Effect of the generalized Euclidean distance on disparity analyses of morphological matrices

EZCURRA, MARTÍN D.; LEHMANN, OSCAR EMILIO RODRIGO; LLOYD, GRAEME T.; BUTLER, RICHARD J.

Puerto Madryn

Congreso; Reunión de Comunicaciones de la Asociación Paleontológica Argentina; 2018

Universidad Nacional de la Patagonia San Juan Bosco

A large number of palaeontological studies dealing with morphological disparity has been published over the last decade. A critical step of these studies is the transformation of the morphological matrix into a distance matrix. The generalized Euclidean distance (GED) is the most extensively used distance measure to do this, in part because it allows the use of matrices with high amounts of missing data without the need to remove taxa if a subsequent ordination of the data set is desired to reduce dimensionality. The GED accomplishes this by replacing the missing dissimilarities with a mean weighted dissimilarity. Previous studies suggested that the GED may generate a bias in the morphospace and in some disparity measures, but a detailed analysis of this effect was lacking. By studying over 150 morphological matrices, we find that 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 percentages of missing data. Results recovered using an alternative distance measure, Maximum Observed Rescaled Distance (MORD), are more robust to the presence of missing data. This is possibly because MORD does not replace the missing dissimilarities with a mean value. We recommend against using the GED for matrices with a high amount of missing data.