Coding Meristic Characters for Phylogenetic Analysis: A Comparison of Step-Matrix Gap-Weighting and Generalized Frequency Coding

Abstract

Meristic characters, or counts of discrete serially ho-mologous structures, are a distinctive and ubiquitousclass of quantitative organismal variation. Meristic char-acters share many properties with morphometric char-acters (i.e., measurements, proportions, etc.): they arereadily described numerically, they usually vary withinand among taxa, and they often appear to follow similarunderlying frequency distributions (e.g., Burbrink, 2001;Allsteadt et al., 2006). Based on these similarities, meris-tic characters are generally lumped with morphometriccharactersintothebroadercategoryof“quantitativecon-tinuouscharacters”forphylogenyreconstruction.Meris-tic characters also exhibit properties that differ subtly,butperhapsimportantly,frommorphometriccharacters.It has been increasingly recognized that morphologicalsystematists often code intrinsically quantitative char-acters as qualitative by artificially compartmentalizingvariation into relatively few ordered states (e.g., inter-clavicle,medianprocess:0=normallength;1=reduced;Etheridge and de Queiroz, 1988). This practice alwaysproduces arbitrary character states with morphometricdata. In contrast, meristic characters may be viewed asdiscrete traits that, depending on the range of variation,showacontinuumfrombinarytransformations,throughmultistate polymorphic characters, to quasicontinu-ous variation analogous to morphometric data (Wiens,2001).Arguments both for and against the inclusion ofquantitative continuous characters are prevalent in thesystematics literature and are beyond the scope of thisarticle (see Rae, 1998; Swiderski et al., 1998; Thiele,1993). Regardless, various authors have shown thatsuch characters do provide substantial phylogenetic in-formation despite the potential for increased levels ofhomoplasy, and thus remain relevant to empirical sys-tematics (e.g., Campbell and Frost, 1993; Wiens, 1995;WiensandServedio,1998).Severalcodingmethodshavebeen developed for incorporating meristic characters inphylogenetic analysis and dealing with the problem ofpartially overlapping character states across taxa. For bi-nary characters, frequency bins have most often beenused; whereas polymorphic multistate characters havebeen analyzed using majority methods, segment cod-ing, gap coding, gap weighting, step matrices, and var-ious statistical similarity analyses (e.g., Colless, 1980;Mabee and Humphries, 1993; Mickevich and Johnson,1976; Swiderski et al., 1998; Thiele, 1993; Wiens, 1993).Wiens (1998, 2000) and Wiens and Servedio (1997, 1998)evaluated several classes of coding methods and con-cluded that frequency methods were generally most ef-fective. In recent years, two methods that augment andimprove on previous approaches have become widelyused for coding meristic (and other quantitatively de-fined) characters for phylogenetic analysis: step-matrixgap-weighting (SMGW; Wiens, 2001) and general-ized frequency coding (GFC; Smith and Gutberlet,2001).SMGW is an application of step matrices (Wiens,1995) to the gap-weighting method introduced by Thiele(1993). In gap weighting, taxa are assigned states basedon range-standardized mean values of a trait, with thenumber of possible states scaled to the maximum num-ber allowed by the software used to infer phylogenies(e.g.,32statesforPAUP*;Swofford,1993).Gapsbetweenmeans are weighted based on the magnitude of theirdifferences so that larger differences in trait means be-tween taxa translate into larger weights. A limitation ofthe step-matrix approach is that the number of distinctstates is potentially restricted by the software used tobuild phylogenies (e.g., PAUP* only allows 32 states, sodata sets with over 32 taxa would likely not be amenableto SMGW). The purported advantage of SMGW is thatstep matrices allow more fine-grained weighting thansimple gap weighting by increasing the trait range from32 states to 1000 states (the maximum cost betweenstatesinastepmatrixusingPAUP*).Thus,charactersaretreated as approximations of a continuous scale (Wiens,2001).GFC can be viewed as a method that combines ele-ments of both gap weighting (as implemented by Thiele,1993) and the frequency bins method of Wiens (1993).In GFC, each quantitative character is divided into sub-charactersthatcorrespondwitheachcharacterstate.Thefrequency of specimens falling into a given subcharac-ter is described with frequency bins; the overall effectis that cumulative frequency distributions of characterstates per taxa are constructed for each character. A po-tential advantage of GFC is that frequency distributionsare simply translated into phlyogenetically analyzabledata, maximizing information content while eliminat-ing the need for further data manipulation (Smith andGutberlet, 2001). The primary operational difference be-tween these methods is that character states within taxaare coded using estimates of cumulative frequencies of