Is ACCTRAN better than DELTRAN?

When parsimony ancestral character reconstruction is ambiguous, it is often resolved in favour of the more complex character state. Hence, secondary loss (secondary ‘‘absence’’) of a complex feature is favoured over parallel gains of that feature as this preserves the stronger hypothesis of homology. We believe that such asymmetry in character state complexity is important information for understanding character evolution in general. However, we here point out an inappropriate link that is commonly made between this approach and the accelerated transformation (ACCTRAN) algorithm. In ACCTRAN, changes are assigned along branches of a phylogenetic tree as close to the root as possible. This has been taken to imply that ACCTRAN will minimize hypotheses of parallel origins of complex traits and thus that ACCTRAN is philosophically better justified than the alternatives, such as delayed transformation (DELTRAN), where changes are assigned along branches as close to the tips as possible. We provide simple examples to show that such views are mistaken and that neither ACCTRAN nor DELTRAN consistently minimize parallel gain of complex traits. We therefore do not see theoretical grounds for favouring the popular ACCTRAN algorithm. The Willi Hennig Society 2008. Character optimization is the process by which alternative reconstructions of a character on a cladogram are evaluated. Under parsimony, when alternative reconstructions are equally costly, character optimization is ambiguous (Farris, 1970). The popular algorithms for resolving ambiguous character optimization are accelerated transformation (ACCTRAN), where changes are assigned along branches of a phylogenetic tree as close to the root as possible (passing up), and delayed transformation (DELTRAN), where changes are assigned along branches as close to the tips as possible (Farris, 1970; Swofford and Maddison, 1987). As originally proposed (Farris, 1970) and developed (Swofford and Maddison, 1987, 1992), ACCTRAN and DELTRAN were not presented as one being in some general way superior to the other. Today, however, ACCTRAN is much more widely used than DELTRAN. For example, Google Scholar finds 1730 references to ACCTRAN but approximately 720 to DELTRAN (897 hits, minus about 20% that refer to a computer language) and almost all papers that mention DELTRAN also use ACCTRAN, sometimes preferentially. This note points out that we believe current preference for ACCTRAN stems from a mistaken link made by De Pinna (1991) between a philosophical justification for preferring reversals over parallelism and ACCTRAN. De Pinna s philosophical argument based on asymmetry in character state complexity (see below) has received considerable acceptance and we certainly see merit in it. However, neither it nor any other argument we have seen offers theoretical grounds for preferring ACCTRAN over DELTRAN in general. Rather, we argue that each case must be evaluated independently with respect to the complexity of character states (see below). We start by briefly reviewing some of the basic properties of ACCTRAN and DELTRAN. *Corresponding author: E-mail address: [email protected] The Willi Hennig Society 2008 Cladistics 10.1111/j.1096-0031.2008.00229.x Cladistics 24 (2008) 1–7 Some properties of ACCTRAN and DELTRAN ACCTRAN and DELTRAN represent just two among many alternative most parsimonious reconstructions (MPRs) on any given tree (Miyakawa and Narushima, 2004). They represent extremes of the distribution of MPRs in ‘‘MPR-space’’ (all MPRs for a given tree, see Minaka, 1993); for example, ACCTRAN is the MPR that minimizes the lengths of all subtrees of a given tree (Minaka, 1993)—the so-called ‘‘First Theorem on ACCTRAN’’ (Miyakawa and Narushima, 2004). As stated by Miyakawa and Narushima (2004, p. 171) ‘‘... ACCTRAN on a rooted el-tree [any given tree] is the unique MPR on the tree for which the lengths of all subtrees are minimized, that is, the subtree-complete maximum-parsimonity of ACCTRANs’’ (see also Narushima and Misheva, 2002). Based on this property, Minaka (1993) proposed the ‘‘distortion index’’ calculated as the cumulative difference between the lengths of all subtrees of a given MPR compared with that of ACCTRAN. Minaka (1993) found that DELTRAN was the MPR that maximizes the distortion index. Of course, all MPRs are, by definition, equal in terms of the length of the total tree. However, ACCTRAN monotonically spreads change so as to minimize the length of all subtrees while DELTRAN maximally distorts monotonicity by distributing change unevenly among subtrees—as stated byMinaka (1993, p. 292) ‘‘... this means that in DELTRAN optimization, the total amounts of character state changes are more unevenly scattered over the full tree than in ACCTRAN.’’ This property is important as ACCTRAN, by evenly spreading change, may better fit assumptions of rate constancy incorporated in many popular models used for phylogenetic reconstructions, especially of molecular data. On the other hand, DELTRAN may be more appropriate in cases where rate constancy is unlikely, as may be the case with morphological characters showing character state asymmetries. ACCTRAN and DELTRAN represent opposite MPR extremes, respectively maximizing ambiguous character state change as close to the root, or the tips, as possible. This means that ACCTRAN will, on average, lead to greater estimated branch lengths between internal nodes than DELTRAN, while DELTRAN will, on average, lead to greater estimated terminal branch lengths than ACCTRAN. This property is important if those branch lengths are subsequently used as information, e.g. to date the splitting of lineages using a molecular clock or other methods. It is also important as ACCTRAN and DELTRAN may represent reasonable upper and lower bound estimates of internal and terminal branch lengths and hence provide a good framework for sensitivity analyses. For example, Forest et al. (2005) used both to date phylogenetic trees and, unsurprisingly, found that ACCTRAN tended to give older age estimates for nodes. Although ACCTRAN and DELTRAN have been by far the best studied, many alternative options may be possible for a given character on a tree (Maddison and Maddison, 2002). For example, one might chose the MPR that maximizes similarity of reconstructed internal nodes to a given terminal (species) in the tree, or choose the MPR that maximally reconstructs a given character state (e.g. ‘‘1’’) on terminal branches. For morphological studies, in particular, or studies using molecular phylogenies to trace morphological ⁄behavioural traits, one MPR property that is often sought is one that maximizes parallel loss over convergent gains of complex traits (De Pinna, 1991). In spite of frequent claims to the contrary, this last condition is not satisfied by ACCTRAN (see below). Asymmetry in character state complexity De Pinna (1991, p. 386) argued that ‘‘... absences stand at a lower ontological level as observations, when compared to presences (Nelson and Platnick, 1981: 29; Patterson, 1982: 30).’’ In other words, there can be asymmetry in the information content of primary homology statements of character states. Complex features share detailed similarities strengthening the conjecture of homology between them, whereas absences are a weaker form of primary homology statements (see also Rieppel and Kearney, 2002). Therefore, a theoretical basis may exist for favouring some equally parsimonious optimizations over others. In the absence of compelling evidence to the contrary, ambiguous optimization is better resolved in favour of secondary losses (reversals) over parallel gains of complex structures. This is more consistent with the stronger conjecture of homology based on observable detailed similarity, rather than mere absence (De Pinna, 1991); complexity tests similarity (Agnarsson and Coddington, 2008; see also Richter, 2005; Scholtz, 2005; Agnarsson et al., 2007). When characters lack asymmetry in character state complexity (e.g. the states ‘‘red’’ and ‘‘blue’’), little, if any, grounds exist to favour one optimization over another (Richter, 2005). However, we believe that De Pinna (1991) erred when he concluded that ACCTRAN is a superior algorithm for preserving strong homology statements (see Examples, below). He claimed (De Pinna, 1991, p. 388) that ACCTRAN favours reversals over parallelism and that therefore ‘‘... ACCTRAN optimization better conforms with the notion that the conjecture of primary homology should be held valid unless demonstrated false by parsimony considerations. It thus can be considered as a theoretically superior algorithm for tracing character 2 I. Agnarsson and J.A. Miller / Cladistics 24 (2008) 1–7