Our simulated characters evolved gradually; they are continuous and have a unimodal distribution (S6). They were discretized because phenotypic data are often available in discrete form (in descriptions, for instance), and most available parsimony and all 3ta programs require this. Thus, these reflect the data routinely analysed by systematists. In this case, we created 10 states per character to retain much of the original information while producing data that can easily be analysed by almost any phylogenetic package (Laurin and Germain, 2011), and to allow detection of the spurious relationships yielded by homoplasy in the data (Bardin et al., 2013). This procedure yielded many significant results (Table 1; Table 2). We show that unordered parsimony performs far worse than ordered methods on such data, with a loss in resolving power between 13.4% and 29.3% compared to ordered parsimony and with between 4.7% and 15.6% more artefactual resolution (results always statistically significant). Thus, a significant decrease in performance is expected when characters are not ordered as morphoclines. This result highlights the information content of character ordering schemes (Wilkinson, 1992), and we infer that coding continuous characters as fully unordered significantly decreases resolving power and increases artefactual resolution in empirical datasets. We also quantified the differences in resolving power between ordered parsimony and 3ta, which differ in the way they handle reversals as evidence for the support of a clade (among others). These differences vary between 1.3% (non-significant) and 6.3% (Table 1) for the resolving power, and between 0.0% (non-significant) and 9.4% for the artefactual resolution. We also have quantified resolving power when polarization errors, produced by varying outgroup branch length, are introduced (i.e., when polarization is based on an outgroup including a variable proportion of plesiomorphies). Further work could be done to quantify the effect of incorrect state ordering schemes as incorrect morphocline assumptions.
Recently, Grand et al. (2013) found that 3ta yielded significantly greater resolving power and more artefactual resolution than ordered parsimony. In our study, based on an extended set of matrices, taxa and characters, ordered parsimony yielded the greatest resolving power and the fewest artefactual resolutions. The use of exact hypothetical ancestors to root trees in Grand et al. (2013) may explain the contrasting results. Moreover, the present work yields a better understanding of the impact of evolutionary assumptions about character state order and reversals. Further simulations could be done, using different evolutionary models, such as irreversible characters, to see if they yield different results about the performance of parsimony (with ordered stares or not) and 3ta.