Reversals in phylogenetics
A particularly controversial issue in cladistics concerns the treatment of reversals. Proponents of parsimony (Kluge, 1994; Farris et al., 1995; Farris, 1997; Farris and Kluge, 1998) and 3ta (De Laet and Smets, 1998; Siebert and Williams, 1998) have been deeply divided on this particular issue. In parsimony, a transformational approach to homology using the Wagner (Farris et al., 1970) and Fitch (Fitch, 1971) parsimony algorithms treats characters from the perspective of unrooted character-transformation trees (Slowinski, 1993). Reversals provide information and can serve for clade support because they are evidence of secondary homology with the appropriate test of maximizing congruence. This maximization of congruence leads to search the pattern with the minimum of ad hoc hypotheses that are convergences and reversals. For Farris (2012), reversals can be inferred a priori in the inference of primary homologies but also from an analysis: ‘More fundamentally, even if (as I have seen other authors suggest) Hennig would have preferred to distinguish apomorphies from plesiomorphies before starting to construct the tree, he was obviously willing to revise assessments of plesiomorphy during tree construction, for Hennig did in fact recognize reversals and apply them as synapomorphies’. This is the most widespread point of view in cladistics, which prevails in systematic paleontology, and the only point of view represented in probabilistic methods, which prevail in molecular systematics and are starting to be used on phenotypic characters as well (Müller and Reisz, 2006). Assumptions of 3ta are much less familiar. In 3ta, hierarchical hypotheses of homology, i.e. a nested set of character states, are submitted to a test of congruence. The test either accepts or rejects the relevance of the hypothesis. Convergence is one of the multiple explanations of rejection. ‘Parsimony-like reversals’, i.e. the generation of hypotheses of homology not proposed by the systematist but generated by the method, violate hierarchical classifications. Thus, they cannot be justified in 3ta rationale. Evolutionary reversals, i.e., losses of instances of character-states, are not used in 3ta to support nodes; they represent only homoplasies, i.e. mistaken hypotheses of homology.
For instance, the evolutionary hypothesis (generated after an initial analysis by inferring character history on a tree) involving three conditions deduced a posteriori from an analysis: 0 (‘absent’), 1 (‘present’) and 0* (‘secondary absence’; scored the same in a matrix but interpreted differently from primitive absence on a tree) is interpreted differently under parsimony and 3ta. The secondary absence can be explicitly represented as an apomorphy in the primary homology hypothesis (0(1(0*))), under parsimony. Another interpretation (3ta) consists in disregarding secondary absence as synapomorphic but to consider it as a particular case of absence: (0,1(0*)). Here, neither the absence nor the reversal is considered as a state (neither plesiomorphy, nor apomorphy) because the absence is not a state in 3ta (in Fig. 3, 0*, 0** and 0*** are not considered in 3ta). Parsimony proponents favour the first option, which yields support for six clades in the phasmatodea phylogeny (Fig. 3A). To summarize, the first interpretation (parsimony) considers a loss as an homology and a synapomorphy (because it supports a clade), an homoplasy (because the primary hypothesis is falsified by the distribution of the other characters) and a plesiomorphy (as defined in the matrix), according to Brower and de Pinna (2014). The second interpretation considers a loss as uninformative: it is neither an homology nor a synapomorphy (because it supports no clade), it is not an homoplasy (because the primary hypothesis is in agreement with the distribution of the other characters) and it is not a plesiomorphy (because the absence is not a state in 3ta; it is the root, including all). 3ta proponents favour this interpretation: only one clade in the Phasmatodea phylogeny is supported, and the only synapomorphy is the homology reflecting the first appearance of wings. These two interpretations are thus in perfect opposition. Here we emphasize that Brownian motion is only coherent with the assumptions entailed by the first interpretation: reversals (i.e., secondary absence) are treated as apomorphies in the primary homology hypotheses (as an order with parsimony, or as a hierarchy with 3ta). Our simulations produce informative reversals under Brownian motion, which can be exploited only under a parsimony viewpoint of these reversals: our results present a quantification of the loss in resolving power and artefactual resolution in 3ta if true and informative reversals are present (i.e. if true reversals are simulated and ‘hidden’ into the same state as the plesiomorphy but which support a clades of the known tree). Thus, our results must be interpreted accordingly. Irreversible characters might yield different results and will be tackled in another study.
We take this opportunity to propose a nomenclatural clarification about reversals (based on the example in Fig. 3A) as secondary homology hypotheses; thus, this clarification is valid both for parsimony and for 3ta. First rounds of reversals are generally called ‘secondary losses’ (e.g. (Carine and Scotland, 1999), when in fact, only the absence should be considered secondary and the loss in itself should be considered as an event that appeared for the first time (i.e., primary). Thus, a character state is primitively absent (primary absence; state 0 on Fig. 3). It can then appear; this is a primary appearance (of state 1), denoted +1 on Fig. 3A. It can be subsequently lost (-1, reversal to state 0, but identified as 0* on Fig. 3a, for greater clarity); this should be called a primary loss, which results in a secondary absence. After this, a secondary gain (+2) can lead to secondary presence (1* in Fig. 3A), and a secondary loss (-2) can lead to ternary absence (0** in Fig. 3), etc.