Biases with the Generalized Euclidean Distance measure in disparity analyses with high levels of missing data

LEHMANN, OSCAR E. R.; EZCURRA, MARTÍN D.; BUTLER, RICHARD J.; LLOYD, GRAEME T.

PALAEONTOLOGY

WILEY-BLACKWELL PUBLISHING, INC

Año: 2019 vol. 62 p. 837 - 849

0031-0239

The Generalized Euclidean Distance (GED)measure has been extensively used to conduct morphologicaldisparity analyses based on palaeontological matrices of discretecharacters. This is in part because some implementationsallow the use of morphological matrices with highpercentages of missing data without needing to prune taxafor a subsequent ordination of the data set. Previous studieshave suggested that this way of using the GED may generatea bias in the resulting morphospace, but a detailed study ofthis possible effect has been lacking. Here, we test whetherthe percentage of missing data for a taxon artificially influencesits position in the morphospace, and if missing dataaffects pre- and post-ordination disparity measures. We findthat this use of the GED creates a systematic bias, wherebytaxa with higher percentages of missing data are placed closerto the centre of the morphospace than those with morecomplete scorings. This bias extends into pre- and postordinationcalculations of disparity measures and can leadto erroneous interpretations of disparity patterns, especiallyif specimens present in a particular time interval or cladehave distinct proportions of missing information. We suggestthat this implementation of the GED should be usedwith caution, especially in cases with high percentages ofmissing data. Results recovered using an alternative distancemeasure, Maximum Observed Rescaled Distance (MORD),are more robust to missing data. As a consequence, we suggestthat MORD is a more appropriate distance measurethan GED when analysing data sets with high amounts ofmissing data.