (Mooers et al., 1999). We thus contrasted the likelihood in the context of the phylogeny and of a star-tree, wherein all internal branches were set to 0 and wherein the length of each terminal branch corresponded to the total path from the root to the extant species. The phylogenetic and nonphylogenetic models include the same number of parameters and the likelihood values they return can therefore be directly compared, with a difference of two being considered significant (Mooers et al., 1999; Oakley et al., 2005). Phylogenetic Uncertainty Two methods were used for assessing whether phylogenetic uncertainty affects the probabilities of ancestral character states. In a first series of analyses, the phylogenetic robustness of the reconstructions was assessed, for each node of the phylogeny, by reconstructing ancestral character states using the ML optimization described above across the Bayesian sample of trees. For each tree, model selection was performed as described above and results from different models were combined to form the full range of probabilities of ancestral character states at a node across trees. In order to circumvent the issues associated with the fact, that not all of the trees necessarily contain the internal nodes of interest, reconstructions were performed using a ‘most recent common ancestor’ approach that identifies, for each tree, the most recent common ancestor to a group of species and reconstructs the state at the node, then combines this information across trees (Pagel et al., 2004). In a second series of analyses, we examined the impact of the choice of a range of model parameters within and among trees by using the Markov chain model implemented by Bayes Multistate to estimate the posterior probability distributions of rate coefficients and ancestral states (Pagel et al., 2004). The rate at which parameters get changed (‘ratedev’) was set at the beginning of each run so that the acceptance rate of the proposed changes globally ranges between 20% and 50%. Priors of the rate parameters were derived from their likelihood surface as proposed by Pagel et al. (2004). For that purpose, the magnitude of a rate coefficient was manually allowed to vary from low to high values, calculating the likelihood on the 50% majority-rule consensus tree, whose branch lengths were averaged over the 400 sampled trees. This operation was repeated for the other parameter. The resulting likelihood curves were treated as a beta distribution, taking the mode as the mean and calculating the standard deviation on the assumption that the mean ± three times the standard deviation includes all of the rates. Rate coefficients and ancestral character states, reconstructed using the most recent common ancestor approach, were sampled every 100 generations to ensure independence from successive samplings. The chain was run for 4,000,000 generations so that each tree was visited approximately 100 times by the chain on average. The within-and among-tree proportion of the variation in model parameters and ancestral character state reconstructions was partitioned by one-way analysis of variance depending on the factor ‘tree number.’ Comparison Among Methods of Ancestral Character State Reconstruction We examined whether congruent estimates of ancestral character states were produced by methods employing (I) a single set of model parameters optimized by ML onto a single, ML tree (II) a set of single model parameters each individually optimized by ML onto a sample of trees; and (III) a Markov chain visiting a sample of trees to produce the posterior probability distribution of model parameters and ancestral character states. After having calculated the average probabilities at each node in methods II, and III, we used correlation coefficients to estimate the extent to which changes in character states from a node to another varied in a correlated fashion when node states were estimated using methods I, II and III, respectively. In order to test whether a reconstruction method returned on average higher probabilities of ancestral character states, we contrasted the probabilities of the most likely reconstruction at each node (or the average probability of the most likely character state at a node in methods II and III) by a pairwise Student's t test across nodes. Results Phylogenetic Reconstruction The ITS region and the atpB-rbcL intergenic spacer respectively included 4.5% and 6.1% of variable sites within Brachytheciastrum. Both partitions yielded congruent topologies and were therefore combined. The substitution model selected for the combined data set was the Hasegawa et al. model (see, e.g., Nei and Kumar, 2000, for reference) with a gamma distribution (α = 0.1149) to model among-site heterogeneity. The model implemented a transition/transversion ratio of 1.7654 and A, C, and G nucleotide proportions of 0.2975, 0.1953, and 0.2136, respectively. Heuristic searches using these settings resulted in a unique ML tree (−lnL = 2526.51). Allowing the fit of different rate parameters, base compositions, and shapes of the gamma distribution for each of the molecular partitions with highly divergent GC contents, transition-transversion ratios, and patterns of rate heterogeneity resulted in a substantial improvement of the likelihood (−lnL = 2349.38). Three morphospecies were resolved as polyphyletic assemblages in the optimal topology. Constraining successively each of those morphospecies to monophyly resulted in a significant decrease in log-likelihood (Δ lnL = 23.53, P = 0.02 for B. collinum; Δ lnL = 29.6, P = 0.02 for B. dieckei; and Δ lnL = 22.72, P = 0.03 for B. trachypodium). The log-likelihoods returned by increasingly complex models implementing one to three HKY rate matrices during the Bayesian analysis of the combined DNA data set are represented as a function of the standard deviation of the rate parameters in Figure 1. The curve shows a sharp cut-off point at the two-rate matrix model. Beyond that level of complexity, the log-likelihoods returned by models employing more parameters exhibited a very slow increase, whereas standard deviations of rate parameters substantially increased. The two-rate matrix model was therefore selected for producing the Bayesian sample of trees used to compute branch posterior probabilities (Fig. 2) and for assessing phylogenetic uncertainty in ancestral character state reconstruction. The reconstructions were performed on each of the 14 nodes exhibiting > 50% posterior probabilities. Figure 1 View largeDownload slide Plot of the standard deviation of the transition/transversion ratio of the HKY substitution model over the 400 MCMC sample of trees as a function of the average log-likelihoods returned by increasingly complex substitution models implementing one (1r) to three (3r) rate matrices, with or without Γ distributions to model within-matrix rate heterogeneity. Figure 1 View largeDownload slide Plot of the standard deviation of the transition/transversion ratio of the HKY substitution model over the 400 MCMC sample of trees as a function of the average log-likelihoods returned by increasingly complex substitution models implementing one (1r) to three (3r) rate matrices, with or without Γ distributions to model within-matrix rate heterogeneity. Figure 2 View largeDownload slide Phylogram of the 50% majority-rule consensus of the 400 MCMC sample of trees with branch lengths averaged over the whole sample from the Bayesian analysis of ITS and atpB-rbcL sequences in Brachytheciastrum using a mixture model with two-rate matrices. Number below the branches correspond to the proportions in which they appear in the 400 sampled trees. Pie diagrams indicate the probabilities of ancestral state for stem leaf cell width (character 16: white: > 8 μ m; black: < 8 μ m) derived from a maximum likelihood optimization of the parameters of the model of morphological evolution on the ML tree. Figure 2 View largeDownload slide Phylogram of the 50% majority-rule consensus of the 400 MCMC sample of trees with branch lengths averaged over the whole sample from the Bayesian analysis of ITS and atpB-rbcL sequences in Brachytheciastrum using a mixture model with two-rate matrices. Number below the branches correspond to the proportions in which they appear in the 400 sampled trees. Pie diagrams indicate the probabilities of ancestral state for stem leaf cell width (character 16: white: > 8 μ m; black: < 8 μ m) derived from a maximum likelihood optimization of the parameters of the model of morphological evolution on the ML tree. Reconstruction of Ancestral Character States Models employing genetic branch lengths (or a transformation thereof by means of the scaling parameter κ) to determine the probability of change exhibited a better fit on the data as compared to equal distance models depending on the investigated trees (Table 2). On the ML tree, κ was significantly higher than 0 for four characters. For these characters however, the hypothesis that κ = 0 could not be significantly rejected in the majority of trees of the Bayesian sample. By contrast, in other characters, for which κ was not found significantly different than 0 on the ML tree, a small proportion of trees from the Bayesian sample often supported κ values significantly higher than 0. κ values sampled by the MCMC procedure had an average ranging between 0.54 ± 0.38 and 1.62 ± 0.97 depending on the character investigated, and were characterized by very wide intervals of confidence often encompassing 0 (see, for example, the posterior probability distribution of κ or character 16 in Fig. 3). Figure 3 View largeDownload slide Histogram, represented as normal distributions, of the parameters of the model of morphological evolution for stem leaf cell width in Brachytheciastrum (character 16). (a) Distribution of the single rate parameter q selected by a likelihood-ratio test and optimized by ML on each of the 400 Bayesian sample of trees. The other model parameter, κ, was found to significantly differ from 0 in none of the 400 sampled trees as assessed by a likelihood ratio test. (b and c): Distributions of q01, q10, and κ, sampled every 100 of 4,000,000 generations of a MCMC exploring the space of the 400 sampled trees. Figure 3 View largeDownload slide Histogram, represented as normal distributions, of the parameters of the model of morphological evolution for stem leaf cell width in Brachytheciastrum (character 16). (a) Distribution of the single rate parameter q selected by a likelihood-ratio test and optimized by ML on each of the 400 Bayesian sample of trees. The other model parameter, κ, was found to significantly differ from 0 in none of the 400 sampled trees as assessed by a likelihood ratio test. (b and c): Distributions of q01, q10, and κ, sampled every 100 of 4,000,000 generations of a MCMC exploring the space of the 400 sampled trees. Table 2 Models of morphological evolution in Brachytheciastrum: model parameters (I) optimized by ML on the ML tree; (II) optimized by ML on each of the trees of a Bayesian sample; and (III) sampled by a MCMC visiting the space of a Bayesian sample of trees. (1) κ-Transformed branch lengths determine the probability of change significantly better than branches of equal length (κ = 0) when twice the log-likelihood ratio is higher than a χ2 variate with 1 df. (2) Two-rate models implementing different forward (q01) and backward (q10) transition rates are preferred over single-rate models (q) when twice the log-likelihood ratio is higher than a χ2 variate with 1 df. (3) P(0) is the probability (I) or the average probability ± SD (II and III) of state 0 at the root. (4) Average ± SD of the posterior probability distribution. I II III Character κ(1) qij(2) p(0)(3) κ(1):average ± SD Single-and two rate models(2): mean rate ± SD p(0)(3) κ(4) q01 and q10(4) p(0)(3) 1 1.27 q01 = q10 = 117.27 0.87 92 trees : 1.88 ± 0.67 q01 = q10 = 919.16 ± 245.93 0.89 ± 0.10 1.24 ± 0.71 37.51 ± 25.59; 0.79 ± 0.20 308 trees: 0 q01 = 0.10 ± 0.23; q10 = 1.1 ± 2.22 0.32 ± 0.02 45.26 ± 23.68 2 1.4 q01 = q10 = 1000 0.63 58 trees: 1.72 ± 0.61 q01 = q10 = 990.96 ± 68.82 0.64 ± 0.18 1.20 ± 0.81 387.37 ± 258.53; 0.53 ± 0.20 342 trees: 0 q01 = 0.14 (0.31); q10 = 0.71 ± 1.31 0.16 ± 0.09 637.81 ± 252.26 3 0 q01 = q10 = 0.31 0.71 399 trees: 0 q01 = q10 = 2.45 ± 3.84 0.62 ± 0.08 0.71 ± 0.49 608.03 ± 234.69; 0.54 ± 0.10 1 tree: 1.71 q01 = q10 = 1000 0.72 568.88 ± 238.93 4 0 q01 = q10 = 0.03 1.00 400 trees: 0 q01 = q10 = 0.03 ± 0.01 1.00 ± 0.00 1.41 ± 0.75 289.49 ± 287.56; 0.87 ± 0.19 557.08 ± 276.19 5 0 q01 = q10 = 0.15 0.97 3 trees: 1.29 ± 0.28 q01 = q10 = 1000 ± 0.00 0.55 ± 0.10 0.80 ± 0.54 384.92 ± 218.5; 0.55 ± 0.12 397 trees: 0 42 trees: q01 = 5.09 ± 0.87; q10 = 12.73 ± 2.18 0.51 ± 0.03 674.37 ± 237.69 355 trees: q01 = q10 = 0.21 ± 0.04 0.91 ± 0.05 6 0 q01 = q10 = 0.23 0.89 396 trees: 0 q01 = q10 = 1.88 ± 3.49 0.74 ± 0.16 0.81 ± 0.55 431.31 ± 219.21; 0.54 ± 0.09 4 trees: 1.58 ± 0.61 q01 = q10 = 1000 ± 0.00 0.69 ± 0.17 684.21 ± 227.21 7 1.3 q01 = q10 = 1000 0.53 47 trees: 1.55 ± 0.46 q01 = q10 = 942.95 ± 222.66 0.69 ± 0.14 1.39 ± 0.89 452.65 ± 245.42; 0.62 ± 0.18 353 trees: 0 1 tree: q01 = 0.00; q10 = 0.28 0.00 597.49 ± 259.87 352 trees: q01 = q10 = 0.22 ± 0.02 0.54 ± 0.05 8 0 q01 = q10 = 0.23 0.82 4 trees: 2.04 ± 0.66 q01 = q10 = 1000 ± 0.00 0.59 ± 0.11 0.66 ± 0.44 57.46 ± 23.57; 0.57 ± 0.13 396 trees: 0 q01 = q10 = 1.06 ± 2.38 0.66 ± 0.09 61.00 ± 23.76 9 1.46 q01 = q10 = 1000 0.21 13 trees: 1.41 ± 0.29 q01 = q10 = 925.37 ± 269.07 0.21 ± 0.16 1.1 ± 0.67 57.90 ± 26.91; 0.29 ± 0.22 387 trees: 0 q01 = q10 = 0.16 ± 0.02 0.10 ± 0.05 48.60 ± 25.36 10 0 q01 = q10 = 0.05 0.97 38 trees: 2.05 ± 0.72 q01 = q10 = 960.03 ± 178.70 0.18 ± 0.24 1.62 ± 0.97 416.82 ± 239.15; 0.82 ± 0.20 362 trees: 0 166 trees: q01 = q10 = 0.05 ± 0.00 0.97 ± 0.00 584.48 ± 271.26 196 trees: q01 = 0.00 ± 0.00; q10 = 0.49 ± 0.00 0.23 ± 0.25 11 0 q01 = q10 = 0.10 0.50 15 trees: 1.52 ± 0.45 q01 = q10 = 939.91 ± 232.72 0.50 ± 0.05 1.44 ± 0.55 573.31 ± 246.80; 0.74 ± 0.18 385 trees: 0 q01 = q10 = 0.11 ± 0.02 0.50 ± 0.05 450.66 ± 260.97 12 0 q01 = q10 = 0.09 0.99 4 trees: 0.79 ± 0.95 1 tree. q01 = q10 = 1000 0.56 0.96 ± 0.57 297.89 ± 223.62; 0.67 ± 0.20 396 trees: 0 13 trees: q01 = 3.44 ± 0.16; q10 = 14.64 ± 0.70 0.50 ± 0.00 638.50 ± 248.90 383 trees: q01 = q10 = 0.09 ± 0.02 0.99 ± 0.00 13 0 q01 = q10 = 9.67 0.50 400 trees: 0 q01 = q10 = 9.67 ± 0.00 0.50 ± 0.00 0.54 ± 0.38 581.31 ± 232.27; 0.50 ± 0.00 613.40 ± 230.27 14 0 q01 = q10 = 9.67 0.50 400 trees: 0 q01 = q10 = 5.41 ± 4.49 0.47 ± 0.05 0.71 ± 0.33 633.38 ± 230.46; 0.50 ± 0.01 557.50 ± 234.50 15 0 q01 = 3.55 q10 = 15.08 0.50 19 trees: 1.13 ± 0.34 q01 = q10 = 637.85 ± 426.38 0.85 ± 0.10 0.66 ± 0.47 268.45 ± 192.00; 0.55 ± 0.12 381 trees: 0 q01 = 3.53 ± 0.60, q10 = 15.02 ± 2.56 0.50 ± 0.01 660.63 ± 234.20 16 0 q01 = q10 = 0.11 0.98 400 trees: 0 q01 = q10 = 0.16 ± 0.03 0.93 ± 0/04 0.84 ± 0.45 32.30 ± 26.71; 0.56 ± 0.27 55.26 ± 25.92 17 0 q01 = q10 = 0.20 0.73 58 trees: 1.64 ± 0.50 q01 = q10 = 915.14 ± 255.21 0.38 ± 0.15 1.50 ± 0.93 574.08 ± 257.24; 0.57 ± 0.20 342 trees: 0 6 trees: q01 = 4.39 ± 3.98; q10 = 1.75 ± 1.59 0.50 ± 0.01 481.04 ± 249.15 336 trees: q01 = q10 = 0.21 ± 0.05 0.66 ± 0.07 18 0 q01 = q10 = 0.06 1.00 400 trees: 0 q01 = q10 = 0.06 ± 0.00 1.00 ± 0.00 0.66 ± 0.46 172.38 ± 179.48; 0.58 ± 0.17 660.78 ± 237.63 19 0 q01 = q10 = 0.03 1.00 1 tree: 2.15 q01 = q10 = 1000 1.00 1.39 ± 0.90 328.03 ± 295.79; 0.79 ± 0.23 399 trees: 0 3 trees: q01 = 0.00 ± 0.00; q10 = 0.69 ± 0.00 0.00 ± 0.00 595.75 ± 272.47 396 trees: q01 = q10 = 0.03 ± 0.00 1.00 ± 0.00 I II III Character κ(1) qij(2) p(0)(3) κ(1):average ± SD Single-and two rate models(2): mean rate ± SD p(0)(3) κ(4) q01 and q10(4) p(0)(3) 1 1.27 q01 = q10 = 117.27 0.87 92 trees : 1.88 ± 0.67 q01 = q10 = 919.16 ± 245.93 0.89 ± 0.10 1.24 ± 0.71 37.51 ± 25.59; 0.79 ± 0.20 308 trees: 0 q01 = 0.10 ± 0.23; q10 = 1.1 ± 2.22 0.32 ± 0.02 45.26 ± 23.68 2 1.4 q01 = q10 = 1000 0.63 58 trees: 1.72 ± 0.61 q01 = q10 = 990.96 ± 68.82 0.64 ± 0.18 1.20 ± 0.81 387.37 ± 258.53; 0.53 ± 0.20 342 trees: 0 q01 = 0.14 (0.31); q10 = 0.71 ± 1.31 0.16 ± 0.09 637.81 ± 252.26 3 0 q01 = q10 = 0.31 0.71 399 trees: 0 q01 = q10 = 2.45 ± 3.84 0.62 ± 0.08 0.71 ± 0.49 608.03 ± 234.69; 0.54 ± 0.10 1 tree: 1.71 q01 = q10 = 1000 0.72 568.88 ± 238.93 4 0 q01 = q10 = 0.03 1.00 400 trees: 0 q01 = q10 = 0.03 ± 0.01 1.00 ± 0.00 1.41 ± 0.75 289.49 ± 287.56; 0.87 ± 0.19 557.08 ± 276.19 5 0 q01 = q10 = 0.15 0.97 3 trees: 1.29 ± 0.28 q01 = q10 = 1000 ± 0.00 0.55 ± 0.10 0.80 ± 0.54 384.92 ± 218.5; 0.55 ± 0.12 397 trees: 0 42 trees: q01 = 5.09 ± 0.87; q10 = 12.73 ± 2.18 0.51 ± 0.03 674.37 ± 237.69 355 trees: q01 = q10 = 0.21 ± 0.04 0.91 ± 0.05 6 0 q01 = q10 = 0.23 0.89 396 trees: 0 q01 = q10 = 1.88 ± 3.49 0.74 ± 0.16 0.81 ± 0.55 431.31 ± 219.21; 0.54 ± 0.09 4 trees: 1.58 ± 0.61 q01 = q10 = 1000 ± 0.00 0.69 ± 0.17 684.21 ± 227.21 7 1.3 q01 = q10 = 1000 0.53 47 trees: 1.55 ± 0.46 q01 = q10 = 942.95 ± 222.66 0.69 ± 0.14 1.39 ± 0.89 452.65 ± 245.42; 0.62 ± 0.18 353 trees: 0 1 tree: q01 = 0.00; q10 = 0.28 0.00 597.49 ± 259.87 352 trees: q01 = q10 = 0.22 ± 0.02 0.54 ± 0.05 8 0 q01 = q10 = 0.23 0.82 4 trees: 2.04 ± 0.66 q01 = q10 = 1000 ± 0.00 0.59 ± 0.11 0.66 ± 0.44 57.46 ± 23.57; 0.57 ± 0.13 396 trees: 0 q01 = q10 = 1.06 ± 2.38 0.66 ± 0.09 61.00 ± 23.76 9 1.46 q01 = q10 = 1000 0.21 13 trees: 1.41 ± 0.29 q01 = q10 = 925.37 ± 269.07 0.21 ± 0.16 1.1 ± 0.67 57.90 ± 26.91; 0.29 ± 0.22 387 trees: 0 q01 = q10 = 0.16 ± 0.02 0.10 ± 0.05 48.60 ± 25.36 10 0 q01 = q10 = 0.05 0.97 38 trees: 2.05 ± 0.72 q01 = q10 = 960.03 ± 178.70 0.18 ± 0.24 1.62 ± 0.97 416.82 ± 239.15; 0.82 ± 0.20 362 trees: 0 166 trees: q01 = q10 = 0.05 ± 0.00 0.97 ± 0.00 584.48 ± 271.26 196 trees: q01 = 0.00 ± 0.00; q10 = 0.49 ± 0.00 0.23 ± 0.25 11 0 q01 = q10 = 0.10 0.50 15 trees: 1.52 ± 0.45 q01 = q10 = 939.91 ± 232.72 0.50 ± 0.05 1.44 ± 0.55 573.31 ± 246.80; 0.74 ± 0.18 385 trees: 0 q01 = q10 = 0.11 ± 0.02 0.50 ± 0.05 450.66 ± 260.97 12 0 q01 = q10 = 0.09 0.99 4 trees: 0.79 ± 0.95 1 tree. q01 = q10 = 1000 0.56 0.96 ± 0.57 297.89 ± 223.62; 0.67 ± 0.20 396 trees: 0 13 trees: q01 = 3.44 ± 0.16; q10 = 14.64 ± 0.70 0.50 ± 0.00 638.50 ± 248.90 383 trees: q01 = q10 = 0.09 ± 0.02 0.99 ± 0.00 13 0 q01 = q10 = 9.67 0.50 400 trees: 0 q01 = q10 = 9.67 ± 0.00 0.50 ± 0.00 0.54 ± 0.38 581.31 ± 232.27; 0.50 ± 0.00 613.40 ± 230.27 14 0 q01 = q10 = 9.67 0.50 400 trees: 0 q01 = q10 = 5.41 ± 4.49 0.47 ± 0.05 0.71 ± 0.33 633.38 ± 230.46; 0.50 ± 0.01 557.50 ± 234.50 15 0 q01 = 3.55 q10 = 15.08 0.50 19 trees: 1.13 ± 0.34 q01 = q10 = 637.85 ± 426.38 0.85 ± 0.10 0.66 ± 0.47 268.45 ± 192.00; 0.55 ± 0.12 381 trees: 0 q01 = 3.53 ± 0.60, q10 = 15.02 ± 2.56 0.50 ± 0.01 660.63 ± 234.20 16 0 q01 = q10 = 0.11 0.98 400 trees: 0 q01 = q10 = 0.16 ± 0.03 0.93 ± 0/04 0.84 ± 0.45 32.30 ± 26.71; 0.56 ± 0.27 55.26 ± 25.92 17 0 q01 = q10 = 0.20 0.73 58 trees: 1.64 ± 0.50 q01 = q10 = 915.14 ± 255.21 0.38 ± 0.15 1.50 ± 0.93 574.08 ± 257.24; 0.57 ± 0.20 342 trees: 0 6 trees: q01 = 4.39 ± 3.98; q10 = 1.75 ± 1.59 0.50 ± 0.01 481.04 ± 249.15 336 trees: q01 = q10 = 0.21 ± 0.05 0.66 ± 0.07 18 0 q01 = q10 = 0.06 1.00 400 trees: 0 q01 = q10 = 0.06 ± 0.00 1.00 ± 0.00 0.66 ± 0.46 172.38 ± 179.48; 0.58 ± 0.17 660.78 ± 237.63 19 0 q01 = q10 = 0.03 1.00 1 tree: 2.15 q01 = q10 = 1000 1.00 1.39 ± 0.90 328.03 ± 295.79; 0.79 ± 0.23 399 trees: 0 3 trees: q01 = 0.00 ± 0.00; q10 = 0.69 ± 0.00 0.00 ± 0.00 595.75 ± 272.47 396 trees: q01 = q10 = 0.03 ± 0.00 1.00 ± 0.00 View Large The two-rate model significantly improved the likelihood over the single-rate model for only one character on the ML tree (character 15; Table 2). In the Bayesian sample of trees, restricting these two parameters to be equal for that character did not result in a significant decrease in log-likelihood in 19 of the 400 sampled trees. For most other characters, for which a single-rate model was favored based on the single ML tree, the two-rate model returned significantly higher log-likelihood values than the single-rate model for a portion of the trees from the Bayesian sample. This was especially true for characters 1, 2, and 10, for which the two-rate model was favored by the data over the single-rate model in > 50% of the sampled trees. Although the values of the two rate parameters sampled by the MCMC procedure strongly overlapped for each character (see, for example, the posterior probability distributions of q01 and q10 for character 16 in Fig. 3), they always significantly (P < 0.001) differed from each other on average across the whole sample of trees. The reconstructions of ancestral character states using a ML optimization of model parameters onto the ML tree, a ML optimization of model parameters onto the Bayesian sample of trees, and a MCMC sample of model parameters were all significantly correlated across nodes for each of the 19 investigated characters, most often with r > 0.90 (P < 0.001) (Table 3; see also for example the reconstruction of ancestral character states for stem leaf cell width using the three procedures in Figs. 2 and 4). However, when rates were optimized by ML onto the Bayesian sample of trees, the selection of one-versus two-rate-models based on the result of a likelihood-ratio test greatly influenced the estimates of ancestral states at the root in the case of character states with unique or rare occurrences (see, e.g., characters 1, 2, 10, and 19 in Table 2). Table 3 Comparison of ancestral character state reconstruction in Brachytheciastrum when model parameters are (I) optimized by ML on the ML tree; (II) optimized by ML on each of the trees of a Bayesian sample; and (III) sampled by a MCMC visiting the space of a Bayesian sample of trees. (a) Correlation coefficient r between the P(0) at each node derived from alternative methods across the 14 nodes. In methods II and III, the p(0) at each node are an average over the n = 400 and n = 40,000 observations, respectively. All p-values of r are < 0.001 except when otherwise noted: NS, P > 0.05; * P < 0.05: ** P < 0.01.—: all probabilities of ancestral character states equal to 0.5 across nodes. (b) Comparison of the mean (± SD) probability of the most likely reconstruction across nodes when reconstructions are performed using method I, II, and III. In methods II and III, the probability of the most likely reconstruction at a node is an average over the n = 400 and n = 40,000 observations, respectively. All the P-values associated to a pairwise Student's t test for testing whether a method returns on average higher probabilities of ancestral character state than another across the 14 nodes are < 0.001 except when otherwise noted (see above). a Character rI/II rI/III rII/III b 1 0.80 0.99 0.92 mI = 0.96 ± 0.09 > mIII = 0.88 ± 0.09 > mII = 0.72 ± 0.08 2 0.71** 0.92 0.92 mI = 0.88 ± 0.17 > mII = 0.74 ± 0.11* = mIII = 0.72 ± 0.10 3 0.99 0.92 0.94 mI = 0.73 ± 0.17 > mII = 0.64 ± 0.11 > mIII = 0.57 ± 0.05** 4 0.99 0.99 0.99 mI = 0.99 ± 0.00 = mII = 0.99 ± 0.02 > mIII = 0.90 ± 0.04 5 0.96 0.80 0.85 mI = 0.87 ± 0.17 > mII = 0.77 ± 0.15 > mIII = 0.60 ± 0.06 6 0.95 0.67** 0.80 mI = 0.80 ± 0.16 > mII = 0.70 ± 0.13 > mIII = 0.59 ± 0.07 7 0.77** 0.89 0.92 mI = 0.80 ± 0.21 = mII = 0.80 ± 0.17 > mIII = 0.72 ± 0.12** 8 0.98 0.88 0.92 mI = 0.76 ± 0.17 > mII = 0.67 ± 0.12 > mIII = 0.63 ± 0.09* 9 0.87 0.92 0.97 mI = 0.90 ± 0.15 = mII = 0.84 ± 0.17 > mIII = 0.78 ± 0.15** 10 0.93 0.97 0.96 mI = 0.93 ± 0.15 > mII = 0.77 ± 0.10 = mIII = 0.84 ± 0.12 11 0.99 0.97 0.97 mI = 0.89 ± 0.20 > mII = 0.87 ± 0.20** = mIII = 0.88 ± 0.14 12 0.95 0.88 0.94 mI = 0.93 ± 0.14 = mII = 0.89 ± 0.16 > mIII = 0.71 ± 0.09 13 — — — mI = 0.50 ± 0.00 = mII = 0.50 ± 0.00 = mIII = 0.52 ± 0.01 14 — — 0.63* mI = 0.50 ± 0.00 < mII = 0.55 ± 0.04** = mIII = 0.60 ± 0.11 15 — — 0.90 mI = 0.50 ± 0.00 < mII = 0.52 ± 0.00 < mIII = 0.57 ± 0.04 16 0.98 0.90 0.92 mI = 0.88 ± 0.18 = mII = 0.84 ± 0.17 > mIII = 0.70 ± 0.14 17 0.98 0.70** 0.84 mI = 0.80 ± 0.16 = mII = 0.80 ± 0.15 = mIII = 0.76 ± 0.11 18 0.97 0.78 0.84 mI = 0.96 ± 0.13 = mII = 0.95 ± 0.13 > mIII = 0.60 ± 0.03 19 0.99 0.56* 0.58* mI = 0.99 ± 0.00 = mII = 0.99 ± 0.03 > mIII = 0.82 ± 0.04 a Character rI/II rI/III rII/III b 1 0.80 0.99 0.92 mI = 0.96 ± 0.09 > mIII = 0.88 ± 0.09 > mII = 0.72 ± 0.08 2 0.71** 0.92 0.92 mI = 0.88 ± 0.17 > mII = 0.74 ± 0.11* = mIII = 0.72 ± 0.10 3 0.99 0.92 0.94 mI = 0.73 ± 0.17 > mII = 0.64 ± 0.11 > mIII = 0.57 ± 0.05** 4 0.99 0.99 0.99 mI = 0.99 ± 0.00 = mII = 0.99 ± 0.02 > mIII = 0.90 ± 0.04 5 0.96 0.80 0.85 mI = 0.87 ± 0.17 > mII = 0.77 ± 0.15 > mIII = 0.60 ± 0.06 6 0.95 0.67** 0.80 mI = 0.80 ± 0.16 > mII = 0.70 ± 0.13 > mIII = 0.59 ± 0.07 7 0.77** 0.89 0.92 mI = 0.80 ± 0.21 = mII = 0.80 ± 0.17 > mIII = 0.72 ± 0.12** 8 0.98 0.88 0.92 mI = 0.76 ± 0.17 > mII = 0.67 ± 0.12 > mIII = 0.63 ± 0.09* 9 0.87 0.92 0.97 mI = 0.90 ± 0.15 = mII = 0.84 ± 0.17 > mIII = 0.78 ± 0.15** 10 0.93 0.97 0.96 mI = 0.93 ± 0.15 > mII = 0.77 ± 0.10 = mIII = 0.84 ± 0.12 11 0.99 0.97 0.97 mI = 0.89 ± 0.20 > mII = 0.87 ± 0.20** = mIII = 0.88 ± 0.14 12 0.95 0.88 0.94 mI = 0.93 ± 0.14 = mII = 0.89 ± 0.16 > mIII = 0.71 ± 0.09 13 — — — mI = 0.50 ± 0.00 = mII = 0.50 ± 0.00 = mIII = 0.52 ± 0.01 14 — — 0.63* mI = 0.50 ± 0.00 < mII = 0.55 ± 0.04** = mIII = 0.60 ± 0.11 15 — — 0.90 mI = 0.50 ± 0.00 < mII = 0.52 ± 0.00 < mIII = 0.57 ± 0.04 16 0.98 0.90 0.92 mI = 0.88 ± 0.18 = mII = 0.84 ± 0.17 > mIII = 0.70 ± 0.14 17 0.98 0.70** 0.84 mI = 0.80 ± 0.16 = mII = 0.80 ± 0.15 = mIII = 0.76 ± 0.11 18 0.97 0.78 0.84 mI = 0.96 ± 0.13 = mII = 0.95 ± 0.13 > mIII = 0.60 ± 0.03 19 0.99 0.56* 0.58* mI = 0.99 ± 0.00 = mII = 0.99 ± 0.03 > mIII = 0.82 ± 0.04 View Large The reconstructions reveal that the investigated characters are extremely homoplastic, as shown by their very low rescaled consistency index (Table 4) and their tendency to shift between states many times independently along the phylogeny (see for example character 16 in Fig. 4). The probabilities of the reconstructions also indicate that three characters (13, 14, and 15) exhibit no phylogenetic signal, as the reconstructions are systematically equivocal at each internal node (Table 3). For six characters, the phylogeny did not provide a better description of trait evolution than the star-like tree. However, significance of the phylogenetic signal, as tested by the comparison of the log-likelihoods returned by a phylogenetic vs star-like tree, was found for only four characters (Table 4). Figure 4 View largeDownload slide Distribution of p(0) values, represented as normal probability distributions, for stem leaf cell width (character 16: 0: > 8 μ m; 1: < 8 μ m) at each of the 14 nodes N, derived from a ML optimization of model parameters for each of the 400 sampled trees (column a) and sampled every 100 of 4,000,000 generations by a MCMC visiting the space of the 400 sampled trees (column b). Figure 4 View largeDownload slide Distribution of p(0) values, represented as normal probability distributions, for stem leaf cell width (character 16: 0: > 8 μ m; 1: < 8 μ m) at each of the 14 nodes N, derived from a ML optimization of model parameters for each of the 400 sampled trees (column a) and sampled every 100 of 4,000,000 generations by a MCMC visiting the space of the 400 sampled trees (column b). Table 4 Homoplasy and phylogenetic content of 19 morphological traits in Brachytheciastrum. RC is the rescaled consistency index. Values in parentheses indicate the range of variation of the RC in the Bayesian sample of trees. Significance of the phylogenetic content is tested by comparing the log-likelihoods returned by the model of morphological evolution applied on the ML tree and on a star-like tree with genetic (κ = 1) or equal branch length (κ = 0). Phylogenetic models provide a significantly better representation of trait evolution when the log-likelihood difference with non-phylogenetic models is > 2 (in bold). −ln L (ML tree) −ln L (star-like tree) Character RC Genetic Equal Genetic Equal 1 (0.000) 0.000 (0.000) 5.54 5.64 4.55 3.97 2 (0.000) 0.000 (0.111) 8.71 9.09 8.86 8.45 3 (0.028) 0.074 (0.167) 14.29 13.31 13.02 13.76 4 (0.000) 1.000 (1.000) 4.92 4.60 6.14 6.14 5 (0.000) 0.100 (0.200) 10.31 11.75 12.00 11.99 6 (0.020) 0.086(0.238) 11.17 12.50 12.61 12.76 7 (0.000) 0.000 (0.040) 9.95 11.31 11.54 11.24 8 (0.012) 0.111 (0.111) 11.82 12.84 13.82 13.76 9 (0.000) 0.067 (0.125) 9.10 10.88 13.37 12.76 10 (0.000) 0.000 (0.000) 5.58 5.91 4.97 6.14 11 (0.074) 0.167 (0.259) 9.30 9.45 12.29 13.85 12 (0.000) 0.111 (0.333) 8.71 8.39 8.88 8.45 13 (0.012) 0.028 (0.074) 15.92 13.84 13.82 13.76 14 (0.012) 0.048 (0.111) 12.59 13.84 13.85 13.84 15 (0.000) 0.000 (0.000) 10.76 9.53 9.07 9.70 16 (0.000) 0.100 (0.200) 10.61 9.56 12.76 12.76 17 (0.000) 0.040 (0.100) 10.59 11.00 11.67 11.99 18 (0.000) 0.000 (1.000) 7.31 5.89 6.14 6.14 19 — 3.94 3.33 3.58 3.58 −ln L (ML tree) −ln L (star-like tree) Character RC Genetic Equal Genetic Equal 1 (0.000) 0.000 (0.000) 5.54 5.64 4.55 3.97 2 (0.000) 0.000 (0.111) 8.71 9.09 8.86 8.45 3 (0.028) 0.074 (0.167) 14.29 13.31 13.02 13.76 4 (0.000) 1.000 (1.000) 4.92 4.60 6.14 6.14 5 (0.000) 0.100 (0.200) 10.31 11.75 12.00 11.99 6 (0.020) 0.086(0.238) 11.17 12.50 12.61 12.76 7 (0.000) 0.000 (0.040) 9.95 11.31 11.54 11.24 8 (0.012) 0.111 (0.111) 11.82 12.84 13.82 13.76 9 (0.000) 0.067 (0.125) 9.10 10.88 13.37 12.76 10 (0.000) 0.000 (0.000) 5.58 5.91 4.97 6.14 11 (0.074) 0.167 (0.259) 9.30 9.45 12.29 13.85 12 (0.000) 0.111 (0.333) 8.71 8.39 8.88 8.45 13 (0.012) 0.028 (0.074) 15.92 13.84 13.82 13.76 14 (0.012) 0.048 (0.111) 12.59 13.84 13.85 13.84 15 (0.000) 0.000 (0.000) 10.76 9.53 9.07 9.70 16 (0.000) 0.100 (0.200) 10.61 9.56 12.76 12.76 17 (0.000) 0.040 (0.100) 10.59 11.00 11.67 11.99 18 (0.000) 0.000 (1.000) 7.31 5.89 6.14 6.14 19 — 3.94 3.33 3.58 3.58 View Large The uncertainty associated with the reconstructions significantly varied depending on the procedure used to compute the model parameters. The probabilities of the most likely character state were indeed globally higher when reconstructions were performed using the ML optimization of rate parameters on the ML tree and lower when sampling model parameters from a MCMC (Table 3). The reconstructions performed on the Bayesian sample of trees using a ML rate optimization on each tree returned intermediate values of uncertainty. Indeed, the probabilities associated with the reconstruction of the most likely state did not significantly differ on average across nodes for nine of the 19 characters when using the ML optimization of rate parameters on the ML tree and the Bayesian sample of trees. By contrast, the probabilities of the most likely state were significantly higher when using the ML optimization of rate on the ML tree than when sampling rates from the MCMC for all but four characters. Within-and among-tree variance of the posterior probabilities of the likelihood, model parameters, and reconstructions of ancestral character states, were partitioned in Table 5. The posterior probabilities of the likelihood, model parameters, and reconstructions of ancestral character states all significantly differed among trees for each character mostly at the 0.001 level, although the proportion of among-tree variance substantially varied. Proportion of among-tree variance was the highest for κ, with average values ranging between 21% and 79%, and the lowest for the rate parameters, with average values ranging between < 1% and 14%, depending on the characters investigated. Table 5 Proportion of among-tree variance of the log-likelihoods lh, model parameters, and probabilities of ancestral character states sampled from their posterior probability distribution. (1) Proportion of among-tree variance of P(0) at internal nodes: average proportion ± SD across the 14 nodes. All P-values of the F-statistics < 0.001 except when otherwise noted: NS, P > 0.05; * P < 0.05; ** P < 0.01. Character lh q01 q10 κ Ancestral character states (1) 1 0.41 0.07 0.02 0.65 0.17 ± 0.09 2 0.24 0.12 0.03 0.61 0.29 ± 0.11 3 0.18 NS 0.02 0.33 0.25 ± 0.10 4 0.29 0.11 0.04 0.62 0.24 ± 0.07 5 0.13 0.02 0.02 0.41 0.24 ± 0.08 6 0.17 0.02 NS 0.43 0.27 ± 0.10 7 0.74 0.13 0.08 0.76 0.48 ± 0.17 8 0.32 0.13 0.08 0.76 0.34 ± 0.13 9 0.47 0.05 0.07 0.77 0.34 ± 0.20 10 0.39 0.09 0.02 0.69 0.23 ± 0.18 11 0.47 0.02 0.05 0.49 0.36 ± 0.22 12 0.29 0.10 0.04 0.45 0.35 ± 0.11 13 0.01** NS NS 0.21 0.15 ± 0.09 14 NS NS NS NS NS 15 0.02 0.04 0.01* 0.26 0.17 ± 0.07 16 0.52 0.10 0.02 0.67 0.42 ± 0.18 17 0.76 0.07 0.13 0.79 0.45 ± 0.18 18 0.10 0.14 0.02 0.26 0.30 ± 0.07 19 0.14 0.09 0.03 0.49 0.15 ± 0.05 Character lh q01 q10 κ Ancestral character states (1) 1 0.41 0.07 0.02 0.65 0.17 ± 0.09 2 0.24 0.12 0.03 0.61 0.29 ± 0.11 3 0.18 NS 0.02 0.33 0.25 ± 0.10 4 0.29 0.11 0.04 0.62 0.24 ± 0.07 5 0.13 0.02 0.02 0.41 0.24 ± 0.08 6 0.17 0.02 NS 0.43 0.27 ± 0.10 7 0.74 0.13 0.08 0.76 0.48 ± 0.17 8 0.32 0.13 0.08 0.76 0.34 ± 0.13 9 0.47 0.05 0.07 0.77 0.34 ± 0.20 10 0.39 0.09 0.02 0.69 0.23 ± 0.18 11 0.47 0.02 0.05 0.49 0.36 ± 0.22 12 0.29 0.10 0.04 0.45 0.35 ± 0.11 13 0.01** NS NS 0.21 0.15 ± 0.09 14 NS NS NS NS NS 15 0.02 0.04 0.01* 0.26 0.17 ± 0.07 16 0.52 0.10 0.02 0.67 0.42 ± 0.18 17 0.76 0.07 0.13 0.79 0.45 ± 0.18 18 0.10 0.14 0.02 0.26 0.30 ± 0.07 19 0.14 0.09 0.03 0.49 0.15 ± 0.05 View Large Discussion Comparison of ML and Bayesian Reconstructions of Ancestral States in Discrete Characters The analysis of comparative data in a phylogenetic context involves a logical suite of steps for selecting an appropriate model of evolution (Blomberg et al., 2003). Using a ‘genetic distance’ model (Oakley et al., 2005) taking branch lengths (or a transformation thereof by means of the scaling parameter κ) to determine the probability of change on the most likely tree resulted in a significant increase in log-likelihood over an equal distance (also termed ‘punctuational’ [Pagel, 1994] or ‘speciational change’ [Mooers et al. 1999]) model for four characters. A restriction of the branches of the most likely tree to identical lengths (κ = 0), i.e., imposing identical probabilities of change along all the branches of the phylogeny, as if transitions were associated to speciation events followed by periods of stasis, could thus not be rejected for the majority of characters by the likelihood ratio test. The lack of influence of branch lengths in describing the evolution of traits is seemingly frequent in binary characters (Pagel, online documentation available at http://www.ams.rdg.ac.uk/zoology/pagel/). However, a significant improvement of fit of the genetic distance model over the equal model was found for 14 of the 19 characters in a proportion of trees from the Bayesian sample ranging between < 1% and 23%, which may indicate that genetic versus equal-distance model selection by likelihood-ratio test tends to vary with phylogenetic uncertainty. The posterior probability distribution of the scaling parameter κ, whose mode ranged between 0.54 ± 0.38 and 1.62 ± 0.97 with wide confidence intervals often encompassing 0 across the investigated traits, further suggests that the fit of an equal or genetic distance model strongly varied from one tree to another, as shown by the proportion of among-tree variance of κ (between 21% and 79% depending on the character investigated). This supports Blomberg et al.'s (2003) view, that the dichotomy between two models is unnecessary. Rather, the MCMC allows one to sample a choice of branch length transformations depending on their posterior probabilities and to apply them on a sample of trees whose branches continuously vary from being equal to one another to varying proportionally to genetic distances. The models that were employed for reconstructing ancestral character states onto the most likely tree included a single transition rate in 18 of the 19 studied characters. Allowing forward and backward transition rates to differ resulted in a significant improvement of fit for the one remaining character. This supports the idea, that small to medium sized trees of 5 to 95 tips rarely offer enough data to allow one to prefer two-rate models when reconstructing ancestor states (Mooers and Schluter, 1999). However, the results suggest that single-rate models advocated by Schluter et al. (1997) should not be systematically used without checking the performance of more complicated models, even with rather small trees. This is especially true as the choice of a single-or two-rate model based upon the result of a likelihood-ratio test strongly varies with phylogenetic uncertainty. Indeed, in 9 of the 19 characters investigated in Brachytheciastrum, evolution was significantly better described by a two-rate model over the single-rate model in a proportion ranging between 1% to 85% of the Bayesian sample of trees. The posterior probability distribution of q01 and q10 further shows that the rate parameters, although overlapping, tend on average to significantly differ from each other both among, but mostly within trees, as shown by their among-tree variance ranging between < 1% and 14% in the investigated characters. Thus, evidence against a hypothesis of identical backward and forward transitions can emerge from the posterior probability distribution of the rate parameters, whereas the single-tree approach would not allow the rejection of that hypothesis (Pagel and Lutzoni, 2002). Recent investigation showed, however, that the inferred differences in rates might be a methodological artifact (Stireman, 2005). Indeed, because the model employed assumes stationary frequencies of 0.5, high transition rates towards the most common state at the tips are often inferred (Nosil and Mooers, 2005). Despite differences in model selection when optimizing model parameters onto a single ML tree, or a Bayesian sample of trees, and when sampling parameters from a MCMC, reconstructions of ancestral character states were strongly correlated across nodes, often at r > 0.9, for all the characters. Reconstructing ancestral character states using the different approaches implemented here thus consistently reflected the same evolutionary patterns. This observation seems to be independent from the strength of the phylogenetic signal present in the data. Indeed, we also found high correlation coefficients among probabilities of ancestral states at a node derived from the three different approaches, when analyzing a set of eight morphological characters displaying a strong phylogenetic signal (as shown by both strong departures from 0.5 at internal nodes and the highly significant rejection of a star-like tree as an appropriate representation of trait evolution) in the moss genus Timmia (data not shown, available from the authors on request). Strong discrepancies among reconstruction methods were only observed at the root in the case of character states with unique or rare occurrences when single-versus two-rate models were selected based upon the results of a likelihood-ratio test. As already observed by Schluter et al. (1997), the unique or rare state at the tips of short branches will often reappear at the root, accompanied by a high transition rate away from this state when two-rate models are employed, as if the state was a relict whose rarity among contemporary species was the result of a high transition rate away from the rare state. The major difference among the investigated reconstruction methods resides in the uncertainty associated with ancestral character state reconstructions. Reconstructing ancestral states onto a single, most likely tree only takes mapping uncertainty into account. By contrast, reconstructions on a Bayesian sample of trees allowed the importance of phylogenetic uncertainty to be considered in the confidence that one can have in the reconstructions and systematically returned on average significantly lower confidence levels. An attractive feature of the Bayesian approach of ancestral state reconstruction is that it does not only consider the range of possible reconstructions among trees, but also the range of possible reconstructions on the same tree depending on a range of parameters. This was especially important with the investigated data set as, although among-tree differences accounted, on average across nodes, for 15% to 48% of the total variance of the reconstruction depending on the character studied, most of the variance was found within trees due to variation in the rate parameter estimates. The Bayesian approach of ancestral character state reconstruction thus offers 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. Consequences for Morphological Evolution in Brachytheciastrum Phylogenetic signal was found in 16 of the 19 investigated characters, as shown by the departure of ancestral state probabilities from 0.5. This suggests that the probabilities of ancestral states at a node depend on their probabilities at the previous node, making the data appropriate for investigating differences in ancestral states reconstructions by different methods. However, although the phylogenetic model offered a better representation of trait evolution than the nonphylogenetic one for 13 characters, significance of the improvement in log-likelihood resulting from the use of the phylogenetic model was significant for only four characters. For the other ones, phylogenetic dependence in the data could neither be significantly accepted or rejected. As has been shown for continuous characters (Freckleton et al., 2002), this equivocal result most likely reflects a lack of power of the likelihood-ratio test due to the small size of the phylogeny. However, the lack of significance in the presence of phylogenetic signal, together with the sometimes weak average departure of ancestral state probabilities from 0.5 across nodes, point to an overall weak signal for most characters. Due to the weakness of the signal in the data, but also owing to the high level of homoplasy in morphological characters (see below), a phylogenetic hypothesis inferred from all the morphological characters using the ML model of Lewis (2001) in a Bayesian framework proved to be completely unresolved (data not shown). Previous attempts at resolving moss phylogenies using the MP criterion on morphological traits also failed to converge to well-resolved and supported hypotheses (see Buck et al. [2000] for a review). The results thus suggest that the possibilities to recover the evolutionary history of mosses based on the morphology of extant species are extremely limited. The utility of morphology for phylogeny reconstruction has recently been questioned on several grounds (Scotland et al. 2003; but see Jenner, 2004; Wiens 2004; Smith and Turner, 2005). The problem is especially acute in mosses. Indeed, as compared for example to vertebrates and flowering plants, for which classification was successfully tested with phylogenetic analyses of morphology (e.g., Kress et al., 2001; Jenner, 2004; Wiens, 2004) and for which it is argued, that molecular and morphological data sets yield similar numbers of relevant characters (Lee, 2004), mosses exhibit fairly simple morphologies, whose transformation may be rather cryptic, and hence offer fewer characters to infer relationships. Relying entirely on a model incorporating molecular branch lengths may be misleading in some instances (Cunningham, 1999), most notably when adaptive radiations result in a great deal of evolutionary changes along short internal branches, so that character changes are reconstructed as having occurred considerably after the actual radiation took place (Lewis, 2001). Due to the extremely limited possibilities of inferring morphology-based phylogenies in mosses, the study of morphological evolution in such organisms must, however, rest on the estimation of molecular phylogenies. In this case, morphology receives a limited role, which chiefly consists, as advocated by Scotland et al. (2003), of studying morphological characters in the context of a molecular phylogeny. The ITS has been one of the most widely exploited source of molecular variation at the species level but there has been an increasing concern about their reliability for phylogenetic reconstruction, especially due to the existence of paralogs and pseudogenes (Alvarez and Wendel, 2003; Bailey et al., 2003; Razafimandimbison et al., 2004). The 5.8S gene was almost invariant among taxa of the studied species complex, with a substitution rate 10,000 times lower than that expected in the nearby spacers. The presence of pseudogenes in the present data is therefore very unlikely, as the evolutionary rates of pseudogenes are expected to increase dramatically and reach values similar to those of other noncoding regions (Razafimandimbison et al., 2004). The occurrence of multiple paralogs in the PCR product usually results in conflicting base calls during sequencing (see, e.g., Forest and Bruneau [2000]; Vanderpoorten et al. [2004]). No such conflict was observed at any position in ITS sequences of Brachytheciastrum. A scenario, where different paralogous copies would have been randomly lost in the course of the evolutionary history of the species, so that extant species possess a single copy that is not homologous to that of the other species, is also possible, but would require a number of rearrangements that may not be very likely at low taxonomic level. The observed patterns of molecular variation in extant species may also be the result of hybridization or retention of polymorphisms that appeared before speciation, but the congruent phylogenetic signal in the nuclear and chloroplast sequence data does not support these hypotheses. The proposed phylogeny thus seems appropriate for reconstructing patterns of morphological evolution, at least at the level of well-supported nodes. The reconstructions reflected a strong parallel evolution in character transformations. Indeed, the average rescaled consistency index (RC) was 0.107, with a single character exhibiting an RC of 1, whereas all of the other RCs were below 0.167 and reached 0 in six characters. Such frequent shifts in character states have usually been interpreted as evidence for high transition rates (Cunningham, 1999; den Bakker et al., 2004; Rüber et al., 2004). Fast rates of morphological evolution have previously been documented in mosses (Vanderpoorten et al., 2002; Vanderpoorten and Jacquemart, 2004) and may account for the weakness of the phylogenetic signal displayed by most characters. Everything happens as if historical signal had been erased during a period of radiation (Mooers et al., 1999; Oakley et al., 2005), which may coincide with the rapid diversification experienced by the Hypnales early in their relatively recent history (Shaw et al., 2003a). This problem may be compounded by subsequent rampant reduction, resulting in the loss of symplesiomorphies (Goffinet et al., 2004). As a consequence, it is not surprising that the characters used in the taxonomy of Brachytheciastrum have led to the recognition of poly-or paraphyletic species. Conversely, B. velutinum and B. olympicum, which have usually been synomized (Ignatov and Huttunen, 2002), are here resolved as two unrelated monophyletic lineages. The present reconstructions of ancestral character states, however, failed to identify any synapomorphic transition for these species. This suggests that the key characters that have been used for species description are poor indicators of phylogenetic relationships and hence should be viewed as poor taxonomic characters. In Brachytheciastrum, as in many pleurocarpous moss genera, species have been defined based on gametophytic features that have recurrently undergone parallel evolution. Traditional species circumscriptions emphasize particularly the global habit and shape of the leaf (e.g., the orientation, density, and shape of stem leaves [Fig. 5a, b]). Brachytheciastrum trachypodium, for example, differs from B. velutinum by its straight leaves that are scarcely tapered before mid-leaf, whereas those of B. velutinum are often falcate and taper from just above the auricles (Corley, 1990). The present analyses clearly suggest that variation in leaf shape and orientation has repeatedly occurred both among and within the boundaries of traditionally recognized species. The recurrent homoplastic transitions of states found in those mosses explain why Brachytheciastrum itself lacks any morphological synapomorphy (Vanderpoorten et al., 2005). As a consequence, species previously included within the genus based on phenetic grounds, such as B. appleyardiae or B. bolanderi, were shown to belong to other genera sometimes included within different sub-families of the highly diverse family Brachytheciaceae (Blockeel et al., 2005; Vanderpoorten et al., 2005). Figure 5 View largeDownload slide Illustration of characters that have traditionally been used in the taxonomy of Brachytheciastrum. (a) Stem leaf shape (character 8): abruptly tapered from the base in B. bellicum (1),B. trachypodium (2), and B. velutinum (4) or progressively acuminate from the middle in B. collinum (3). (b) Leaves dense (character 3) and straight (character 6) (1: B. collinum) or loose and falcate (2: B. velutinum) (reproduced, with permission, from Corley [1990]; Buck et al. [2001]; and Ignatov and Ignatova [2004]). Figure 5 View largeDownload slide Illustration of characters that have traditionally been used in the taxonomy of Brachytheciastrum. (a) Stem leaf shape (character 8): abruptly tapered from the base in B. bellicum (1),B. trachypodium (2), and B. velutinum (4) or progressively acuminate from the middle in B. collinum (3). (b) Leaves dense (character 3) and straight (character 6) (1: B. collinum) or loose and falcate (2: B. velutinum) (reproduced, with permission, from Corley [1990]; Buck et al. [2001]; and Ignatov and Ignatova [2004]). The focus on key characters with a low phylogenetic component and high transition rates may explain why moss taxonomy, wherein (morpho)species polyphyly is the rule rather than the exception (Shaw, 2000; Shaw and Allen, 2000; Stech and Dohrmann, 2004; Vanderpoorten et al., 2004; Stech and Wagner, 2005; Werner et al., 2005a, 2005b), is particularly unstable and vulnerable to phylogenetic testing (see Goffinet and Buck [2004] for a review). Ranker et al. (2004) similarly found that the characters that have been traditionally used for taxonomy in grammitid ferns are among the most homoplastic, whereas other, potentially informative features have been regarded as having no taxonomic value or have been ignored. In mosses unfortunately, currently investigated morphological characters often fail to provide synapomorphies (Vanderpoorten et al., 2002, 2005; Goffinet et al., 2004), calling for further morphological investigations. Indeed, as opposed to well-worked groups of organisms such as vertebrates and flowering plants (Scotland et al., 2003; but see Wiens, 2004 and Lee, 2006), phylogenetically informative variation in morphology may not have already been fully scrutinized and analyzed in mosses. Morphogenetic and spermatogenetic characters in particular offer a promising tool for interpreting and reinforcing evolutionary scenarios derived from the analyses of molecular data (Renzaglia et al., 2000; Duckett et al., 2004; Pressel et al., 2005). The main problem is that the traditional phenetic species concept based on examination of a few key characters may not be appropriate in taxa with reduced morphologies such as mosses. Specifically, cryptic speciation, wherein genetic differentiation extends beyond the morphospecies level, has been increasingly documented (Shaw, 2001; McDaniel and Shaw, 2003; Shaw et al., 2003b; Feldberg et al., 2004; Werner and Guerra, 2004). Although one interpretation of our phylogeny would be that Brachytheciastrum consists of two species, namely B. olympicum and a set of coalescing populations belonging to B. velutinum, we refrain to make any formal taxonomic change as a redefinition of the species concept in mosses is, obviously, urgently needed. Acknowledgements Many thanks are due to Paul Lewis, Todd Oakley, and two anonymous reviewers for their very constructive comments and to Andrew Meade and Mark Pagel for their advices and for providing us with an unreleased version of Bayes Multistate. Thanks also to Tom Blockeel, Bill Buck, Lars Hedenäs, Misha Ignatov, Rosa Maria Ros, Cecilia Sergio, and André Sotiaux for the loan of specimens; to Norm Wickett for assistance in the lab; and to Jessica Budke for sharing the sequences used in the second data set. Misha Ignatov kindly provided us with original observations used in the morphological data matrix. Financial support was provided by the National Science Foundation through grant DEB-0089633 to BG and through the Belgian National Funds for Scientific Research (FNRS) to AV. References Alvarez I., Wendel J. F.. Ribosomal ITS sequences and plant phylogenetic inference, Mol. Phylogenet. Evol. , 2003, vol. 29 (pg. 417- 434) Google Scholar CrossRef Search ADS PubMed Bailey C. 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Branch leaves all-sided (terete, julaceous) (0) or complanate (1) 6. Stem leaves straight (0) or falcate-secund (including slightly so) (1) 7. Acumen hair-like (2 cells wide > 150 μ m) absent (0) or present (1) 8. Stem leaves progressively acuminate (0) or abruptly tapered from the base (1), as measured by the level where the half-width of the leaf is reached 9. Leaf width > 0.4 mm (0) or < 0.4 mm (1) 10. Stem leaf margin serrulate to serrate (0) or serrulate to entire (1) 11. Costa ending (1) or not (0) in a spine in stem leaves 12. Costa serrate in stem leaves (1) or not (0) 13. Costa serrate in branch leaves (1) or not (0) 14. Prorae absent (0) or present (1) at the back of branch leaves 15. Cells shorter (0) or longer (1) than 100 μ m 16. Cells > 8 μ m (0) or < 8 μ m (1) wide 17. Length to width cell ratio < 10:1 (0) or > 10:1 (1) 18. Large cells at leaf insertion forming a sharply curving group (1) or not (0) 19. Leaves plicate (1) or not (0) 1. Pseudoparaphyllia triangular (0) or acuminate (1) 2. Axillary hair upper cell < 1/2 of hair length (0) or > 1/2 of hair length (1) 3. Leaves dense (stem not seen between leaves) (0) or loose (1) 4. Leaves not straight standing (0) or straight standing (1) 5. Branch leaves all-sided (terete, julaceous) (0) or complanate (1) 6. Stem leaves straight (0) or falcate-secund (including slightly so) (1) 7. Acumen hair-like (2 cells wide > 150 μ m) absent (0) or present (1) 8. Stem leaves progressively acuminate (0) or abruptly tapered from the base (1), as measured by the level where the half-width of the leaf is reached 9. Leaf width > 0.4 mm (0) or < 0.4 mm (1) 10. Stem leaf margin serrulate to serrate (0) or serrulate to entire (1) 11. Costa ending (1) or not (0) in a spine in stem leaves 12. Costa serrate in stem leaves (1) or not (0) 13. Costa serrate in branch leaves (1) or not (0) 14. Prorae absent (0) or present (1) at the back of branch leaves 15. Cells shorter (0) or longer (1) than 100 μ m 16. Cells > 8 μ m (0) or < 8 μ m (1) wide 17. Length to width cell ratio < 10:1 (0) or > 10:1 (1) 18. Large cells at leaf insertion forming a sharply curving group (1) or not (0) 19. Leaves plicate (1) or not (0) View Large Appendix 2 Matrix of morphological characters defined in Appendix 1 scored for all the specimens. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 bellicum 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 collinum a 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 collinum b 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 collinum c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 collinum d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 collinum e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 dieckei a 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 dieckei b 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 dieckei c 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 dieckei d 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 fendleri 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 leibergii 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 olympicum a 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 olympicum b 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 olympicum c 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 trachypodium a 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 trachypodium b 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 trachypodium c 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 velutinum a 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 velutinum b 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 velutinum c 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 bellicum 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 collinum a 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 collinum b 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 collinum c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 collinum d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 collinum e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 dieckei a 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 dieckei b 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 dieckei c 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 dieckei d 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 fendleri 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 leibergii 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 olympicum a 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 olympicum b 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 olympicum c 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 trachypodium a 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 trachypodium b 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 trachypodium c 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 velutinum a 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 velutinum b 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 velutinum c 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 View Large © 2006 Society of Systematic Biologists http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Systematic Biology Oxford University Press http://www.deepdyve.com/lp/oxford-university-press/mapping-uncertainty-and-phylogenetic-uncertainty-in-ancestral-sX20l0A04b

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Publisher: Oxford University Press
Copyright: © 2006 Society of Systematic Biologists
ISSN: 1063-5157
eISSN: 1076-836X
DOI: 10.1080/10635150601088995
Publisher site: See Article on Publisher Site

Abstract

Abstract 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. Ancestral character-state reconstruction, Bayesian inference, comparative methods, moss, uncertainty The study of trait evolution and diversification has traditionally relied on fossil records, comparisons between fossils and extant forms, and among groups of extant species and estimated divergence times (Mooers et al., 1999). The exponential development of molecular techniques and statistical tools has more recently enabled the exploration of diversification and adaptation of traits in a phylogenetic context (Pagel, 1998; Martins, 2000). Phylogenetic reconstruction of ancestral character states offers a unique framework in evolutionary studies when fossil evidence is not available, either due to the nature of the investigated traits (e.g., behavioral or molecular evolution) or in groups of taxa, wherein fossil evidence is absent or exceedingly scarce. This endeavor involves the reconstruction of ancestral character states on phylogenetic trees according to some evolutionary model or set of assumptions (Pagel, 1999a) globally termed ‘comparative methods.’ Comparative methods can be used to discover, in a manner that might be described as ‘statistical paleontology,’ the diversity of biological traits exhibited by ancestral species, but also the nature of the underlying evolutionary process, i.e., the mode, tempo, and phylogenetic component of the evolution (Pagel, 1998). Maximum parsimony has been the most widely used principle for inferring character-state transformations onto a phylogenetic tree. The parsimony criterion singles out the solution requiring the minimum amount of changes on a tree. A range of alternative reconstructions on the same tree however exists, creating a source of error known as ‘mapping uncertainty’ (Ronquist, 2004) or ‘within-tree uncertainty’ (Pagel et al., 2004). By contrast, maximum likelihood estimators have enabled an assessment of the accuracy of reconstructions (Cunningham et al., 1998; Cunningham, 1999). Under the likelihood criterion, branch lengths are used to determine the probability of change. Furthermore, and perhaps more importantly, ML methods implement explicit models of evolution and therefore enable one to make and test hypotheses regarding evolutionary processes by contrasting the fit of different models to the data. The characterization of the phylogenetic ‘signal’ or component of evolution, i.e., the fact that phylogenetically related organisms tend to resemble each other more than distantly related ones (Blomberg and Garland, 2002), has for example important consequences for the understanding of trait evolution itself (Mooers et al., 1999). Non-phylogenetic models indeed assume that no change occurred in the internal branches and that all changes are restricted to terminal branches, as if the historical signal had been erased in the course of the evolutionary history (Mooers et al., 1999; Oakley et al., 2005). In turn, phylogenetic models assume that the branching pattern of the phylogeny predicts phenotypic evolution. The fit of alternative phylogenetic and nonphylogenetic models, which can be tested by standard likelihood-ratio tests (Oakley et al., 2005), can have important consequences in comparative studies involving across-species trait correlations that are not appropriately described by conventional statistical methods disregarding phylogenetic dependence in the data (Freckleton et al., 2002; Pagel, 2002; Blomberg et al., 2003). Comparative studies have traditionally been performed onto one or a few trees. Phylogenies are, however, rarely known without error. Different estimates of the phylogenetic tree can return different answers to the comparative question (Miller and Venable, 2003; Ober, 2003; Thompson and Oldroyd, 2004), causing a second source of uncertainty known as ‘phylogenetic uncertainty’ (Pagel and Lutzoni, 2002; Ronquist, 2004; Pagel et al., 2004). In this context, Markov chain Monte Carlo methods offer a formal framework to sample phylogenies according to their posterior probabilities. A straightforward way of taking phylogenetic uncertainty into account when reconstructing ancestral character states is to find the best-fit model on each tree and derive the corresponding ancestral character states as proposed, for example, by the program package Mesquite (Maddison and Maddison, 2005). This procedure enables an assessment of among-tree variation in ancestral character state reconstruction but does not account for the uncertainty associated with the estimation of the rate parameters themselves on each individual tree. Most recently, a Bayesian Markov chain Monte Carlo procedure was proposed to derive the posterior probability distribution of rate coefficients and ancestral character states (Pagel and Lutzoni, 2002; Pagel et al., 2004). At each iteration, the chain proposes a new combination of rate parameters and randomly selects a new tree from the Bayesian sample. The likelihood of the new combination is calculated and this new state of the chain is accepted or rejected following evaluation by the Metropolis-Hastings term. In an attempt to examine trait evolution along a phylogeny, one is thus left with a series of possible, not necessarily complementary approaches. If the limitations of the MP criterion for character state reconstruction have already been emphasized (Cunningham et al., 1998; Cunningham, 1999), the Bayesian approach of phylogenetic uncertainty is fairly recent and has therefore been applied only in a few cases to comparative studies (e.g., Lutzoni et al., 2001; Pagel et al., 2004). In mosses, the second most diverse phylum of land plants after the Angiosperms, fossil evidence is exceedingly rare (Goffinet, 2000) and comparative methods constitute a tool of prime importance to test hypotheses on the phylogenetic component of morphological evolution and the soundness of characters traditionally used in taxonomy. Although molecular phylogenies are becoming increasingly available to test previous taxonomic concepts (see [Goffinet and Buck 2004] for a review), morphological evolution has rarely been explicitly revisited by formally reconstructing ancestral shifts in character states (Vanderpoorten et al., 2002). In this paper, we test species concepts in the moss genus Brachytheciastrum by retracing the evolution of traditional taxonomic characters in a phylogenetic context. We seek for an appropriate model of evolution for reconstructing ancestral character states within the genus, contrasting results from (1) a ML optimization of rate parameters on a single, ML tree; (2) a ML optimization of rate parameters applied to a Bayesian sample of trees; and (3) a Bayesian sample of rate parameters used to produce the posterior probability distribution of ancestral character states. Methods Taxon Sampling, Molecular and Morphological Data Brachytheciastrum is one of 41 genera of the highly diverse pleurocarpous moss family Brachytheciaceae (Hypnales), which, with slightly less than 600 species, represent one of the most diverse families of pleurocarpous mosses (Ignatov and Huttunen, 2002). Brachytheciastrum currently includes nine species that form a strongly supported clade sister to Homalothecium (Vanderpoorten et al., 2005). One species of the latter, H. megaptilum, was selected as outgroup. Within the ingroup, multiple specimens belonging to eight of the nine species were sampled depending on the availability of sufficiently recent collections (Table 1). Each species was therefore represented by one (e.g., B. bellicum, currently only known from the type locality [Buck et al., 2001]) to several accessions. A set of 19 variable morphological characters, including the ones that have been used in the original species descriptions and a series of others that have recently been used in species-level taxonomy of the Brachytheciaceae (Ignatov and Huttunen, 2002), was scored for each of these specimens ( Appendices 1 and 2). Table 1 Taxon sampling, voucher information, and GenBank accession numbers for the ITS region and the atpB-rbcL intergenic spacer. Taxon ITS atpB-rbcL Voucher (herbarium where deposited) Locality (country; province, region, or state) bellicum AY737458 AY663293 Cano & Ros 9510 (MUR) Morocco, Rif collinum a AY737478 AY663296 Sotiaux 14574 (LG) France, Hautes Alpes collinum b AY737459 AY663297 Buck 23168 (NY) USA, OR collinum c AY736258 AY736265 Ignatov 31/55 (MHA) Russia, Altai collinum d AY736257 AY736264 Euragina 5. V 2002 (MHA) Russia, Astrakhan collinum e AY736256 AY736263 Czernyadievk £53 (MHA) Russia, Kamchatka dieckei a AY737460 AY663298 Sergio sn (LISU) Portugal, Beira Alta dieckei b AY737475 AY663319 Sergio & Seneca 8163 (NY) Portugal, Beira Alta dieckei c AY737476 AY663313 Canos & Ros 9512 (NY) Morocco, Rif dieckei d AY737477 AY663316 Cano & Ros 9513 (NY) Morocco, Rif fendleri AY737461 AY663302 Weber & Wittmann B112193 (NY) USA, CO leibergii AY737462 AY663301 Buck 37564 (NY) USA, OR olympicum a AY737474 AY736271 Düll exs 268 (LG) USA, CA olympicum b AY737472 AY736270 Düll exs 359 (LG) USA, CA olympicum c AY952446 AY952447 Seregin et al. M-255 (MW) Cyprus, Troodos Range trachypodium a AY736260 AY736267 Ignatov 31/229 1992 (MHA) Russia, Altai trachypodium b AY736261 AY736268 Ignatov 00-1055 6.IX. 2000 (MHA) Russia, Yakytia trachypodium c AY736259 AY736266 23. VII 1976 H. Roivainen (MHA) Russia, Caucasus velutinum a AY737473 AY663299 Sotiaux 27346 (LG) Belgium, Luxembourg velutinum b AY737464 AY663300 Vanderpoorten B51 (LG) Belgium, Liège velutinum c AY736262 AY736269 Ignatov 15.9.1996 (MHA) Russia, Kursk Homalothecium megaptilum AY737455 AY663307 Vanderpoorten 4691 (LG) Canada, BC Taxon ITS atpB-rbcL Voucher (herbarium where deposited) Locality (country; province, region, or state) bellicum AY737458 AY663293 Cano & Ros 9510 (MUR) Morocco, Rif collinum a AY737478 AY663296 Sotiaux 14574 (LG) France, Hautes Alpes collinum b AY737459 AY663297 Buck 23168 (NY) USA, OR collinum c AY736258 AY736265 Ignatov 31/55 (MHA) Russia, Altai collinum d AY736257 AY736264 Euragina 5. V 2002 (MHA) Russia, Astrakhan collinum e AY736256 AY736263 Czernyadievk £53 (MHA) Russia, Kamchatka dieckei a AY737460 AY663298 Sergio sn (LISU) Portugal, Beira Alta dieckei b AY737475 AY663319 Sergio & Seneca 8163 (NY) Portugal, Beira Alta dieckei c AY737476 AY663313 Canos & Ros 9512 (NY) Morocco, Rif dieckei d AY737477 AY663316 Cano & Ros 9513 (NY) Morocco, Rif fendleri AY737461 AY663302 Weber & Wittmann B112193 (NY) USA, CO leibergii AY737462 AY663301 Buck 37564 (NY) USA, OR olympicum a AY737474 AY736271 Düll exs 268 (LG) USA, CA olympicum b AY737472 AY736270 Düll exs 359 (LG) USA, CA olympicum c AY952446 AY952447 Seregin et al. M-255 (MW) Cyprus, Troodos Range trachypodium a AY736260 AY736267 Ignatov 31/229 1992 (MHA) Russia, Altai trachypodium b AY736261 AY736268 Ignatov 00-1055 6.IX. 2000 (MHA) Russia, Yakytia trachypodium c AY736259 AY736266 23. VII 1976 H. Roivainen (MHA) Russia, Caucasus velutinum a AY737473 AY663299 Sotiaux 27346 (LG) Belgium, Luxembourg velutinum b AY737464 AY663300 Vanderpoorten B51 (LG) Belgium, Liège velutinum c AY736262 AY736269 Ignatov 15.9.1996 (MHA) Russia, Kursk Homalothecium megaptilum AY737455 AY663307 Vanderpoorten 4691 (LG) Canada, BC View Large Preliminary investigation (Vanderpoorten et al., 2005) suggested that the atpB-rbcL intergenic spacer (cpDNA) and the ITS region (nrDNA) may exhibit the appropriate level of variation to discriminate species in the genus. These two loci were amplified and sequenced for each accession according to the protocols described in Vanderpoorten et al. (2002). Due to the difficulties encountered with the amplification of the chloroplast locus in several accessions, a specific set of primers was designed within conserved regions at the 5’ and 3' ends of the molecule from the available sequences of the genus: atpB : GGGACCAATAATTTGAGTAATACGTCC (Tm = 65.8°C); rbcL : GGTGACATAGGTCCCTCCC (Tm = 63.2°C). Phylogenetic Analyses Phylogenetic analyses of DNA sequences were conducted by maximizing the likelihood under the assumptions of a model of nucleotide substitution. The hierarchical likelihood-ratio test (hLRT) has been the most popular method to select, among increasingly complex models, the one that best fits the data with a minimum of estimated parameters. hLRTs do, however, not allow for non-nested comparisons or simultaneous comparison of multiple models. Their use for model selection has therefore been recently questioned. In this context, other selection techniques, including the Bayesian information criterion (BIC) and Akaike information criterion, have been proposed (see Huelsenbeck et al. [2004] and Posada and Buckley [2004] for reviews). Here, we selected the model in the decision theory framework developed by Minin et al. (2003), which is based on the BIC but incorporates branch length error as a performance measure. Simulations suggested that models selected with this criterion result in slightly more accurate branch length estimates, an essential feature of the phylogeny in a character-state reconstruction context. Model selection was done using the program DT-ModSel (Minin et al., 2003). The selected model was implemented in heuristic searches with 300 random addition replicates with TBR branch swapping to find the most likely tree in PAUP* (Swofford, 2002). Branches of zero length were collapsed during the search. No taxon was resolved as part of two distinct clades supported each by > 70% Bayesian proportions (BP, see below) in analyses of the nuclear and chloroplast data sets and these partitions were therefore combined into a single matrix (TreeBase accession number M2985). The score of the candidate trees that resulted from the heuristic search was reassessed by specifically modeling base composition, substitution rates, and rate heterogeneity for the chloroplast locus and each of the different partitions of the ITS region, namely ITS1, the 5.8S rRNA gene, and ITS2, using the algorithms implemented by PAML (Yang, 1997). Within each partition, rate heterogeneity was modeled using a discrete gamma distribution with eight categories. A phylogram of the final tree selected for its highest likelihood was eventually constructed with TreeView (Page, 1996). Significant departure of alternative topologies involving a morphological taxon concept from the optimal molecular topologies was tested by constraining the accessions of the same morphospecies to monophyly. Optimal constrained topologies were sought under maximum likelihood. Significant departure from the unconstrained optimal topology was tested using the procedure described by Shimodaira and Hasagawa (1999) with 1000 replicates of full optimization. Support for clades was assessed using a Bayesian procedure employing a mixture model that simultaneously implements several rate matrices without a priori partitioning of the data (Pagel and Meade, 2004). Four chains of 1,000,000 iterations were run and trees were sampled every 10,000 generations to ensure independence of successive trees. The number of generations needed to reach stationarity in the Markov chain Monte Carlo algorithm was estimated by visual inspection of the plot of the ML score at each sampling point. The trees of the ‘burn-in’ for each run were excluded from the tree set, and the 100 remaining trees from each run were combined to form the full sample of trees assumed to be representative of the posterior probability distribution. The sampling size, comparable to that used in other studies (e.g., Pagel et al., 2004), allowed the chains to visit most of the frequently occurring topologies, as shown by the similarity of the posteriors returned by each of the four runs. We contrasted the performances of increasingly complex models employing one to three rate matrices, and with or without gamma distributions, to model within-matrix rate heterogeneity, by plotting the log-likelihood values against the standard deviation of the rate matrix parameters, looking for a cut-off point that corresponds to a slowing in the improvement to the overall log-likelihood and a sharp increase in the standard deviation of the model parameters. Morphological Evolution Model Optimization and Test of Hypotheses The phylogeny was used to study the evolution for each individual morphological character. The probabilities of change in a branch were calculated by estimating the instantaneous rates of transitions among all possible pairs of states by implementing the Markov model of the software Multistate. We used the ‘global’ approach, wherein model parameters are first fixed and then used to derive the set of most likely ancestral character states (Pagel, 1999b). ‘Local’ estimators, by contrast, allow for alternative hypotheses of ancestral states to be tested at each individual node, but do not represent the most likely estimates because different rates are fitted after the node under scrutiny has been set to its two possible states (Mooers, 2004). Global reconstructions, which, for reasons that are still unclear, are more accurate than local ones (Mooers, 2004), provide true posterior probabilities of states across nodes, and thus yield the single best description of the past (Pagel, 1999b; Mooers, 2004). The model includes two parameters: the instantaneous transition rate q and a parameter (κ) used to perform branch length transformations in order to improve the fit of the model to the data. κ differentially stretches or compresses individual branches. κ > 1 stretches long branches more than shorter ones, indicating that longer branches contribute more to trait evolution (as if the rate of evolution accelerates within a long branch). κ < 1 compresses longer branches more than shorter ones. At the extreme, κ = 0 is consistent with a mode of evolution, in which trait evolution is independent of the length of the branch (Pagel, 1994). We tested whether models directly employing genetic distances (or a transformation thereof) to determine the probability of change, i.e., models allowing for continuous changes along the branches, described the evolution of the traits significantly better than ‘speciational’ models employing branches of equal lengths. To this end, we contrasted the fit of a model, wherein κ was restricted to 0 (all branches of equal length), with the fit of a model, wherein κ was free to take its most likely value. The two models differ in one parameter and can thus be compared by a likelihood-ratio test, according to which the more complicated model provides a significantly better representation of the data if twice the difference in log-likelihood returned by the respective models is higher than a chi-square variate with one degree of freedom (Pagel, 1994). Finally, we used a likelihood ratio to test whether applying a model including a forward and backward transition rate significantly improved the likelihood as compared to a single rate model. All the parameters were then fixed to calculate the probabilities of ancestral character states across all nodes. In binary characters, evidence for phylogenetic signal in the data is found anytime the probabilities of ancestral states differ from 0.5 and signal intensity is proportional to departure of ancestral state probabilities from 0.5 (A. Meade and M. Pagel, personal communication). Indeed, the probabilities of change along each branch are weighted by the prior probability of state at the beginning of the branch (Pagel, 1999b). Thus, when all ancestral state probabilities equal 0.5, the state at a node is independent of the state at the previous node, as if there was no history in the tree. In this case, our experience is that transition rates acquire very large values, so that the transitions probabilities pii(t) and pij(t) do not depart from the 0.5 stationary frequencies assumed by the model (see Lewis, 2001:915). The significance of the phylogenetic signal was tested by comparing the fit of phylogenetic vs nonphylogenetic models to the data (Mooers et al., 1999). We thus contrasted the likelihood in the context of the phylogeny and of a star-tree, wherein all internal branches were set to 0 and wherein the length of each terminal branch corresponded to the total path from the root to the extant species. The phylogenetic and nonphylogenetic models include the same number of parameters and the likelihood values they return can therefore be directly compared, with a difference of two being considered significant (Mooers et al., 1999; Oakley et al., 2005). Phylogenetic Uncertainty Two methods were used for assessing whether phylogenetic uncertainty affects the probabilities of ancestral character states. In a first series of analyses, the phylogenetic robustness of the reconstructions was assessed, for each node of the phylogeny, by reconstructing ancestral character states using the ML optimization described above across the Bayesian sample of trees. For each tree, model selection was performed as described above and results from different models were combined to form the full range of probabilities of ancestral character states at a node across trees. In order to circumvent the issues associated with the fact, that not all of the trees necessarily contain the internal nodes of interest, reconstructions were performed using a ‘most recent common ancestor’ approach that identifies, for each tree, the most recent common ancestor to a group of species and reconstructs the state at the node, then combines this information across trees (Pagel et al., 2004). In a second series of analyses, we examined the impact of the choice of a range of model parameters within and among trees by using the Markov chain model implemented by Bayes Multistate to estimate the posterior probability distributions of rate coefficients and ancestral states (Pagel et al., 2004). The rate at which parameters get changed (‘ratedev’) was set at the beginning of each run so that the acceptance rate of the proposed changes globally ranges between 20% and 50%. Priors of the rate parameters were derived from their likelihood surface as proposed by Pagel et al. (2004). For that purpose, the magnitude of a rate coefficient was manually allowed to vary from low to high values, calculating the likelihood on the 50% majority-rule consensus tree, whose branch lengths were averaged over the 400 sampled trees. This operation was repeated for the other parameter. The resulting likelihood curves were treated as a beta distribution, taking the mode as the mean and calculating the standard deviation on the assumption that the mean ± three times the standard deviation includes all of the rates. Rate coefficients and ancestral character states, reconstructed using the most recent common ancestor approach, were sampled every 100 generations to ensure independence from successive samplings. The chain was run for 4,000,000 generations so that each tree was visited approximately 100 times by the chain on average. The within-and among-tree proportion of the variation in model parameters and ancestral character state reconstructions was partitioned by one-way analysis of variance depending on the factor ‘tree number.’ Comparison Among Methods of Ancestral Character State Reconstruction We examined whether congruent estimates of ancestral character states were produced by methods employing (I) a single set of model parameters optimized by ML onto a single, ML tree (II) a set of single model parameters each individually optimized by ML onto a sample of trees; and (III) a Markov chain visiting a sample of trees to produce the posterior probability distribution of model parameters and ancestral character states. After having calculated the average probabilities at each node in methods II, and III, we used correlation coefficients to estimate the extent to which changes in character states from a node to another varied in a correlated fashion when node states were estimated using methods I, II and III, respectively. In order to test whether a reconstruction method returned on average higher probabilities of ancestral character states, we contrasted the probabilities of the most likely reconstruction at each node (or the average probability of the most likely character state at a node in methods II and III) by a pairwise Student's t test across nodes. Results Phylogenetic Reconstruction The ITS region and the atpB-rbcL intergenic spacer respectively included 4.5% and 6.1% of variable sites within Brachytheciastrum. Both partitions yielded congruent topologies and were therefore combined. The substitution model selected for the combined data set was the Hasegawa et al. model (see, e.g., Nei and Kumar, 2000, for reference) with a gamma distribution (α = 0.1149) to model among-site heterogeneity. The model implemented a transition/transversion ratio of 1.7654 and A, C, and G nucleotide proportions of 0.2975, 0.1953, and 0.2136, respectively. Heuristic searches using these settings resulted in a unique ML tree (−lnL = 2526.51). Allowing the fit of different rate parameters, base compositions, and shapes of the gamma distribution for each of the molecular partitions with highly divergent GC contents, transition-transversion ratios, and patterns of rate heterogeneity resulted in a substantial improvement of the likelihood (−lnL = 2349.38). Three morphospecies were resolved as polyphyletic assemblages in the optimal topology. Constraining successively each of those morphospecies to monophyly resulted in a significant decrease in log-likelihood (Δ lnL = 23.53, P = 0.02 for B. collinum; Δ lnL = 29.6, P = 0.02 for B. dieckei; and Δ lnL = 22.72, P = 0.03 for B. trachypodium). The log-likelihoods returned by increasingly complex models implementing one to three HKY rate matrices during the Bayesian analysis of the combined DNA data set are represented as a function of the standard deviation of the rate parameters in Figure 1. The curve shows a sharp cut-off point at the two-rate matrix model. Beyond that level of complexity, the log-likelihoods returned by models employing more parameters exhibited a very slow increase, whereas standard deviations of rate parameters substantially increased. The two-rate matrix model was therefore selected for producing the Bayesian sample of trees used to compute branch posterior probabilities (Fig. 2) and for assessing phylogenetic uncertainty in ancestral character state reconstruction. The reconstructions were performed on each of the 14 nodes exhibiting > 50% posterior probabilities. Figure 1 View largeDownload slide Plot of the standard deviation of the transition/transversion ratio of the HKY substitution model over the 400 MCMC sample of trees as a function of the average log-likelihoods returned by increasingly complex substitution models implementing one (1r) to three (3r) rate matrices, with or without Γ distributions to model within-matrix rate heterogeneity. Figure 1 View largeDownload slide Plot of the standard deviation of the transition/transversion ratio of the HKY substitution model over the 400 MCMC sample of trees as a function of the average log-likelihoods returned by increasingly complex substitution models implementing one (1r) to three (3r) rate matrices, with or without Γ distributions to model within-matrix rate heterogeneity. Figure 2 View largeDownload slide Phylogram of the 50% majority-rule consensus of the 400 MCMC sample of trees with branch lengths averaged over the whole sample from the Bayesian analysis of ITS and atpB-rbcL sequences in Brachytheciastrum using a mixture model with two-rate matrices. Number below the branches correspond to the proportions in which they appear in the 400 sampled trees. Pie diagrams indicate the probabilities of ancestral state for stem leaf cell width (character 16: white: > 8 μ m; black: < 8 μ m) derived from a maximum likelihood optimization of the parameters of the model of morphological evolution on the ML tree. Figure 2 View largeDownload slide Phylogram of the 50% majority-rule consensus of the 400 MCMC sample of trees with branch lengths averaged over the whole sample from the Bayesian analysis of ITS and atpB-rbcL sequences in Brachytheciastrum using a mixture model with two-rate matrices. Number below the branches correspond to the proportions in which they appear in the 400 sampled trees. Pie diagrams indicate the probabilities of ancestral state for stem leaf cell width (character 16: white: > 8 μ m; black: < 8 μ m) derived from a maximum likelihood optimization of the parameters of the model of morphological evolution on the ML tree. Reconstruction of Ancestral Character States Models employing genetic branch lengths (or a transformation thereof by means of the scaling parameter κ) to determine the probability of change exhibited a better fit on the data as compared to equal distance models depending on the investigated trees (Table 2). On the ML tree, κ was significantly higher than 0 for four characters. For these characters however, the hypothesis that κ = 0 could not be significantly rejected in the majority of trees of the Bayesian sample. By contrast, in other characters, for which κ was not found significantly different than 0 on the ML tree, a small proportion of trees from the Bayesian sample often supported κ values significantly higher than 0. κ values sampled by the MCMC procedure had an average ranging between 0.54 ± 0.38 and 1.62 ± 0.97 depending on the character investigated, and were characterized by very wide intervals of confidence often encompassing 0 (see, for example, the posterior probability distribution of κ or character 16 in Fig. 3). Figure 3 View largeDownload slide Histogram, represented as normal distributions, of the parameters of the model of morphological evolution for stem leaf cell width in Brachytheciastrum (character 16). (a) Distribution of the single rate parameter q selected by a likelihood-ratio test and optimized by ML on each of the 400 Bayesian sample of trees. The other model parameter, κ, was found to significantly differ from 0 in none of the 400 sampled trees as assessed by a likelihood ratio test. (b and c): Distributions of q01, q10, and κ, sampled every 100 of 4,000,000 generations of a MCMC exploring the space of the 400 sampled trees. Figure 3 View largeDownload slide Histogram, represented as normal distributions, of the parameters of the model of morphological evolution for stem leaf cell width in Brachytheciastrum (character 16). (a) Distribution of the single rate parameter q selected by a likelihood-ratio test and optimized by ML on each of the 400 Bayesian sample of trees. The other model parameter, κ, was found to significantly differ from 0 in none of the 400 sampled trees as assessed by a likelihood ratio test. (b and c): Distributions of q01, q10, and κ, sampled every 100 of 4,000,000 generations of a MCMC exploring the space of the 400 sampled trees. Table 2 Models of morphological evolution in Brachytheciastrum: model parameters (I) optimized by ML on the ML tree; (II) optimized by ML on each of the trees of a Bayesian sample; and (III) sampled by a MCMC visiting the space of a Bayesian sample of trees. (1) κ-Transformed branch lengths determine the probability of change significantly better than branches of equal length (κ = 0) when twice the log-likelihood ratio is higher than a χ2 variate with 1 df. (2) Two-rate models implementing different forward (q01) and backward (q10) transition rates are preferred over single-rate models (q) when twice the log-likelihood ratio is higher than a χ2 variate with 1 df. (3) P(0) is the probability (I) or the average probability ± SD (II and III) of state 0 at the root. (4) Average ± SD of the posterior probability distribution. I II III Character κ(1) qij(2) p(0)(3) κ(1):average ± SD Single-and two rate models(2): mean rate ± SD p(0)(3) κ(4) q01 and q10(4) p(0)(3) 1 1.27 q01 = q10 = 117.27 0.87 92 trees : 1.88 ± 0.67 q01 = q10 = 919.16 ± 245.93 0.89 ± 0.10 1.24 ± 0.71 37.51 ± 25.59; 0.79 ± 0.20 308 trees: 0 q01 = 0.10 ± 0.23; q10 = 1.1 ± 2.22 0.32 ± 0.02 45.26 ± 23.68 2 1.4 q01 = q10 = 1000 0.63 58 trees: 1.72 ± 0.61 q01 = q10 = 990.96 ± 68.82 0.64 ± 0.18 1.20 ± 0.81 387.37 ± 258.53; 0.53 ± 0.20 342 trees: 0 q01 = 0.14 (0.31); q10 = 0.71 ± 1.31 0.16 ± 0.09 637.81 ± 252.26 3 0 q01 = q10 = 0.31 0.71 399 trees: 0 q01 = q10 = 2.45 ± 3.84 0.62 ± 0.08 0.71 ± 0.49 608.03 ± 234.69; 0.54 ± 0.10 1 tree: 1.71 q01 = q10 = 1000 0.72 568.88 ± 238.93 4 0 q01 = q10 = 0.03 1.00 400 trees: 0 q01 = q10 = 0.03 ± 0.01 1.00 ± 0.00 1.41 ± 0.75 289.49 ± 287.56; 0.87 ± 0.19 557.08 ± 276.19 5 0 q01 = q10 = 0.15 0.97 3 trees: 1.29 ± 0.28 q01 = q10 = 1000 ± 0.00 0.55 ± 0.10 0.80 ± 0.54 384.92 ± 218.5; 0.55 ± 0.12 397 trees: 0 42 trees: q01 = 5.09 ± 0.87; q10 = 12.73 ± 2.18 0.51 ± 0.03 674.37 ± 237.69 355 trees: q01 = q10 = 0.21 ± 0.04 0.91 ± 0.05 6 0 q01 = q10 = 0.23 0.89 396 trees: 0 q01 = q10 = 1.88 ± 3.49 0.74 ± 0.16 0.81 ± 0.55 431.31 ± 219.21; 0.54 ± 0.09 4 trees: 1.58 ± 0.61 q01 = q10 = 1000 ± 0.00 0.69 ± 0.17 684.21 ± 227.21 7 1.3 q01 = q10 = 1000 0.53 47 trees: 1.55 ± 0.46 q01 = q10 = 942.95 ± 222.66 0.69 ± 0.14 1.39 ± 0.89 452.65 ± 245.42; 0.62 ± 0.18 353 trees: 0 1 tree: q01 = 0.00; q10 = 0.28 0.00 597.49 ± 259.87 352 trees: q01 = q10 = 0.22 ± 0.02 0.54 ± 0.05 8 0 q01 = q10 = 0.23 0.82 4 trees: 2.04 ± 0.66 q01 = q10 = 1000 ± 0.00 0.59 ± 0.11 0.66 ± 0.44 57.46 ± 23.57; 0.57 ± 0.13 396 trees: 0 q01 = q10 = 1.06 ± 2.38 0.66 ± 0.09 61.00 ± 23.76 9 1.46 q01 = q10 = 1000 0.21 13 trees: 1.41 ± 0.29 q01 = q10 = 925.37 ± 269.07 0.21 ± 0.16 1.1 ± 0.67 57.90 ± 26.91; 0.29 ± 0.22 387 trees: 0 q01 = q10 = 0.16 ± 0.02 0.10 ± 0.05 48.60 ± 25.36 10 0 q01 = q10 = 0.05 0.97 38 trees: 2.05 ± 0.72 q01 = q10 = 960.03 ± 178.70 0.18 ± 0.24 1.62 ± 0.97 416.82 ± 239.15; 0.82 ± 0.20 362 trees: 0 166 trees: q01 = q10 = 0.05 ± 0.00 0.97 ± 0.00 584.48 ± 271.26 196 trees: q01 = 0.00 ± 0.00; q10 = 0.49 ± 0.00 0.23 ± 0.25 11 0 q01 = q10 = 0.10 0.50 15 trees: 1.52 ± 0.45 q01 = q10 = 939.91 ± 232.72 0.50 ± 0.05 1.44 ± 0.55 573.31 ± 246.80; 0.74 ± 0.18 385 trees: 0 q01 = q10 = 0.11 ± 0.02 0.50 ± 0.05 450.66 ± 260.97 12 0 q01 = q10 = 0.09 0.99 4 trees: 0.79 ± 0.95 1 tree. q01 = q10 = 1000 0.56 0.96 ± 0.57 297.89 ± 223.62; 0.67 ± 0.20 396 trees: 0 13 trees: q01 = 3.44 ± 0.16; q10 = 14.64 ± 0.70 0.50 ± 0.00 638.50 ± 248.90 383 trees: q01 = q10 = 0.09 ± 0.02 0.99 ± 0.00 13 0 q01 = q10 = 9.67 0.50 400 trees: 0 q01 = q10 = 9.67 ± 0.00 0.50 ± 0.00 0.54 ± 0.38 581.31 ± 232.27; 0.50 ± 0.00 613.40 ± 230.27 14 0 q01 = q10 = 9.67 0.50 400 trees: 0 q01 = q10 = 5.41 ± 4.49 0.47 ± 0.05 0.71 ± 0.33 633.38 ± 230.46; 0.50 ± 0.01 557.50 ± 234.50 15 0 q01 = 3.55 q10 = 15.08 0.50 19 trees: 1.13 ± 0.34 q01 = q10 = 637.85 ± 426.38 0.85 ± 0.10 0.66 ± 0.47 268.45 ± 192.00; 0.55 ± 0.12 381 trees: 0 q01 = 3.53 ± 0.60, q10 = 15.02 ± 2.56 0.50 ± 0.01 660.63 ± 234.20 16 0 q01 = q10 = 0.11 0.98 400 trees: 0 q01 = q10 = 0.16 ± 0.03 0.93 ± 0/04 0.84 ± 0.45 32.30 ± 26.71; 0.56 ± 0.27 55.26 ± 25.92 17 0 q01 = q10 = 0.20 0.73 58 trees: 1.64 ± 0.50 q01 = q10 = 915.14 ± 255.21 0.38 ± 0.15 1.50 ± 0.93 574.08 ± 257.24; 0.57 ± 0.20 342 trees: 0 6 trees: q01 = 4.39 ± 3.98; q10 = 1.75 ± 1.59 0.50 ± 0.01 481.04 ± 249.15 336 trees: q01 = q10 = 0.21 ± 0.05 0.66 ± 0.07 18 0 q01 = q10 = 0.06 1.00 400 trees: 0 q01 = q10 = 0.06 ± 0.00 1.00 ± 0.00 0.66 ± 0.46 172.38 ± 179.48; 0.58 ± 0.17 660.78 ± 237.63 19 0 q01 = q10 = 0.03 1.00 1 tree: 2.15 q01 = q10 = 1000 1.00 1.39 ± 0.90 328.03 ± 295.79; 0.79 ± 0.23 399 trees: 0 3 trees: q01 = 0.00 ± 0.00; q10 = 0.69 ± 0.00 0.00 ± 0.00 595.75 ± 272.47 396 trees: q01 = q10 = 0.03 ± 0.00 1.00 ± 0.00 I II III Character κ(1) qij(2) p(0)(3) κ(1):average ± SD Single-and two rate models(2): mean rate ± SD p(0)(3) κ(4) q01 and q10(4) p(0)(3) 1 1.27 q01 = q10 = 117.27 0.87 92 trees : 1.88 ± 0.67 q01 = q10 = 919.16 ± 245.93 0.89 ± 0.10 1.24 ± 0.71 37.51 ± 25.59; 0.79 ± 0.20 308 trees: 0 q01 = 0.10 ± 0.23; q10 = 1.1 ± 2.22 0.32 ± 0.02 45.26 ± 23.68 2 1.4 q01 = q10 = 1000 0.63 58 trees: 1.72 ± 0.61 q01 = q10 = 990.96 ± 68.82 0.64 ± 0.18 1.20 ± 0.81 387.37 ± 258.53; 0.53 ± 0.20 342 trees: 0 q01 = 0.14 (0.31); q10 = 0.71 ± 1.31 0.16 ± 0.09 637.81 ± 252.26 3 0 q01 = q10 = 0.31 0.71 399 trees: 0 q01 = q10 = 2.45 ± 3.84 0.62 ± 0.08 0.71 ± 0.49 608.03 ± 234.69; 0.54 ± 0.10 1 tree: 1.71 q01 = q10 = 1000 0.72 568.88 ± 238.93 4 0 q01 = q10 = 0.03 1.00 400 trees: 0 q01 = q10 = 0.03 ± 0.01 1.00 ± 0.00 1.41 ± 0.75 289.49 ± 287.56; 0.87 ± 0.19 557.08 ± 276.19 5 0 q01 = q10 = 0.15 0.97 3 trees: 1.29 ± 0.28 q01 = q10 = 1000 ± 0.00 0.55 ± 0.10 0.80 ± 0.54 384.92 ± 218.5; 0.55 ± 0.12 397 trees: 0 42 trees: q01 = 5.09 ± 0.87; q10 = 12.73 ± 2.18 0.51 ± 0.03 674.37 ± 237.69 355 trees: q01 = q10 = 0.21 ± 0.04 0.91 ± 0.05 6 0 q01 = q10 = 0.23 0.89 396 trees: 0 q01 = q10 = 1.88 ± 3.49 0.74 ± 0.16 0.81 ± 0.55 431.31 ± 219.21; 0.54 ± 0.09 4 trees: 1.58 ± 0.61 q01 = q10 = 1000 ± 0.00 0.69 ± 0.17 684.21 ± 227.21 7 1.3 q01 = q10 = 1000 0.53 47 trees: 1.55 ± 0.46 q01 = q10 = 942.95 ± 222.66 0.69 ± 0.14 1.39 ± 0.89 452.65 ± 245.42; 0.62 ± 0.18 353 trees: 0 1 tree: q01 = 0.00; q10 = 0.28 0.00 597.49 ± 259.87 352 trees: q01 = q10 = 0.22 ± 0.02 0.54 ± 0.05 8 0 q01 = q10 = 0.23 0.82 4 trees: 2.04 ± 0.66 q01 = q10 = 1000 ± 0.00 0.59 ± 0.11 0.66 ± 0.44 57.46 ± 23.57; 0.57 ± 0.13 396 trees: 0 q01 = q10 = 1.06 ± 2.38 0.66 ± 0.09 61.00 ± 23.76 9 1.46 q01 = q10 = 1000 0.21 13 trees: 1.41 ± 0.29 q01 = q10 = 925.37 ± 269.07 0.21 ± 0.16 1.1 ± 0.67 57.90 ± 26.91; 0.29 ± 0.22 387 trees: 0 q01 = q10 = 0.16 ± 0.02 0.10 ± 0.05 48.60 ± 25.36 10 0 q01 = q10 = 0.05 0.97 38 trees: 2.05 ± 0.72 q01 = q10 = 960.03 ± 178.70 0.18 ± 0.24 1.62 ± 0.97 416.82 ± 239.15; 0.82 ± 0.20 362 trees: 0 166 trees: q01 = q10 = 0.05 ± 0.00 0.97 ± 0.00 584.48 ± 271.26 196 trees: q01 = 0.00 ± 0.00; q10 = 0.49 ± 0.00 0.23 ± 0.25 11 0 q01 = q10 = 0.10 0.50 15 trees: 1.52 ± 0.45 q01 = q10 = 939.91 ± 232.72 0.50 ± 0.05 1.44 ± 0.55 573.31 ± 246.80; 0.74 ± 0.18 385 trees: 0 q01 = q10 = 0.11 ± 0.02 0.50 ± 0.05 450.66 ± 260.97 12 0 q01 = q10 = 0.09 0.99 4 trees: 0.79 ± 0.95 1 tree. q01 = q10 = 1000 0.56 0.96 ± 0.57 297.89 ± 223.62; 0.67 ± 0.20 396 trees: 0 13 trees: q01 = 3.44 ± 0.16; q10 = 14.64 ± 0.70 0.50 ± 0.00 638.50 ± 248.90 383 trees: q01 = q10 = 0.09 ± 0.02 0.99 ± 0.00 13 0 q01 = q10 = 9.67 0.50 400 trees: 0 q01 = q10 = 9.67 ± 0.00 0.50 ± 0.00 0.54 ± 0.38 581.31 ± 232.27; 0.50 ± 0.00 613.40 ± 230.27 14 0 q01 = q10 = 9.67 0.50 400 trees: 0 q01 = q10 = 5.41 ± 4.49 0.47 ± 0.05 0.71 ± 0.33 633.38 ± 230.46; 0.50 ± 0.01 557.50 ± 234.50 15 0 q01 = 3.55 q10 = 15.08 0.50 19 trees: 1.13 ± 0.34 q01 = q10 = 637.85 ± 426.38 0.85 ± 0.10 0.66 ± 0.47 268.45 ± 192.00; 0.55 ± 0.12 381 trees: 0 q01 = 3.53 ± 0.60, q10 = 15.02 ± 2.56 0.50 ± 0.01 660.63 ± 234.20 16 0 q01 = q10 = 0.11 0.98 400 trees: 0 q01 = q10 = 0.16 ± 0.03 0.93 ± 0/04 0.84 ± 0.45 32.30 ± 26.71; 0.56 ± 0.27 55.26 ± 25.92 17 0 q01 = q10 = 0.20 0.73 58 trees: 1.64 ± 0.50 q01 = q10 = 915.14 ± 255.21 0.38 ± 0.15 1.50 ± 0.93 574.08 ± 257.24; 0.57 ± 0.20 342 trees: 0 6 trees: q01 = 4.39 ± 3.98; q10 = 1.75 ± 1.59 0.50 ± 0.01 481.04 ± 249.15 336 trees: q01 = q10 = 0.21 ± 0.05 0.66 ± 0.07 18 0 q01 = q10 = 0.06 1.00 400 trees: 0 q01 = q10 = 0.06 ± 0.00 1.00 ± 0.00 0.66 ± 0.46 172.38 ± 179.48; 0.58 ± 0.17 660.78 ± 237.63 19 0 q01 = q10 = 0.03 1.00 1 tree: 2.15 q01 = q10 = 1000 1.00 1.39 ± 0.90 328.03 ± 295.79; 0.79 ± 0.23 399 trees: 0 3 trees: q01 = 0.00 ± 0.00; q10 = 0.69 ± 0.00 0.00 ± 0.00 595.75 ± 272.47 396 trees: q01 = q10 = 0.03 ± 0.00 1.00 ± 0.00 View Large The two-rate model significantly improved the likelihood over the single-rate model for only one character on the ML tree (character 15; Table 2). In the Bayesian sample of trees, restricting these two parameters to be equal for that character did not result in a significant decrease in log-likelihood in 19 of the 400 sampled trees. For most other characters, for which a single-rate model was favored based on the single ML tree, the two-rate model returned significantly higher log-likelihood values than the single-rate model for a portion of the trees from the Bayesian sample. This was especially true for characters 1, 2, and 10, for which the two-rate model was favored by the data over the single-rate model in > 50% of the sampled trees. Although the values of the two rate parameters sampled by the MCMC procedure strongly overlapped for each character (see, for example, the posterior probability distributions of q01 and q10 for character 16 in Fig. 3), they always significantly (P < 0.001) differed from each other on average across the whole sample of trees. The reconstructions of ancestral character states using a ML optimization of model parameters onto the ML tree, a ML optimization of model parameters onto the Bayesian sample of trees, and a MCMC sample of model parameters were all significantly correlated across nodes for each of the 19 investigated characters, most often with r > 0.90 (P < 0.001) (Table 3; see also for example the reconstruction of ancestral character states for stem leaf cell width using the three procedures in Figs. 2 and 4). However, when rates were optimized by ML onto the Bayesian sample of trees, the selection of one-versus two-rate-models based on the result of a likelihood-ratio test greatly influenced the estimates of ancestral states at the root in the case of character states with unique or rare occurrences (see, e.g., characters 1, 2, 10, and 19 in Table 2). Table 3 Comparison of ancestral character state reconstruction in Brachytheciastrum when model parameters are (I) optimized by ML on the ML tree; (II) optimized by ML on each of the trees of a Bayesian sample; and (III) sampled by a MCMC visiting the space of a Bayesian sample of trees. (a) Correlation coefficient r between the P(0) at each node derived from alternative methods across the 14 nodes. In methods II and III, the p(0) at each node are an average over the n = 400 and n = 40,000 observations, respectively. All p-values of r are < 0.001 except when otherwise noted: NS, P > 0.05; * P < 0.05: ** P < 0.01.—: all probabilities of ancestral character states equal to 0.5 across nodes. (b) Comparison of the mean (± SD) probability of the most likely reconstruction across nodes when reconstructions are performed using method I, II, and III. In methods II and III, the probability of the most likely reconstruction at a node is an average over the n = 400 and n = 40,000 observations, respectively. All the P-values associated to a pairwise Student's t test for testing whether a method returns on average higher probabilities of ancestral character state than another across the 14 nodes are < 0.001 except when otherwise noted (see above). a Character rI/II rI/III rII/III b 1 0.80 0.99 0.92 mI = 0.96 ± 0.09 > mIII = 0.88 ± 0.09 > mII = 0.72 ± 0.08 2 0.71** 0.92 0.92 mI = 0.88 ± 0.17 > mII = 0.74 ± 0.11* = mIII = 0.72 ± 0.10 3 0.99 0.92 0.94 mI = 0.73 ± 0.17 > mII = 0.64 ± 0.11 > mIII = 0.57 ± 0.05** 4 0.99 0.99 0.99 mI = 0.99 ± 0.00 = mII = 0.99 ± 0.02 > mIII = 0.90 ± 0.04 5 0.96 0.80 0.85 mI = 0.87 ± 0.17 > mII = 0.77 ± 0.15 > mIII = 0.60 ± 0.06 6 0.95 0.67** 0.80 mI = 0.80 ± 0.16 > mII = 0.70 ± 0.13 > mIII = 0.59 ± 0.07 7 0.77** 0.89 0.92 mI = 0.80 ± 0.21 = mII = 0.80 ± 0.17 > mIII = 0.72 ± 0.12** 8 0.98 0.88 0.92 mI = 0.76 ± 0.17 > mII = 0.67 ± 0.12 > mIII = 0.63 ± 0.09* 9 0.87 0.92 0.97 mI = 0.90 ± 0.15 = mII = 0.84 ± 0.17 > mIII = 0.78 ± 0.15** 10 0.93 0.97 0.96 mI = 0.93 ± 0.15 > mII = 0.77 ± 0.10 = mIII = 0.84 ± 0.12 11 0.99 0.97 0.97 mI = 0.89 ± 0.20 > mII = 0.87 ± 0.20** = mIII = 0.88 ± 0.14 12 0.95 0.88 0.94 mI = 0.93 ± 0.14 = mII = 0.89 ± 0.16 > mIII = 0.71 ± 0.09 13 — — — mI = 0.50 ± 0.00 = mII = 0.50 ± 0.00 = mIII = 0.52 ± 0.01 14 — — 0.63* mI = 0.50 ± 0.00 < mII = 0.55 ± 0.04** = mIII = 0.60 ± 0.11 15 — — 0.90 mI = 0.50 ± 0.00 < mII = 0.52 ± 0.00 < mIII = 0.57 ± 0.04 16 0.98 0.90 0.92 mI = 0.88 ± 0.18 = mII = 0.84 ± 0.17 > mIII = 0.70 ± 0.14 17 0.98 0.70** 0.84 mI = 0.80 ± 0.16 = mII = 0.80 ± 0.15 = mIII = 0.76 ± 0.11 18 0.97 0.78 0.84 mI = 0.96 ± 0.13 = mII = 0.95 ± 0.13 > mIII = 0.60 ± 0.03 19 0.99 0.56* 0.58* mI = 0.99 ± 0.00 = mII = 0.99 ± 0.03 > mIII = 0.82 ± 0.04 a Character rI/II rI/III rII/III b 1 0.80 0.99 0.92 mI = 0.96 ± 0.09 > mIII = 0.88 ± 0.09 > mII = 0.72 ± 0.08 2 0.71** 0.92 0.92 mI = 0.88 ± 0.17 > mII = 0.74 ± 0.11* = mIII = 0.72 ± 0.10 3 0.99 0.92 0.94 mI = 0.73 ± 0.17 > mII = 0.64 ± 0.11 > mIII = 0.57 ± 0.05** 4 0.99 0.99 0.99 mI = 0.99 ± 0.00 = mII = 0.99 ± 0.02 > mIII = 0.90 ± 0.04 5 0.96 0.80 0.85 mI = 0.87 ± 0.17 > mII = 0.77 ± 0.15 > mIII = 0.60 ± 0.06 6 0.95 0.67** 0.80 mI = 0.80 ± 0.16 > mII = 0.70 ± 0.13 > mIII = 0.59 ± 0.07 7 0.77** 0.89 0.92 mI = 0.80 ± 0.21 = mII = 0.80 ± 0.17 > mIII = 0.72 ± 0.12** 8 0.98 0.88 0.92 mI = 0.76 ± 0.17 > mII = 0.67 ± 0.12 > mIII = 0.63 ± 0.09* 9 0.87 0.92 0.97 mI = 0.90 ± 0.15 = mII = 0.84 ± 0.17 > mIII = 0.78 ± 0.15** 10 0.93 0.97 0.96 mI = 0.93 ± 0.15 > mII = 0.77 ± 0.10 = mIII = 0.84 ± 0.12 11 0.99 0.97 0.97 mI = 0.89 ± 0.20 > mII = 0.87 ± 0.20** = mIII = 0.88 ± 0.14 12 0.95 0.88 0.94 mI = 0.93 ± 0.14 = mII = 0.89 ± 0.16 > mIII = 0.71 ± 0.09 13 — — — mI = 0.50 ± 0.00 = mII = 0.50 ± 0.00 = mIII = 0.52 ± 0.01 14 — — 0.63* mI = 0.50 ± 0.00 < mII = 0.55 ± 0.04** = mIII = 0.60 ± 0.11 15 — — 0.90 mI = 0.50 ± 0.00 < mII = 0.52 ± 0.00 < mIII = 0.57 ± 0.04 16 0.98 0.90 0.92 mI = 0.88 ± 0.18 = mII = 0.84 ± 0.17 > mIII = 0.70 ± 0.14 17 0.98 0.70** 0.84 mI = 0.80 ± 0.16 = mII = 0.80 ± 0.15 = mIII = 0.76 ± 0.11 18 0.97 0.78 0.84 mI = 0.96 ± 0.13 = mII = 0.95 ± 0.13 > mIII = 0.60 ± 0.03 19 0.99 0.56* 0.58* mI = 0.99 ± 0.00 = mII = 0.99 ± 0.03 > mIII = 0.82 ± 0.04 View Large The reconstructions reveal that the investigated characters are extremely homoplastic, as shown by their very low rescaled consistency index (Table 4) and their tendency to shift between states many times independently along the phylogeny (see for example character 16 in Fig. 4). The probabilities of the reconstructions also indicate that three characters (13, 14, and 15) exhibit no phylogenetic signal, as the reconstructions are systematically equivocal at each internal node (Table 3). For six characters, the phylogeny did not provide a better description of trait evolution than the star-like tree. However, significance of the phylogenetic signal, as tested by the comparison of the log-likelihoods returned by a phylogenetic vs star-like tree, was found for only four characters (Table 4). Figure 4 View largeDownload slide Distribution of p(0) values, represented as normal probability distributions, for stem leaf cell width (character 16: 0: > 8 μ m; 1: < 8 μ m) at each of the 14 nodes N, derived from a ML optimization of model parameters for each of the 400 sampled trees (column a) and sampled every 100 of 4,000,000 generations by a MCMC visiting the space of the 400 sampled trees (column b). Figure 4 View largeDownload slide Distribution of p(0) values, represented as normal probability distributions, for stem leaf cell width (character 16: 0: > 8 μ m; 1: < 8 μ m) at each of the 14 nodes N, derived from a ML optimization of model parameters for each of the 400 sampled trees (column a) and sampled every 100 of 4,000,000 generations by a MCMC visiting the space of the 400 sampled trees (column b). Table 4 Homoplasy and phylogenetic content of 19 morphological traits in Brachytheciastrum. RC is the rescaled consistency index. Values in parentheses indicate the range of variation of the RC in the Bayesian sample of trees. Significance of the phylogenetic content is tested by comparing the log-likelihoods returned by the model of morphological evolution applied on the ML tree and on a star-like tree with genetic (κ = 1) or equal branch length (κ = 0). Phylogenetic models provide a significantly better representation of trait evolution when the log-likelihood difference with non-phylogenetic models is > 2 (in bold). −ln L (ML tree) −ln L (star-like tree) Character RC Genetic Equal Genetic Equal 1 (0.000) 0.000 (0.000) 5.54 5.64 4.55 3.97 2 (0.000) 0.000 (0.111) 8.71 9.09 8.86 8.45 3 (0.028) 0.074 (0.167) 14.29 13.31 13.02 13.76 4 (0.000) 1.000 (1.000) 4.92 4.60 6.14 6.14 5 (0.000) 0.100 (0.200) 10.31 11.75 12.00 11.99 6 (0.020) 0.086(0.238) 11.17 12.50 12.61 12.76 7 (0.000) 0.000 (0.040) 9.95 11.31 11.54 11.24 8 (0.012) 0.111 (0.111) 11.82 12.84 13.82 13.76 9 (0.000) 0.067 (0.125) 9.10 10.88 13.37 12.76 10 (0.000) 0.000 (0.000) 5.58 5.91 4.97 6.14 11 (0.074) 0.167 (0.259) 9.30 9.45 12.29 13.85 12 (0.000) 0.111 (0.333) 8.71 8.39 8.88 8.45 13 (0.012) 0.028 (0.074) 15.92 13.84 13.82 13.76 14 (0.012) 0.048 (0.111) 12.59 13.84 13.85 13.84 15 (0.000) 0.000 (0.000) 10.76 9.53 9.07 9.70 16 (0.000) 0.100 (0.200) 10.61 9.56 12.76 12.76 17 (0.000) 0.040 (0.100) 10.59 11.00 11.67 11.99 18 (0.000) 0.000 (1.000) 7.31 5.89 6.14 6.14 19 — 3.94 3.33 3.58 3.58 −ln L (ML tree) −ln L (star-like tree) Character RC Genetic Equal Genetic Equal 1 (0.000) 0.000 (0.000) 5.54 5.64 4.55 3.97 2 (0.000) 0.000 (0.111) 8.71 9.09 8.86 8.45 3 (0.028) 0.074 (0.167) 14.29 13.31 13.02 13.76 4 (0.000) 1.000 (1.000) 4.92 4.60 6.14 6.14 5 (0.000) 0.100 (0.200) 10.31 11.75 12.00 11.99 6 (0.020) 0.086(0.238) 11.17 12.50 12.61 12.76 7 (0.000) 0.000 (0.040) 9.95 11.31 11.54 11.24 8 (0.012) 0.111 (0.111) 11.82 12.84 13.82 13.76 9 (0.000) 0.067 (0.125) 9.10 10.88 13.37 12.76 10 (0.000) 0.000 (0.000) 5.58 5.91 4.97 6.14 11 (0.074) 0.167 (0.259) 9.30 9.45 12.29 13.85 12 (0.000) 0.111 (0.333) 8.71 8.39 8.88 8.45 13 (0.012) 0.028 (0.074) 15.92 13.84 13.82 13.76 14 (0.012) 0.048 (0.111) 12.59 13.84 13.85 13.84 15 (0.000) 0.000 (0.000) 10.76 9.53 9.07 9.70 16 (0.000) 0.100 (0.200) 10.61 9.56 12.76 12.76 17 (0.000) 0.040 (0.100) 10.59 11.00 11.67 11.99 18 (0.000) 0.000 (1.000) 7.31 5.89 6.14 6.14 19 — 3.94 3.33 3.58 3.58 View Large The uncertainty associated with the reconstructions significantly varied depending on the procedure used to compute the model parameters. The probabilities of the most likely character state were indeed globally higher when reconstructions were performed using the ML optimization of rate parameters on the ML tree and lower when sampling model parameters from a MCMC (Table 3). The reconstructions performed on the Bayesian sample of trees using a ML rate optimization on each tree returned intermediate values of uncertainty. Indeed, the probabilities associated with the reconstruction of the most likely state did not significantly differ on average across nodes for nine of the 19 characters when using the ML optimization of rate parameters on the ML tree and the Bayesian sample of trees. By contrast, the probabilities of the most likely state were significantly higher when using the ML optimization of rate on the ML tree than when sampling rates from the MCMC for all but four characters. Within-and among-tree variance of the posterior probabilities of the likelihood, model parameters, and reconstructions of ancestral character states, were partitioned in Table 5. The posterior probabilities of the likelihood, model parameters, and reconstructions of ancestral character states all significantly differed among trees for each character mostly at the 0.001 level, although the proportion of among-tree variance substantially varied. Proportion of among-tree variance was the highest for κ, with average values ranging between 21% and 79%, and the lowest for the rate parameters, with average values ranging between < 1% and 14%, depending on the characters investigated. Table 5 Proportion of among-tree variance of the log-likelihoods lh, model parameters, and probabilities of ancestral character states sampled from their posterior probability distribution. (1) Proportion of among-tree variance of P(0) at internal nodes: average proportion ± SD across the 14 nodes. All P-values of the F-statistics < 0.001 except when otherwise noted: NS, P > 0.05; * P < 0.05; ** P < 0.01. Character lh q01 q10 κ Ancestral character states (1) 1 0.41 0.07 0.02 0.65 0.17 ± 0.09 2 0.24 0.12 0.03 0.61 0.29 ± 0.11 3 0.18 NS 0.02 0.33 0.25 ± 0.10 4 0.29 0.11 0.04 0.62 0.24 ± 0.07 5 0.13 0.02 0.02 0.41 0.24 ± 0.08 6 0.17 0.02 NS 0.43 0.27 ± 0.10 7 0.74 0.13 0.08 0.76 0.48 ± 0.17 8 0.32 0.13 0.08 0.76 0.34 ± 0.13 9 0.47 0.05 0.07 0.77 0.34 ± 0.20 10 0.39 0.09 0.02 0.69 0.23 ± 0.18 11 0.47 0.02 0.05 0.49 0.36 ± 0.22 12 0.29 0.10 0.04 0.45 0.35 ± 0.11 13 0.01** NS NS 0.21 0.15 ± 0.09 14 NS NS NS NS NS 15 0.02 0.04 0.01* 0.26 0.17 ± 0.07 16 0.52 0.10 0.02 0.67 0.42 ± 0.18 17 0.76 0.07 0.13 0.79 0.45 ± 0.18 18 0.10 0.14 0.02 0.26 0.30 ± 0.07 19 0.14 0.09 0.03 0.49 0.15 ± 0.05 Character lh q01 q10 κ Ancestral character states (1) 1 0.41 0.07 0.02 0.65 0.17 ± 0.09 2 0.24 0.12 0.03 0.61 0.29 ± 0.11 3 0.18 NS 0.02 0.33 0.25 ± 0.10 4 0.29 0.11 0.04 0.62 0.24 ± 0.07 5 0.13 0.02 0.02 0.41 0.24 ± 0.08 6 0.17 0.02 NS 0.43 0.27 ± 0.10 7 0.74 0.13 0.08 0.76 0.48 ± 0.17 8 0.32 0.13 0.08 0.76 0.34 ± 0.13 9 0.47 0.05 0.07 0.77 0.34 ± 0.20 10 0.39 0.09 0.02 0.69 0.23 ± 0.18 11 0.47 0.02 0.05 0.49 0.36 ± 0.22 12 0.29 0.10 0.04 0.45 0.35 ± 0.11 13 0.01** NS NS 0.21 0.15 ± 0.09 14 NS NS NS NS NS 15 0.02 0.04 0.01* 0.26 0.17 ± 0.07 16 0.52 0.10 0.02 0.67 0.42 ± 0.18 17 0.76 0.07 0.13 0.79 0.45 ± 0.18 18 0.10 0.14 0.02 0.26 0.30 ± 0.07 19 0.14 0.09 0.03 0.49 0.15 ± 0.05 View Large Discussion Comparison of ML and Bayesian Reconstructions of Ancestral States in Discrete Characters The analysis of comparative data in a phylogenetic context involves a logical suite of steps for selecting an appropriate model of evolution (Blomberg et al., 2003). Using a ‘genetic distance’ model (Oakley et al., 2005) taking branch lengths (or a transformation thereof by means of the scaling parameter κ) to determine the probability of change on the most likely tree resulted in a significant increase in log-likelihood over an equal distance (also termed ‘punctuational’ [Pagel, 1994] or ‘speciational change’ [Mooers et al. 1999]) model for four characters. A restriction of the branches of the most likely tree to identical lengths (κ = 0), i.e., imposing identical probabilities of change along all the branches of the phylogeny, as if transitions were associated to speciation events followed by periods of stasis, could thus not be rejected for the majority of characters by the likelihood ratio test. The lack of influence of branch lengths in describing the evolution of traits is seemingly frequent in binary characters (Pagel, online documentation available at http://www.ams.rdg.ac.uk/zoology/pagel/). However, a significant improvement of fit of the genetic distance model over the equal model was found for 14 of the 19 characters in a proportion of trees from the Bayesian sample ranging between < 1% and 23%, which may indicate that genetic versus equal-distance model selection by likelihood-ratio test tends to vary with phylogenetic uncertainty. The posterior probability distribution of the scaling parameter κ, whose mode ranged between 0.54 ± 0.38 and 1.62 ± 0.97 with wide confidence intervals often encompassing 0 across the investigated traits, further suggests that the fit of an equal or genetic distance model strongly varied from one tree to another, as shown by the proportion of among-tree variance of κ (between 21% and 79% depending on the character investigated). This supports Blomberg et al.'s (2003) view, that the dichotomy between two models is unnecessary. Rather, the MCMC allows one to sample a choice of branch length transformations depending on their posterior probabilities and to apply them on a sample of trees whose branches continuously vary from being equal to one another to varying proportionally to genetic distances. The models that were employed for reconstructing ancestral character states onto the most likely tree included a single transition rate in 18 of the 19 studied characters. Allowing forward and backward transition rates to differ resulted in a significant improvement of fit for the one remaining character. This supports the idea, that small to medium sized trees of 5 to 95 tips rarely offer enough data to allow one to prefer two-rate models when reconstructing ancestor states (Mooers and Schluter, 1999). However, the results suggest that single-rate models advocated by Schluter et al. (1997) should not be systematically used without checking the performance of more complicated models, even with rather small trees. This is especially true as the choice of a single-or two-rate model based upon the result of a likelihood-ratio test strongly varies with phylogenetic uncertainty. Indeed, in 9 of the 19 characters investigated in Brachytheciastrum, evolution was significantly better described by a two-rate model over the single-rate model in a proportion ranging between 1% to 85% of the Bayesian sample of trees. The posterior probability distribution of q01 and q10 further shows that the rate parameters, although overlapping, tend on average to significantly differ from each other both among, but mostly within trees, as shown by their among-tree variance ranging between < 1% and 14% in the investigated characters. Thus, evidence against a hypothesis of identical backward and forward transitions can emerge from the posterior probability distribution of the rate parameters, whereas the single-tree approach would not allow the rejection of that hypothesis (Pagel and Lutzoni, 2002). Recent investigation showed, however, that the inferred differences in rates might be a methodological artifact (Stireman, 2005). Indeed, because the model employed assumes stationary frequencies of 0.5, high transition rates towards the most common state at the tips are often inferred (Nosil and Mooers, 2005). Despite differences in model selection when optimizing model parameters onto a single ML tree, or a Bayesian sample of trees, and when sampling parameters from a MCMC, reconstructions of ancestral character states were strongly correlated across nodes, often at r > 0.9, for all the characters. Reconstructing ancestral character states using the different approaches implemented here thus consistently reflected the same evolutionary patterns. This observation seems to be independent from the strength of the phylogenetic signal present in the data. Indeed, we also found high correlation coefficients among probabilities of ancestral states at a node derived from the three different approaches, when analyzing a set of eight morphological characters displaying a strong phylogenetic signal (as shown by both strong departures from 0.5 at internal nodes and the highly significant rejection of a star-like tree as an appropriate representation of trait evolution) in the moss genus Timmia (data not shown, available from the authors on request). Strong discrepancies among reconstruction methods were only observed at the root in the case of character states with unique or rare occurrences when single-versus two-rate models were selected based upon the results of a likelihood-ratio test. As already observed by Schluter et al. (1997), the unique or rare state at the tips of short branches will often reappear at the root, accompanied by a high transition rate away from this state when two-rate models are employed, as if the state was a relict whose rarity among contemporary species was the result of a high transition rate away from the rare state. The major difference among the investigated reconstruction methods resides in the uncertainty associated with ancestral character state reconstructions. Reconstructing ancestral states onto a single, most likely tree only takes mapping uncertainty into account. By contrast, reconstructions on a Bayesian sample of trees allowed the importance of phylogenetic uncertainty to be considered in the confidence that one can have in the reconstructions and systematically returned on average significantly lower confidence levels. An attractive feature of the Bayesian approach of ancestral state reconstruction is that it does not only consider the range of possible reconstructions among trees, but also the range of possible reconstructions on the same tree depending on a range of parameters. This was especially important with the investigated data set as, although among-tree differences accounted, on average across nodes, for 15% to 48% of the total variance of the reconstruction depending on the character studied, most of the variance was found within trees due to variation in the rate parameter estimates. The Bayesian approach of ancestral character state reconstruction thus offers 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. Consequences for Morphological Evolution in Brachytheciastrum Phylogenetic signal was found in 16 of the 19 investigated characters, as shown by the departure of ancestral state probabilities from 0.5. This suggests that the probabilities of ancestral states at a node depend on their probabilities at the previous node, making the data appropriate for investigating differences in ancestral states reconstructions by different methods. However, although the phylogenetic model offered a better representation of trait evolution than the nonphylogenetic one for 13 characters, significance of the improvement in log-likelihood resulting from the use of the phylogenetic model was significant for only four characters. For the other ones, phylogenetic dependence in the data could neither be significantly accepted or rejected. As has been shown for continuous characters (Freckleton et al., 2002), this equivocal result most likely reflects a lack of power of the likelihood-ratio test due to the small size of the phylogeny. However, the lack of significance in the presence of phylogenetic signal, together with the sometimes weak average departure of ancestral state probabilities from 0.5 across nodes, point to an overall weak signal for most characters. Due to the weakness of the signal in the data, but also owing to the high level of homoplasy in morphological characters (see below), a phylogenetic hypothesis inferred from all the morphological characters using the ML model of Lewis (2001) in a Bayesian framework proved to be completely unresolved (data not shown). Previous attempts at resolving moss phylogenies using the MP criterion on morphological traits also failed to converge to well-resolved and supported hypotheses (see Buck et al. [2000] for a review). The results thus suggest that the possibilities to recover the evolutionary history of mosses based on the morphology of extant species are extremely limited. The utility of morphology for phylogeny reconstruction has recently been questioned on several grounds (Scotland et al. 2003; but see Jenner, 2004; Wiens 2004; Smith and Turner, 2005). The problem is especially acute in mosses. Indeed, as compared for example to vertebrates and flowering plants, for which classification was successfully tested with phylogenetic analyses of morphology (e.g., Kress et al., 2001; Jenner, 2004; Wiens, 2004) and for which it is argued, that molecular and morphological data sets yield similar numbers of relevant characters (Lee, 2004), mosses exhibit fairly simple morphologies, whose transformation may be rather cryptic, and hence offer fewer characters to infer relationships. Relying entirely on a model incorporating molecular branch lengths may be misleading in some instances (Cunningham, 1999), most notably when adaptive radiations result in a great deal of evolutionary changes along short internal branches, so that character changes are reconstructed as having occurred considerably after the actual radiation took place (Lewis, 2001). Due to the extremely limited possibilities of inferring morphology-based phylogenies in mosses, the study of morphological evolution in such organisms must, however, rest on the estimation of molecular phylogenies. In this case, morphology receives a limited role, which chiefly consists, as advocated by Scotland et al. (2003), of studying morphological characters in the context of a molecular phylogeny. The ITS has been one of the most widely exploited source of molecular variation at the species level but there has been an increasing concern about their reliability for phylogenetic reconstruction, especially due to the existence of paralogs and pseudogenes (Alvarez and Wendel, 2003; Bailey et al., 2003; Razafimandimbison et al., 2004). The 5.8S gene was almost invariant among taxa of the studied species complex, with a substitution rate 10,000 times lower than that expected in the nearby spacers. The presence of pseudogenes in the present data is therefore very unlikely, as the evolutionary rates of pseudogenes are expected to increase dramatically and reach values similar to those of other noncoding regions (Razafimandimbison et al., 2004). The occurrence of multiple paralogs in the PCR product usually results in conflicting base calls during sequencing (see, e.g., Forest and Bruneau [2000]; Vanderpoorten et al. [2004]). No such conflict was observed at any position in ITS sequences of Brachytheciastrum. A scenario, where different paralogous copies would have been randomly lost in the course of the evolutionary history of the species, so that extant species possess a single copy that is not homologous to that of the other species, is also possible, but would require a number of rearrangements that may not be very likely at low taxonomic level. The observed patterns of molecular variation in extant species may also be the result of hybridization or retention of polymorphisms that appeared before speciation, but the congruent phylogenetic signal in the nuclear and chloroplast sequence data does not support these hypotheses. The proposed phylogeny thus seems appropriate for reconstructing patterns of morphological evolution, at least at the level of well-supported nodes. The reconstructions reflected a strong parallel evolution in character transformations. Indeed, the average rescaled consistency index (RC) was 0.107, with a single character exhibiting an RC of 1, whereas all of the other RCs were below 0.167 and reached 0 in six characters. Such frequent shifts in character states have usually been interpreted as evidence for high transition rates (Cunningham, 1999; den Bakker et al., 2004; Rüber et al., 2004). Fast rates of morphological evolution have previously been documented in mosses (Vanderpoorten et al., 2002; Vanderpoorten and Jacquemart, 2004) and may account for the weakness of the phylogenetic signal displayed by most characters. Everything happens as if historical signal had been erased during a period of radiation (Mooers et al., 1999; Oakley et al., 2005), which may coincide with the rapid diversification experienced by the Hypnales early in their relatively recent history (Shaw et al., 2003a). This problem may be compounded by subsequent rampant reduction, resulting in the loss of symplesiomorphies (Goffinet et al., 2004). As a consequence, it is not surprising that the characters used in the taxonomy of Brachytheciastrum have led to the recognition of poly-or paraphyletic species. Conversely, B. velutinum and B. olympicum, which have usually been synomized (Ignatov and Huttunen, 2002), are here resolved as two unrelated monophyletic lineages. The present reconstructions of ancestral character states, however, failed to identify any synapomorphic transition for these species. This suggests that the key characters that have been used for species description are poor indicators of phylogenetic relationships and hence should be viewed as poor taxonomic characters. In Brachytheciastrum, as in many pleurocarpous moss genera, species have been defined based on gametophytic features that have recurrently undergone parallel evolution. Traditional species circumscriptions emphasize particularly the global habit and shape of the leaf (e.g., the orientation, density, and shape of stem leaves [Fig. 5a, b]). Brachytheciastrum trachypodium, for example, differs from B. velutinum by its straight leaves that are scarcely tapered before mid-leaf, whereas those of B. velutinum are often falcate and taper from just above the auricles (Corley, 1990). The present analyses clearly suggest that variation in leaf shape and orientation has repeatedly occurred both among and within the boundaries of traditionally recognized species. The recurrent homoplastic transitions of states found in those mosses explain why Brachytheciastrum itself lacks any morphological synapomorphy (Vanderpoorten et al., 2005). As a consequence, species previously included within the genus based on phenetic grounds, such as B. appleyardiae or B. bolanderi, were shown to belong to other genera sometimes included within different sub-families of the highly diverse family Brachytheciaceae (Blockeel et al., 2005; Vanderpoorten et al., 2005). Figure 5 View largeDownload slide Illustration of characters that have traditionally been used in the taxonomy of Brachytheciastrum. (a) Stem leaf shape (character 8): abruptly tapered from the base in B. bellicum (1),B. trachypodium (2), and B. velutinum (4) or progressively acuminate from the middle in B. collinum (3). (b) Leaves dense (character 3) and straight (character 6) (1: B. collinum) or loose and falcate (2: B. velutinum) (reproduced, with permission, from Corley [1990]; Buck et al. [2001]; and Ignatov and Ignatova [2004]). Figure 5 View largeDownload slide Illustration of characters that have traditionally been used in the taxonomy of Brachytheciastrum. (a) Stem leaf shape (character 8): abruptly tapered from the base in B. bellicum (1),B. trachypodium (2), and B. velutinum (4) or progressively acuminate from the middle in B. collinum (3). (b) Leaves dense (character 3) and straight (character 6) (1: B. collinum) or loose and falcate (2: B. velutinum) (reproduced, with permission, from Corley [1990]; Buck et al. [2001]; and Ignatov and Ignatova [2004]). The focus on key characters with a low phylogenetic component and high transition rates may explain why moss taxonomy, wherein (morpho)species polyphyly is the rule rather than the exception (Shaw, 2000; Shaw and Allen, 2000; Stech and Dohrmann, 2004; Vanderpoorten et al., 2004; Stech and Wagner, 2005; Werner et al., 2005a, 2005b), is particularly unstable and vulnerable to phylogenetic testing (see Goffinet and Buck [2004] for a review). Ranker et al. (2004) similarly found that the characters that have been traditionally used for taxonomy in grammitid ferns are among the most homoplastic, whereas other, potentially informative features have been regarded as having no taxonomic value or have been ignored. In mosses unfortunately, currently investigated morphological characters often fail to provide synapomorphies (Vanderpoorten et al., 2002, 2005; Goffinet et al., 2004), calling for further morphological investigations. Indeed, as opposed to well-worked groups of organisms such as vertebrates and flowering plants (Scotland et al., 2003; but see Wiens, 2004 and Lee, 2006), phylogenetically informative variation in morphology may not have already been fully scrutinized and analyzed in mosses. Morphogenetic and spermatogenetic characters in particular offer a promising tool for interpreting and reinforcing evolutionary scenarios derived from the analyses of molecular data (Renzaglia et al., 2000; Duckett et al., 2004; Pressel et al., 2005). The main problem is that the traditional phenetic species concept based on examination of a few key characters may not be appropriate in taxa with reduced morphologies such as mosses. Specifically, cryptic speciation, wherein genetic differentiation extends beyond the morphospecies level, has been increasingly documented (Shaw, 2001; McDaniel and Shaw, 2003; Shaw et al., 2003b; Feldberg et al., 2004; Werner and Guerra, 2004). Although one interpretation of our phylogeny would be that Brachytheciastrum consists of two species, namely B. olympicum and a set of coalescing populations belonging to B. velutinum, we refrain to make any formal taxonomic change as a redefinition of the species concept in mosses is, obviously, urgently needed. Acknowledgements Many thanks are due to Paul Lewis, Todd Oakley, and two anonymous reviewers for their very constructive comments and to Andrew Meade and Mark Pagel for their advices and for providing us with an unreleased version of Bayes Multistate. Thanks also to Tom Blockeel, Bill Buck, Lars Hedenäs, Misha Ignatov, Rosa Maria Ros, Cecilia Sergio, and André Sotiaux for the loan of specimens; to Norm Wickett for assistance in the lab; and to Jessica Budke for sharing the sequences used in the second data set. Misha Ignatov kindly provided us with original observations used in the morphological data matrix. Financial support was provided by the National Science Foundation through grant DEB-0089633 to BG and through the Belgian National Funds for Scientific Research (FNRS) to AV. References Alvarez I., Wendel J. F.. Ribosomal ITS sequences and plant phylogenetic inference, Mol. Phylogenet. Evol. , 2003, vol. 29 (pg. 417- 434) Google Scholar CrossRef Search ADS PubMed Bailey C. 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Branch leaves all-sided (terete, julaceous) (0) or complanate (1) 6. Stem leaves straight (0) or falcate-secund (including slightly so) (1) 7. Acumen hair-like (2 cells wide > 150 μ m) absent (0) or present (1) 8. Stem leaves progressively acuminate (0) or abruptly tapered from the base (1), as measured by the level where the half-width of the leaf is reached 9. Leaf width > 0.4 mm (0) or < 0.4 mm (1) 10. Stem leaf margin serrulate to serrate (0) or serrulate to entire (1) 11. Costa ending (1) or not (0) in a spine in stem leaves 12. Costa serrate in stem leaves (1) or not (0) 13. Costa serrate in branch leaves (1) or not (0) 14. Prorae absent (0) or present (1) at the back of branch leaves 15. Cells shorter (0) or longer (1) than 100 μ m 16. Cells > 8 μ m (0) or < 8 μ m (1) wide 17. Length to width cell ratio < 10:1 (0) or > 10:1 (1) 18. Large cells at leaf insertion forming a sharply curving group (1) or not (0) 19. Leaves plicate (1) or not (0) 1. Pseudoparaphyllia triangular (0) or acuminate (1) 2. Axillary hair upper cell < 1/2 of hair length (0) or > 1/2 of hair length (1) 3. Leaves dense (stem not seen between leaves) (0) or loose (1) 4. Leaves not straight standing (0) or straight standing (1) 5. Branch leaves all-sided (terete, julaceous) (0) or complanate (1) 6. Stem leaves straight (0) or falcate-secund (including slightly so) (1) 7. Acumen hair-like (2 cells wide > 150 μ m) absent (0) or present (1) 8. Stem leaves progressively acuminate (0) or abruptly tapered from the base (1), as measured by the level where the half-width of the leaf is reached 9. Leaf width > 0.4 mm (0) or < 0.4 mm (1) 10. Stem leaf margin serrulate to serrate (0) or serrulate to entire (1) 11. Costa ending (1) or not (0) in a spine in stem leaves 12. Costa serrate in stem leaves (1) or not (0) 13. Costa serrate in branch leaves (1) or not (0) 14. Prorae absent (0) or present (1) at the back of branch leaves 15. Cells shorter (0) or longer (1) than 100 μ m 16. Cells > 8 μ m (0) or < 8 μ m (1) wide 17. Length to width cell ratio < 10:1 (0) or > 10:1 (1) 18. Large cells at leaf insertion forming a sharply curving group (1) or not (0) 19. Leaves plicate (1) or not (0) View Large Appendix 2 Matrix of morphological characters defined in Appendix 1 scored for all the specimens. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 bellicum 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 collinum a 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 collinum b 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 collinum c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 collinum d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 collinum e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 dieckei a 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 dieckei b 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 dieckei c 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 dieckei d 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 fendleri 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 leibergii 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 olympicum a 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 olympicum b 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 olympicum c 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 trachypodium a 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 trachypodium b 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 trachypodium c 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 velutinum a 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 velutinum b 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 velutinum c 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 bellicum 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 collinum a 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 collinum b 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 collinum c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 collinum d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 collinum e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 dieckei a 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 dieckei b 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 dieckei c 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 dieckei d 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 fendleri 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 leibergii 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 olympicum a 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 olympicum b 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 olympicum c 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 trachypodium a 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 trachypodium b 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 trachypodium c 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 velutinum a 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 velutinum b 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 velutinum c 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 View Large © 2006 Society of Systematic Biologists

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Systematic Biology – Oxford University Press

Published: Dec 1, 2006

Keywords: Keywords Ancestral character-state reconstruction Bayesian inference comparative methods moss uncertainty

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Mapping Uncertainty and Phylogenetic Uncertainty in Ancestral Character State Reconstruction: An Example in the Moss Genus Brachytheciastrum

Mapping Uncertainty and Phylogenetic Uncertainty in Ancestral Character State Reconstruction: An Example in the Moss Genus Brachytheciastrum

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Mapping Uncertainty and Phylogenetic Uncertainty in Ancestral Character State Reconstruction: An Example in the Moss Genus Brachytheciastrum

Mapping Uncertainty and Phylogenetic Uncertainty in Ancestral Character State Reconstruction: An Example in the Moss Genus Brachytheciastrum

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