The BayesTraits analyses indicate that very different models provide the best fit to the data for the manus and pes (). The data for the manus are best fit by the unordered, two-rate model in which the rate of digit acquisition is assumed to be zero (model E); when compared with the remaining models, this model yields 2 ln Bayes factor estimates of 5.124–30.244 (values greater than 6 are conventionally regarded as strong evidence for a model; see Brandley et al. 2005
). Models in which character state transitions are unordered provide a significantly better fit than those in which character state transitions are ordered. As Brandley et al. (2008)
noted, developmental and comparative morphological evidence indicates that digits develop and are lost in an ordered sequence, so that models assuming ordered character state transitions may be preferred a priori
. However, prohibitive computation time prevented us from evaluating an ordered model assuming a rate of digit acquisition of zero, so that we were unable to incorporate both character state ordering and the assumption of irreversible digit loss in a single model. The maximal consistency of ancestral states for the manus and pes inferred assuming an unordered model prohibiting digit acquisition (model E; see below) suggests that the assumption that digit loss is irreversible may be substantially more significant than character state ordering in modelling limb evolution. A single-rate model in which character state transitions are ordered (model B) provides the best fit to the data for the pes; this model yields 2 ln Bayes factor estimates of 1.478–11.744 when compared with the other models.
Table 2. BayesTraits results for the five models examined. Mean values (where applicable) are followed by 95% credible intervals in parentheses. q01, forward transition rate; q10, reverse transition rate; L, likelihood; the Bayes factors reported derive from comparisons (more ...)
The consistency of reconstructed numbers of manual and pedal digits for each combination of the five models examined is presented in . Ancestral states inferred assuming the two models that provide the best fit to the data (model E for the manus and model B for the pes) are the least consistent, implying ancestral digit configurations represented among known species of Lerista for only 62 of 76 internal nodes; inconsistent ancestral states are generally associated with basal nodes and entail digit configurations of either four or five digits for the manus and two or three digits for the pes (). The most consistent ancestral state estimates are obtained where the best-fitting model for the manus (model E) is assumed for both the manus and pes. Ancestral state reconstructions for this combination of models invariably imply ancestral digit configurations observed among known species of Lerista.
Consistency of ancestral character states for the manus and pes for all combinations of the five models examined.
Figure 2. Maximum clade credibility tree with implied ancestral digit configurations for the two models that best explain the data (see text). Digit configurations not represented among known species of Lerista are indicated by an asterisk. The frequencies of implied (more ...)
The substantial proportion of implausible digit configurations implied by ancestral state reconstructions for the two best-fitting models (model E for the manus and model B for the pes) indicate that one or both reconstructions are inaccurate. Several considerations suggest that the inconsistent ancestral states are attributable to the reconstructions for the pes. As indicated in and above, when the reconstructions for the manus (i.e. for the best-fitting model) are considered in combination with ancestral states for the pes inferred assuming a suboptimal model (model E), they imply digit configurations represented among known species of Lerista
for all internal nodes. The reconstructions for the pes (i.e. for the best-fitting model), conversely, are inconsistent with one or more ancestral states for the manus in all instances (). As well as yielding ancestral states that consistently entail implausible digit configurations for internal nodes, the model that best fits the data for the pes may be regarded as inappropriate for inferring patterns of limb reduction or potential re-elaboration, as it assumes identical rates for all transitions; Brandley et al. (2008)
recently presented evidence for significantly different rates of digit acquisition and loss across squamates, so that models assuming a single transition rate may inadequately represent the process of limb evolution. Significantly, the model producing ancestral state estimates consistent with those for the manus (model E) has a marginal likelihood differing negligibly from that for similar models (model C; ), and conforms well with current understanding of squamate limb evolution (which indicates a low frequency of digit acquisition).
An objective means of assessing the plausibility of implied ancestral phenotypes is essential if the criterion of consistency among ancestral states for multiple characters is to be useful. Ancestral phenotypes were evaluated here according to whether they occur among observed states for the terminal nodes of the phylogeny (i.e. known species). This convenient criterion for assessing combinations of inferred ancestral states is only appropriate, however, if the distribution of phenotypes exhibited by known species adequately represents the range of attainable phenotypes; where this is not the case, the absence of particular phenotypes may be attributable to either anagenesis or extinction. All inconsistent ancestral states for the two models that best fit the data entail ancestors possessing well-developed forelimbs and moderately reduced hind limbs (see and above). Although similar phenotypes are observed in the closely related clade Anomalopus
(see Wiens 2009
), known species of Lerista
never exhibit fewer digits for the pes than the manus (indeed, the combination of well-developed forelimbs and substantially reduced hind limbs is exceedingly rare in squamates generally). The phylogenetic distribution of particular (observed) digit configurations indicates that nearly all configurations have evolved independently multiple times (). Moreover, observed digit configurations represent a continuous, relatively limited region of the possible morphospace (the shaded cells in the inset of ). Accordingly, it may be assumed that the potential morphospace available to the immediate ancestor of Lerista
is completely occupied (or nearly so). Insofar as this assumption is valid, our analyses indicate that the two-rate model with unordered character state transitions and a specified rate of digit acquisition of zero (model E) yields accurate ancestral character state reconstructions for both the manus and pes.
Comparisons of implied ancestral phenotypes with phenotypes represented among known species provides an independent, potentially powerful means of evaluating ancestral character state reconstructions. Application of this criterion in assessing inferences of ancestral limb morphology in Lerista indicates that the best-fitting model for the pes yields inaccurate ancestral state estimates, and that alternative (suboptimal) models perform significantly better. Although our results validate concerns that ancestral state reconstructions may seriously mislead inferences of evolutionary patterns, they also demonstrate that this possibility may be substantially negated by considering ancestral state estimates for multiple characters in combination.