A cladistic reconstruction of the ancestral mite harvestman (Arachnida, Opiliones, Cyphophthalmi): portrait of a Paleozoic detritivore

Part 1: Linear parsimony and averaging

We first selected two distinct terminal sets that each: (i) contained representative animals from all the major lineages of the Cyphophthalmi (the families Stylocellidae, Pettalidae, Sironidae, Neogoveidae and Troglosironidae), and (ii) had been used previously to generate phylogenetic hypotheses for Cyphophthalmi. The first of these terminal sets (PET) includes 50 cyphopthalmid terminals predominantly representing the family Pettalidae (de Bivort and Giribet, 2010). The second terminal set (STY) contains 136 cyphophthalmid terminals, mostly from the family Stylocellidae, and 21 opilionid outgroup taxa (Clouse et al., 2009; Clouse and Giribet, 2010). These particular terminal sets were chosen because each had been used to generate distinct (but plausible) phylogenetic hypotheses from three different character sets each (Fig. 1a). Specifically, the PET terminals were previously analysed using: (i) 62 discrete morphological characters; (ii) 78 continuous morphological characters; and (iii) these two data sets in combination (de Bivort and Giribet, 2010; figs 10A,B and 12A (1 : 1, EW), respectively). The STY terminals were previously analysed using: (i) 6571 molecular characters (Clouse and Giribet, 2010; fig. 3); (ii) 51 continuous morphological characters (Clouse et al., 2009; figs 5 and 6); and (iii) these two data sets in combination (Clouse et al., 2009; figs 5 and 6). We refer to the topologies generated by these analyses as PET-D, PET-C, PET-DC, STY-M, STY-C and STY-MC, respectively. The continuous data in both PET and STY consist of raw measurements and shape descriptors (typically ratios of raw measurements), derived from male specimens, analysed for independence, and subjected to collapse of dependent characters (de Bivort et al., 2010).

We evaluated four reconstruction methodologies against each of the six terminal/topology combinations, as follows.

In order to evaluate the “robustness” of methodologies (to variation in terminal set and topology) and “consistency” of particular reconstructions (across methods), we used 18 continuous morphological characters available in both the PET and STY data sets (Table 1). These were identified by first finding any characters in both the STY-C and PET-C continuous data sets that were defined in precisely the same way. Then additional characters were defined using simple mathematical operations on pre-existing STY-C characters so that they would be directly comparable with PET-C characters. The raw 18 characters from both data sets were combined and z-score normalized so that they would be comparable between the STY and PET data sets, and each contributes equally to comparison metrics such as the correlation or Euclidean distance between character reconstructions. In this form, the 18 characters were used to reconstruct their ancestral states on each of the six terminal/topology combinations, using each of the four reconstruction methods. These comparisons evaluate the robustness and consistency of the reconstruction. Previously, the 18 characters were all found to be phylogenetically informative (Clouse et al., 2009; de Bivort et al., 2010); however, basically all continuous characters show some degree of homoplasy because of the flexibility in the states they can assume and their precision.

Trees in the PET terminal set did not contain non-cyphophthalmid outgroups, and were re-rooted manually so that Stylocellidae was sister to the remaining Cyphophthalmi as per Boyer et al. (2007). Reconstructed ancestral characters were extracted from TNT using a custom script. The calculation of nested averaging reconstructions was performed in MATLAB using custom scripts that read parenthetical tree files. Sister group averaging and global averaging methods were performed in Microsoft Excel.

For analyses that could not accommodate a range in reconstructed ancestral character values (such as Euclidean distances and correlation coefficients), we replaced the reconstructed range with its average. P values were assigned to Euclidean distances between alternative reconstructions (Fig. 1b) by a bootstrapping method because we could not identify a statistical distribution known to generically characterize Euclidean distances. Specifically, we assumed that the (16) different reconstructions of character (from the different methods) reflect a distribution of its reconstructed value. By sampling those values independently for each of the 18 characters, we generated randomized “reconstructions” that removed any mutual information between reconstructed characters introduced by each method. Pairs of random reconstructions were generated 10⁵ times, and the Euclidean distance between each pair recorded. The 95th percentile of these values was used as the P = 0.05 cutoff. This approximates the alpha value because bootstrap resampling provides an unbiased estimate of parameters of an unknown distribution, in this case, its 95th percentile.

In order to visualize the respective distances between all pairs of reconstructions simultaneously, we used the data visualization technique multidimensional scaling (Cox and Cox, 2001) to place the reconstructions in a two-dimensional (rather than 18-dimensional) space. This was performed in MATLAB using built-in functions and default non-metric scaling. This option preserves the ordering of the pairwise distances between reconstructions—that is, if one pair of reconstructions is farther apart than another pair, that relationship will also hold in the 2D visualization. The error introduced by this monotonicity requirement was small.

Part 2: Broader reconstruction comparisons

We measured the 18 characters common to PET-C and STY-C for five species in all three non-cyphophthalmid suborders of Opiliones: Eupnoi, Dyspnoi, and Laniatores. These groups lack ozophores and sometimes coxae IV meeting at the midline, so these new character sets were missing some values. This expanded Opiliones continuous data set (OPI-C) was optimized on a tree reflecting the most recent molecular phylogenetic evidence (Giribet et al., 2012), using a wide variety of methodologies, including linear parsimony, squared-change parsimony, averaging, maximum likelihood, and Bayesian. This tree was generated in the program BEAST ver. 1.6.1 (Drummond et al., 2006; Drummond and Rambaut, 2007), and, having been dated, was ultrametric and had branch lengths; this was different from topologies used in Part 1, which lacked branch lengths. The influence of branch lengths for the tree in Part 2 was evaluated by comparing reconstructions using the original tree with those when the branch lengths were all changed to 1. In a landmark version of OPI-C, we retained the original x- and y-coordinates used to calculate the 18 character values and optimized them directly (Catalano et al., 2010) in TNT (Goloboff and Catalano, 2010), using a method that treats the distance between inferred ancestral landmarks like additive characters under a parsimony criterion. The reconstructed landmarks were then used to re-derive the 18 continuous characters for comparison.

We generated ancestral reconstructions with and without branch lengths and outgroups in the programs Mesquite ver. 2.74 (Maddison and Maddison, 2011), BayesTraits (beta version, available from the developers upon request), and the APE phylogenetic analysis package (Paradis et al., 2004) in the R software environment (R Development Core Team 2011). We also performed internal checks to see if different optimizations that are equivalent in theory did give the same ancestral reconstructions, such as comparing squared-change parsimony reconstructions unweighted by branch lengths with squared-change reconstructions weighted by branch lengths but on a tree with all branch lengths set to zero; such tests did result in identical reconstructions.

The Bayesian reconstruction in BayesTraits beta requires an initial Markov Chain Monte Carlo (MCMC) run to generate model parameters, then a final MCMC run for the reconstructions. A two-character test data set did settle on reasonable character reconstructions, but our full data set showed no evidence of settling, even after 55 million generations on one run and 40 million in another. Thus our reconstruction values are the average of 800 000 generations, sampled every 100, after a 250 000-generation burn-in. When testing reconstructions on trees with no outgroups (which required an MRCA at the base of the tree) or using the directional model, reconstructions settled on zeros (i.e. simple global averages given our normalized characters), so these functions appear not to be fully implemented. Because we used normalized data, the constant parameter “datadev” (the Monte Carlo step size, which we kept at the program’s default setting) had the same effect on all characters, regardless of their original magnitude. For all other methodologies, default parameters and settings were used.

Once we identified the methodology that yielded the most robust and consistent reconstructions, we reconstructed all the continuous characters in the original continuous data sets on their corresponding total evidence trees to generate the final set of reconstructed characters. PIPC illustrations were constructed by hand in Adobe Illustrator, beginning with a generic outline of a cyphophthalmid and sequentially imposing the constraints of each reconstructed character, at each step smoothly warping the outline to accommodate the new constraint. Slight contradictions in the position of spatially constrained morphological features (for example, arising from it being possible to determine a constrained position using a sequence of reconstructed characters anterior to posterior as well as posterior to anterior) were resolved if possible by preferring the position constrained most directly (i.e. involving the fewest characters), and then by averaging the alternative positions. Ranges in reconstructed values were replaced with their average for purposes of the illustration.

Part 1: Linear parsimony and averaging

The pairwise Euclidean distances between the reconstructions of each of the 24 terminal/topology/methodology combinations are shown in Fig. 1b. The Euclidean distance between two reconstructions equaled 0 if the reconstructions were identical, and has units of standard deviations, since the characters were z-score normalized. We found little agreement between global averaging and the other three reconstruction methods in Part 1. Reconstructions based on the PET terminal set were in broad agreement, whether the reconstruction method was linear parsimony, nested averaging, or sister group averaging. Only one pair of PET reconstructions (PET-DC and PET-D under linear parsimony) was not more similar than expected by chance alone (P < 0.05, uncorrected for multiple comparisons; see Methods).

This pattern of broad agreement was not observed with the STY trees—suggesting that the robustness of reconstructions to topological variation depends on the terminal set being analysed. However, agreement among STY reconstructions was found in a number of specific instances. For example, STY-M under linear parsimony agreed significantly with STY-M under nested averaging and sister group averaging, as well as STY-MC under sister group averaging. Of 45 non-trivial comparisons made between STY reconstructions, nine were found to be significantly similar. It should be noted that global averaging is independent of topology, and sister group averaging is topology-independent among trees that preserve sister group composition. Thus both of these methods yielded identical reconstructions for each of the three topologies associated with the PET terminal set, and global averaging yielded identical reconstructions for all STY trees. In some cases, some STY reconstructions were surprisingly far from one another (e.g. STY-C and STY-M under linear parsimony). No pairs of STY and PET reconstructions were found to be closer than expected by chance. However (particularly because of the frequent agreement between PET reconstructions) far more agreement between reconstructions was generally found than would be expected by chance (41 of 153 non-trivial comparisons were significant with P < 0.05).

Visualizing the differences between all reconstructions in two dimensions (Fig. 2a) reveals that, while there was little significant pairwise agreement between the STY reconstructions, they do “cluster” together more with each other than with the PET reconstructions, with the exception of the linear parsimony reconstruction of STY-MC. Reconstructions based on STY-C tree under any method other than global averaging exhibit moderate similarity to reconstructions based on any of the PET trees under any method other than global averaging. Considering the topology of the various trees, we observe that all the trees which were rooted with Stylocellidae as sister to the remaining Cyphophthalmi (STY-C and all PET trees) have fairly close reconstructions. STY-MC and STY-M have identical topologies at the family level, except for their resolution at the root, but the STY-M reconstructions are closer to the STY-C reconstructions than they are to those of STY-MC. Moreover, the STY-MC and STY-M reconstructions are farther apart than any other pair of reconstructions, suggesting that reconstructions are more sensitive to the degree of resolution at the optimized node than topology of groups descending from it.

To the extent that the averaging methods (nested, sister group, and global averaging) are insensitive to tree topology, their estimates of ancestral characters will trend toward the mean value of each character across the represented terminals (that is, regress toward the mean). In the case of z-score normalized characters, this mean value is encoded as 0. Thus observing many or all reconstructed ancestral characters to have magnitudes near zero is evidence of this pitfall of averaging methods. We tested this by calculating the average magnitude of the 18 reconstructed character values, for each terminal/topology and reconstruction method (Fig. 2b). Characters reconstructed using global averaging had a comparatively low magnitude, and both linear parsimony and nested averaging tended to produce greater magnitudes, particularly in the STY reconstructions. Reconstructions performed under sister group averaging yielded low-magnitude reconstructions except in STY-MC, which yielded higher magnitude reconstructions because of the presence of several single-species branches emanating from its unresolved root. Note that the reconstructed character values using global averaging (and the standard deviation across them) are not strictly 0, despite the characters being normalized and the method being a simple average. This is because, although global averaging was done separately on PET-C and STY-C, the two data sets were normalized beforehand together.

While the Euclidean distance between two reconstructions (1, 2) reveals their overall similarity, it can potentially obscure agreement in the trends of reconstructed characters, if not their magnitudes. Therefore we looked at the pairwise correlation coefficients between the PET and STY reconstructions to see if agreement could be found in the trends of the reconstructions (Fig. 2c). Indeed, the reconstruction generated using linear parsimony on the PET-DC and STY-MC (Fig. 2d) was highly significant (r = 0.62, P = 0.0043). Since we had originally observed less agreement among STY reconstructions than among PET reconstructions (Fig. 1b), it was not surprising to observe that the correlation between particular STY and PET reconstructions was dependent primarily on which STY reconstruction was being considered. The exception to this was the PET global averaging reconstruction, which was positively correlated with a number of STY reconstructions, despite it being considerably far from them as measured by Euclidean distance (Fig. 2a). The most negative correlation was found between STY and PET under global averaging, but this is an artifact of both character sets being normalized together, while undergoing global averaging separately.

Since the Euclidean distance between the linear parsimony reconstructions of the STY-MC and PET-DC is not especially great (Fig. 2a), and they strongly agree about the trends in ancestral characters (Fig. 2c,d) we concluded that these topologies and this methodology could ultimately form the basis of our visualizations of PIPC. However, before presenting these reconstructions as definitive, we needed to confirm several points. First, the original PET-C and STY-C data sets did not include character values for any outgroup species, thus this information was unavailable during reconstruction, even if the tree being used for reconstruction itself contained outgroups. To what extent does this distort the reconstruction? Second, we have focused on linear parsimony in contrast to averaging as a reconstruction method. Perhaps philosophical alternatives, such as maximum likelihood and Bayesian reconstruction, are definitively preferable. Lastly, such methods allow us to incorporate branch length information. Does that greatly affect reconstructed character values?

Part 2: Broader reconstruction comparisons

To address these questions, we generated a new data set (OPI-C), with measurements of the 18 characters common to PET-C and STY-C for five outgroup species in suborders of Opiliones other than Cyphophthalmi (Gruber, 1978; Tourinho, 2004; Schwendinger, 2006; Bauer and Prieto, 2009; Sharma and Giribet, 2011). We optimized OPI-C on a tree derived from the most recent comprehensive molecular phylogeny of the Cyphophthalmi (Giribet et al., 2012), which included all suborders of Opiliones, all families of Cyphophthalmi, representatives of Pettalidae and Stylocellidae in similar proportions, and branch lengths (Fig. 2e). We also produced a landmark version of OPI-C in which the x- and y-coordinates of all features on the animals (required to calculate the 18 character values) were retained as such for landmark analysis in TNT.

OPI-C was reconstructed on this tree using many different methods: averaging, linear parsimony, landmark optimization, squared-change parsimony, maximum likelihood (under Brownian motion, supported by an analysis of evolutionary model selection described below, and restricted likelihood models), independent contrasts, and Bayesian. The pairwise correlation coefficients between these methods are presented in Fig. 2f. We found that the primary determinant of whether two reconstructions were in agreement was whether they utilized outgroup information. Important exceptions to this pattern were nested averaging (which performs only down-pass calculations, thereby ignoring outgroup information) and linear parsimony implemented in TNT.

Reconstructions generated using linear parsimony in TNT and nested averaging were in the broadest agreement with other reconstructions. They correlated significantly with the reconstructions of essentially all other methods, with the exception of the maximum likelihood methods that ignored outgroups but utilized branch lengths. The only other method that displayed similarly broad agreement was landmark optimization in TNT, although this approach (which uses outgroup information) was not significantly correlated with three of the maximum likelihood and Bayesian methods that also used outgroup information. Sister group averaging exhibited the least agreement. The inclusion or exclusion of branch length information increased the correlation between differing methods only slightly. We expected (Felsenstein, 1985), and observed, that independent contrasts and squared-change parsimony weighted by branch lengths and lacking outgroup data gave identical results.

We tested our 18 overlapping morphometric characters for the best-fit model of evolution on a tree with outgroups and branch lengths using the GEIGER package (Harmon et al., 2008) in R (R Development Core Team, 2011). Each character was fitted to the evolutionary model independently of the other characters. Using the “fitContinuous” command, we generated two comparisons for each character: differences in the log-likelihood between the fit of each model and Brownian motion, and the Akaike information criterion (AIC) measure of information content. The evolutionary models tested included Pagel’s (1999) lambda, kappa, and delta models, Brownian motion, Ornstein–Uhlenbeck (which is Brownian motion with stabilizing selection), and “white noise”, which models a lack of phylogenetic signal. Missing data were replaced by the average of other values for the character when needed.

The log-likelihoods of the fits of evolutionary models for the majority of our 18 characters were not significantly different from the Brownian motion model. Only seven characters had a significantly different likelihood of fit by a model other than Brownian motion, and for all of these the fit of the alternate model was more likely. Using AIC, the same seven characters plus an additional one were better explained by models other than Brownian motion. Three characters were best fit by the white noise model, but for all other characters the white noise model was significantly worse in both the lnL and AIC comparisons.

Maximum likelihood methods generate 95% confidence intervals on reconstructed characters, and linear parsimony in TNT generates ranges for reconstructed characters. Both of these indicate the degree of uncertainty in the reconstruction, and we found them to be of the same order of magnitude—respectively 36% and 12% on average across characters. There was no consistent relationship across methods between the inclusion or exclusion of outgroups and the size of the confidence intervals. For example, the addition of outgroup data to a linear parsimony analysis broadened the range of the reconstruction of body size (character 1) from 2.7% to 25%, but reduced the 95% confidence interval of that character under a Brownian motion model from 50% to 42%.

As an indication of the predisposition of a reconstruction method simply to average character values across taxa, we again calculated the average magnitude of our normalized characters in each reconstruction (Fig. 2f, right) of OPI-C. Sister group averaging and maximum likelihood under Brownian motion (using outgroup data and branch lengths) produced the smallest-magnitude reconstructed characters, i.e. those closest to an average. Landmark optimization produced reconstructed characters with the greatest magnitude, followed by linear parsimony using outgroup data and linear parsimony not using outgroup data. All other methods produced reconstructions with intermediate magnitude characters.

Only one method differed from the others by analysing characters under spatial constraints: landmark optimization, which acts directly on the x- and y-coordinates of the animal features used to measure the continuous characters. This method has the potential advantage of bypassing distortions in the independent optimization of characters that are respectively constrained. For example, optimization could be performed independently on three non-independent characters encoding a numerator, a denominator, and their ratio. We tested whether this distortion was occurring in the linear parsimony reconstructions as follows. The original PET-C and STY-C character sets contain many characters that are the ratio of two raw measurements of the animals. If their reconstructions are to be believed, then the ratio of two reconstructed raw characters should correlate with the reconstructed value of the corresponding ratio character. We evaluated this using the 59 ratio characters present in the PET-C character set (Fig. 2g) and found strong agreement (r = 0.61, P < 10⁻⁶). The two characters falling farthest from the trend line encode two measurements of the width of the ozophores (cone-like scent organs) relative to the body width.

From the comparison of these methods, we conclude the following about the reconstructions generated using linear parsimony in TNT:

Using linear parsimony in TNT, we reconstructed the ancestral values of the original 78 PET-C and 51 STY-C continuous morphological characters on the PET-DC and STY-MC trees, respectively. These values were then un-normalized to yield raw character values that provided constraints for two illustrations of PIPC (Fig. 3), one for each character set. Not surprisingly, given that we chose the reconstruction method that was the most consistent, there is broad agreement in the morphology of PIPC illustrations generated using the PET-C and STY-C characters. Both visualizations reveal small Cyphophthalmi (total body length excluding chelicers 2.5 and 2.9 mm, respectively) with a wide prosoma, entire posterior tergites (i.e. lacking the bilobed posterior found as a sexual dimorphism in the males of many species), lateral ozophores raised from the edge of the carapace (type 2 of Juberthie, 1970), coxae of legs III meeting at the midline, robust second cheliceral articles widest close to their proximal end, and an anal plate in a posterior position. The reconstructions differ qualitatively in a few ways: the ornamentation on the second cheliceral article, the midline modification of the anal plate, and the distance between the lateral margins of the opisthosomal sternites and the lateral margins of the body.

Characters present in PET-C but not in STY-C imply that PIPC had first cheliceral articles tightly articulated with the dorsal scutum and bearing a small dorsal crest, a broad sternal plate, caudal setae (scopulae) of typical length, and thickness typical of most species. Characters present in STY-C but not in PET-C imply that PIPC had either lens-less eyes or no eyes, a larger than average anal gland opening, a bilobed tergite IX, an oval gonostome, short tarsi on the first and fourth legs, with the latter bearing a small adenostyle (a secretory gland of unknown function found on the tarsus of walking leg IV in males of all species,). Notably, the smaller of the two PIPC representations (based on the STY-C data set, Fig. 3b) is based on a data set containing the larger animals (stylocellids, which are on average larger than pettalids). This provides further evidence that, unlike the topology-independent averaging methods, linear parsimony does not simply report the mean character values across terminals. Moreover, the overall appearance of the PIPC image based on the PET-C data set is more like a primitive stylocellid (Giribet, 2002,Clouse et al., 2009) than the image based on the STY-C data set.

The behaviour of character reconstruction methods

In Part 1, we first tested four different reconstruction methods against six different phylogenetic hypotheses, three of which contained mostly pettalid terminals (PET), and three of which were predominantly stylocellid terminals (STY). With the exception of the simplest reconstruction method, global averaging, there was good agreement in the reconstructions generated using the PET terminal set, but only sporadic agreement between pairs of reconstructions generated using the STY terminal set. Nevertheless, reconstructions agreed more within a terminal set than between the two, suggesting that reconstructions are generally sensitive to terminal selection. Moreover, sensitivity to reconstruction methodology also varied with terminal set—PET reconstructions were robust to methodology as well as topology, but STY reconstructions were more sensitive to both topological and methodological changes. The latter data set also revealed that a lack of resolution at the reconstructed node introduces considerable sensitivity to reconstruction method. The robustness to variation in topology and methodology of a particular terminal set should therefore be evaluated while determining what confidence can be placed on an ancestral reconstruction.

By considering the correlation between reconstructions, rather than simply the Euclidean distance between them, we were able to identify reconstructions using either terminal set that agreed about the trends of ancestral characters, if not the magnitude of those characters. Using this comparison, we also considered a wide variety of methods to optimize the OPI-C data set (containing outgroup data for five non-cyphopthalmid species) on an updated molecular tree with branch lengths. Squared-change parsimony and maximum likelihood methods yielded congruent reconstructions, irrespective of the inclusion of branch length data, but dependent on the inclusion or exclusion of outgroup data. Bayesian reconstructions were consistent, irrespective of the inclusion of outgroup data, with the other reconstructions that used outgroup data. Reconstructions by landmark optimization, nested averaging, and linear parsimony in TNT were correlated to all other categories of reconstruction, except squared-change parsimony and maximum likelihood without outgroup data but with branch lengths.

Linear parsimony as implemented in TNT showed broad agreement with the reconstruction method used, as well as insensitivity to the inclusion or exclusion of outgroup data. Moreover, this method also generated the greatest agreement between reconstructions based the distinct STY and PET trees, specifically the PET-DC and STY-MC trees. It is encouraging that the greatest agreement between reconstructions generated with different terminal sets was found using trees based on “total evidence” analyses (combining different data sets), suggesting that the inclusion of as many characters as possible reveals consistent phylogenetic relationships even when the terminal set varies significantly. Consistently, we observed that the reconstruction methods most likely to yield sets of reconstructed characters with values far from the overall mean across terminals were landmark optimization, linear parsimony, and nested averaging. Conversely, global and sister group averaging generally yielded reconstructions less distinct from the mean across terminals.

For the topology tested in Part 2, the inclusion or exclusion of branch length information was not found greatly to affect the ancestral reconstruction. This was a surprising result, as we expected our reconstructions using branch lengths to cluster together. Instead, it seems that the reconstruction of PIP-C is more sensitive to tree topology and the position of the reconstructed node within the tree.

When an ancestral reconstruction is optimized at the root of a tree, the selection of the outgroup would seem to be of critical importance, since its ancestral character states are only one edge away from the root. We chose to root our Cyphophthalmi-only trees using Stylocellidae, based on the best previously available evidence (Boyer et al., 2007). However, recent results (Giribet et al., 2010, 2012) suggest that Pettalidae may be sister to the remaining Cyphophthalmi, as they were found in the STY-M and STY-MC trees. Re-analysis of PET and STY-C trees under this alternative topology did not change the most prominent characteristics of PIPC, which were found to be more pettalid-like already. Specifically, pettalids have the following in common with PIPC: they are, on average, smaller than stylocellids, possess robust chelicerae with only partial ornamentation, and are eyeless or lens-less. PIPC’s most distinctively stylocellid characteristic is its dorsal outline, rather than any specific set of reconstructed characters. This suggests the reconstruction is surprisingly robust to the choice of sister group within Cyphophthalmi, at least with respect to the choice of Stylocellidae or Pettalidae. It is not evident what is causing the dilution of stylocellid characters, even when they are placed as sister to the remaining Cyphophthalmi. The earliest lineages in Stylocellidae are the cave-dwelling members of Fangensis, which have reduced (with a lens) or missing eyes, but those species are also large and long-legged, so their placement at the base of Stylocellidae seems unlikely to drive the reduction of eyes in PIPC while having no effect on overall body and limb size.

PIPC is remarkably at odds with non-cyphophthalmid Opiliones, which are usually larger, extremely long-legged, and distinctly eyed (with eyes that appear to be homologous to those in Cyphophthalmi; Alberti et al., 2008). It would have been a convenient reconstruction if PIPC had appeared stylocellid-like, for this would have suggested a gradual evolution of the usual small cyphophthalmid form from an ancestor that is superficially closer to their sister Opiliones. However, given the appearance of PIPC here, the morphology of the ancestor of all Opiliones is not at all obvious, and remains fruitful ground for further inquiry. From that ancestor, two radically different forms of Opiliones emerged in the Paleozoic, raising interesting questions about the evolution of Opiliones: which characters are more derived, and what ecological factors drove their divergence?

A broader consideration of reconstruction methods

De Queiroz (2000) has argued that differences between the data being optimized for the reconstruction and those used to find the tree are desirable, since optimality criteria minimize the number of ancestral origins for characters of interest and can bias reconstructions. We did this in many cases, optimizing, for example, continuous characters in trees found using molecular data; still, without a detailed examination of this issue, we offer no explicit insight here. But this and other studies—discrete characters on a molecular phylogeny (Hibbitts and Fitzgerald, 2005), continuous morphological data on a discrete morphological phylogeny (Gasparini et al., 2006), and generic averages on a supertree constructed from trees searched off discrete morphological and behavioral data (Hormiga et al., 2000)—emphasize a lack of restrictions in this regard.

Maddison (1991) showed that character reconstructions under parsimony are related to those under maximum likelihood in that squared-change parsimony derives from probabilistic models of tree estimation (Edwards and Cavalli-Sforza, 1964; Cavalli-Sforza and Edwards, 1967). Additionally, Webster and Purvis (2002a) have provided a map of rate and reconstruction equivalencies among different parsimony and likelihood methods. From their map, we were able to confirm the equivalence between unweighted squared-change parsimony and weighted squared-change parsimony when branch lengths are equal; that linear parsimony produces different reconstructions from squared-change parsimony; and that both parsimony methods differ from maximum likelihood with a Brownian motion model of evolution. Webster and Purvis (2002a) do not indicate that independent contrasts gives equivalent reconstructions to other methods, although at the root of the tree it should be the same as squared-change parsimony and likelihood with a Brownian motion model (Felsenstein, 1985; Grafen, 1989); indeed, in our reconstructions, independent contrasts in APE at the base of Cyphophthalmi when there were no outgroups (i.e. at the base of the entire tree) gave equivalent reconstructions to unweighted squared-change parsimony with no outgroups and restricted ML under a Brownian motion model with no outgroups and no branch lengths. Independent contrasts reconstructions were not affected by branch lengths, but rather by optimizing at the base of the tree or an internal node (as when outgroup data were included); independent contrasts reconstructions at internal nodes were equivalent to weighted squared-change parsimony with no outgroups and very close to those from restricted maximum likelihood with no outgroups but branch lengths.

Normally, the model behind the evolution of continuous characters under maximum likelihood is Brownian motion, a random divergence of character state means. The Ornstein–Uhlenbeck modification of this process (Lande, 1976) can be used to constrain divergences, essentially introducing stabilizing selection, and a further modification is to remove the up-pass optimization. Using a stabilizing model and only a down-pass with squared-change calculations leads to Felsenstein’s (1985) independent contrasts, which for any one node is the weighted average of descendant character states (weighted by the branch lengths). The package APE considers Ornstein–Uhlenbeck Brownian motion a generalized Brownian motion model, and indeed, the reconstructions it calculated from our data under maximum likelihood with a Brownian motion model were almost identical to the global average for each character across all terminals. For some characters, including body size, they were strictly identical to the global average (although with confidence intervals).

Other likelihood method variants were difficult to test due to our uncertainty over use of the program. In APE, generalized least squares methods can be used with a variety of correlation models, but produced error messages in our hands. These warnings seemed spurious, but could have indicated problems that led to nonsensical reconstructions (such as an ancestral Cyphophthalmi five times larger than any that exist today or are in the fossil record, under the correlation structure of Martins and Hansen, 1997). As for Bayesian reconstructions, Maddison (1991) has argued that a weighted squared-change parsimony reconstruction also maximizes the posterior probability of the reconstruction, making it equivalent to a Bayesian method. We did not find this to be the case, but we also had large variances from different runs of BayesTraits, uncertainty in the proper settings of the various parameters, and evidence that some functions are still under development.

The fact that various reconstruction methods are related and some of these are equivalent to averages raises the question of whether we gain anything from character optimizations that is not available from just calculating nested averages down the tree, or, worse, a simple global average across terminals. We found here that reconstructions using global averaging were distant from other reconstructions (except maximum likelihood in APE). However, results from nested averaging performed essentially as consistently as linear parsimony in most analyses, with the important exception of not finding congruity between reconstructions based on the STY and PET data sets (Fig. 2c).

A test of optimization methods by Webster and Purvis (2002b) resulted in ancestral reconstructions of Foraminifera that were also different from the average of all the terminals, but just such an average turned out to be a better match for known fossil ancestors than any of the reconstructions. The lesson of their study, however, may be that reconstructions are ultimately dependent on the phylogeny upon which characters are optimized, and its reliability is key. Webster and Purvis (2002b) used a phylogeny constructed using a “stratophenetic” approach, where the author (Fordham, 1986) created species groups with “intuitively defined boundaries” and traced their evolution through geological strata. Thus it is perhaps not surprising that its ancestral nodes were occupied by forms most closely resembling descendant averages, since the author may have been merely averaging shapes when exercising his intuition during tree inference. A second test of reconstruction methods conducted by Webster and Purvis (2002a) on a primate data set also relied on phylogenic estimations, dates, and ancestor hypotheses (including a composite phylogeny with fairly subjective branch lengths; Purvis, 1995) perhaps too rough to indicate which of these methods found the “correct” ancestral morphology. It is important that these methods do not produce just global averages, but ultimately it is difficult to judge their accuracy using such problematic historical hypotheses.

Given the differing philosophies on phylogenetic reconstruction, historical speculation, and assertions about ancient life, acceptance of ancestral reconstruction as a general exercise is varied. However, we feel our work here formalizes a process done casually by ourselves and other opilionid biologists as part of developing new phylogenetic hypotheses and describing newly discovered fossils, which is to wonder what the origins of Opiliones were like (e.g. Garwood et al., 2011). We have shown here that linear parsimony generates reconstructions robust to changes in terminals and topologies, which are quite distinct from simple averages but consistent with reasonable alternative methods, and we have used it to generate an ancestral reconstruction that currently stands as our best estimate of the progenitor for this very old, worldwide group of arthropods.