DOI: 10.5061/dryad.4cv1421
title: Data from: Biases with the Generalized Euclidean Distance in disparity analyses with high levels of missing data

description: The Generalized Euclidean Distance (GED) has been extensively used to
 conduct morphological disparity analyses based on palaeontological
 matrices of discrete characters. This is in part because some
 implementations allow the use of morphological matrices with high
 percentages of missing data without needing to prune taxa for a subsequent
 ordination of the data set. Previous studies have suggested that this way
 of using the GED may generate a bias in the resulting morphospace, but a
 detailed study of this possible effect was still lacking. Here, we test if
 the percentage of missing data for a taxon artificially influences its
 position in the morphospace, and if missing data affects pre- and
 post-ordination disparity measures. We find that this use of the GED
 creates a systematic bias, whereby taxa with higher percentages of missing
 data are placed closer to the centre of the morphospace than those with
 more complete scorings. This bias extends into pre- and post-ordination
 calculations of disparity measures and can lead to erroneous
 interpretations of disparity patterns, especially if specimens present in
 a particular time interval or clade have distinct proportions of missing
 information. We suggest that this implementation of the GED should be used
 with caution, especially in cases with high percentages of missing data.
 Results recovered using an alternative distance measure, Maximum Observed
 Rescaled Distance (MORD), are more robust to missing data. As a
 consequence, we suggest that MORD is a more appropriate distance measure
 than GED when analysing data sets with high amounts of missing data.
description: Supporting Information
 1Formulae used to
 calculate the distances and disparity measures.Supporting Information
 2References for the
 matrices employed.Supporting Information
 3Characteristics of the
 matrices used in this study, along with information regarding the
 particular analyses in which each was used.Supporting Information
 4Histograms for the 126
 matrices with more than 5% of missing data showing the distribution of the
 percentage of missing entries per taxon. The vertical dashed line
 indicates the mean percentage of missing entries.Supporting Information
 5Histograms showing the
 percentage of matrices with significant and negative (black),
 non-significant (light grey), and significant and positive (dark grey)
 Spearman’s correlations for the GED and the MORD, with α = 0.05. The
 distances are calculated based on the first 3 PCos and all the PCos. This
 are the results without any kind of correction for negative eigenvalues.
 Scatter plots for the 126 matrices with more than 5% of missing data
 showing the Euclidean distance to the centroid for each taxon against its
 percentage of missing entries. The distance to the centroid is scaled to 1
 independently for each distance measure in order to fit them in the same
 plot. The red dots correspond to the calculation with GED, while the blue
 dots refer to those made with MORD. A simple regression line is fitted
 through each group in order to illustrate the tendency of the data. The
 number of taxa indicated between brackets corresponds to the untrimmed
 matrices. The subtitle indicates whether the Spearman’s correlation
 between the plotted variables is significant and negative (SN),
 nonsignificant (NS), or significant and positive (SP) at α =
 0.05.Supporting Information
 6Scatter plots for the
 126 matrices with more than 5% of missing data showing the Spearman’s
 correlation coefficient between the Euclidean distance to the centroid for
 each taxon and its percentage of missing entries against the percentage of
 explained variance of the PCos used to calculate the distance to the
 centroid.Supporting Information
 7Histograms for the 33
 matrices with less than 5% of missing data.Supporting Information
 8Results from the 33
 morphological matrices for the studied disparity measures against the
 proportion of randomly-distributed missing entries added to morphological
 matrices, calculated from distance matrices generated from the GED and the
 MORD.Supporting Information
 9Results of simulations
 with groups of taxa and different distributions of missing entries for the
 nine matrices with more than 50 taxa and 50 characters, and less than 5%
 of missing data.Supporting Information
 10Description and results
 of the analysis performed to compare the results of this paper to those of
 Ciampaglio et al. (2001).Matrices for Lehmann et
 al. (2019)Matrices used in the
 analyses, saved in nexus format. Separated by folders for each different
 analysis.Scripts for Lehmann et
 al. (2019)Scripts used for the
 analyses and creation of figures and supplementary
 information.