Use and misuse of discrete character data for morphospace and disparity analyses

Abstract

The measurement of morphological variation in macroevolutionary studies is increasingly based on morphospaces constructed from discrete character data. This trend mostly results from the appropriation of phylogenetic data matrices as character spaces for carrying out disparity analyses. Phylogenetic matrices provide morphological descriptions of taxa as combinations of character states and thus appear, if not conceptually, at least mathematically, comparable to discrete character datasets found in numerical taxonomy or built for disparity purposes. Hence, phylogenetic matrices seem to constitute an abundant source of data readily available for morphospace analyses. Discrete character spaces have generally been described as more flexible than morphospaces capturing continuous shape variation. The discrete coding of morphology allows morphospaces to accommodate more disparate morphologies and the ability of discrete character schemes to handle missing data is also often emphasized. This flexibility comes at a cost, however. Multivariate ordinations of such spaces often provide deceptive visualizations and may invite the use of inappropriate methodologies for their exploration. The large amount of missing data that typifies many phylogenetic datasets is also problematic for the measurement of dissimilarity among taxa and can therefore be detrimental to the assessment of morphological disparity. Here, the properties of discrete character spaces are described and common pitfalls discussed. Graphical and methodological approaches are suggested to circumvent or limit their impact, and greater caution is recommended when using discrete character data for morphospace and disparity inferences.

Megaevolutionary dynamics in reptiles and the role of adaptive radiations in evolutionary innovation

“…Large amounts of missing data, usually above 25%, considerably reduce the overall distance between taxa that can be captured on ordination spaces on both empirical and simulated data sets 47,59 . To reduce the negative impact of missing data, we removed all characters with more than 30% of missing data from the data set, which resulted in a total of 19% missing data on the final data set—safely below the threshold of 25% 47,59,60 . Additionally, inapplicable characters are a big conceptual problem to construct a morphospace.…”

“…Additionally, inapplicable characters are a big conceptual problem to construct a morphospace. Taxa with inapplicable characters will have their placement enforced upon a space they do not reside in (which is conceptually very different from missing data—when they reside in that space, but we currently lack data to place them) 60 . Deleting all inapplicable characters would further decrease the number of utilized characters at about 30%, thus reducing the span of morphological representation in the data set.…”

Morphological disparity in theropod jaws: comparing discrete characters and geometric morphometrics

“…Benson () gives examples of published data matrices that may give apparently high rates for certain clades, such as birds, but it cannot be said whether the evolutionary rates are truly high or simply reflect excessive research interest and coding of many small‐scale anatomical characters. Gerber () highlights problems of excessive missing data and the meaning of the axes in cases where cladistic characters are used, but they and others (Lloyd ; Hopkins & Gerber ) support the use of discrete characters to document disparity when appropriate methods are used to minimize bias and understand the data. Equally, of course, outline and landmark studies may be capturing aspects of shape that have no evolutionary or ecological significance at all or might be simply size‐related (Gould ).…”

“…Anderson & Friedman () recommend that analysts devise metrics that have functional significance, such as ratios of relative lengths of portions of the jaw or limbs. Another productive approach could be to use subsets of discrete character data sets that have hypothesized ecomorphological or evolutionary significance (Gerber ; Stubbs et al . ), such as the appendicular skeleton in the fish–tetrapod transition (Ruta & Wills ), the display crests and feeding apparatus in hadrosaurid dinosaurs (Stubbs et al .…”

“…Describing morphological variation using discrete characters has usually focused on cladistic data sets as a ready source of rich data on trait variation (Wills et al . ; Lloyd ; Gerber ). This approach involves analysing character–taxon matrices where morphologies are scored using character states, including the presence and absence of features, the numbers of certain elements (e.g.…”