Transformation of Quotient Values for their use as Continuous Cladistic Characters

Recent advances in cladistic technology have produced novel methods for introducing morphological data into cladistic analyses, such as the landmark and continuous character functions in the software TNT and RevBayes. While these new methods begin to address the problem of representing morphology, there has been little consideration of how to transform and code the operational taxonomic units’ (OTUs) dimensions into the datamatrix. Indeed, angles, serial counts, percentages and quotient values can be used as continuous characters, but little has been said about how coding these data affect the trees discovered. Logically, counts of elements and angles measured off specimens may be coded directly into continuous character matrices but percentages and quotient values are more problematic, being transformed data. Quotient values and percentages are the simplest way of representing proportional differences between two dimensions and reducing the effect of inter-taxonomic magnitude differences. However, both are demonstrated to be problematic transformations that produce continuous characters with weighted states that are non-representative of morphological variation. Thus, two OTUs may be represented as less/more similar morphologically than other OTUs that display the same degree of morphological variation. Furthermore, the researcher’s choice of which dimension is the divisor and dividend will have a similar affect. To address this problem, a trigonometric solution and a logarithmic solution have been proposed. Another solution called linear transposition scaling (LTS) was recently presented, with the intention of best representing and coding observable morphological variation. All three methods are reviewed to establish the best way to represent and code morphology in a cladistic analysis using continuous characters.