Assessing the robustness of disparity estimates: the impact of morphometric scheme, temporal scale, and taxonomic level in spatangoid echinoids

Abstract

The quantification of disparity is an important aspect of recent macroevolutionary stud ies, and it is usually motivated by theoretical considerations about the pace of innovation and the filling of morphospace. In practice, varying protocols of data collection and analysis have rendered comparisons among studies difficult. The basic question remains, How sensitive is any given dis parity signal to different aspects of sampling and data analysis? Here we explore this issue in the context of the radiation of the echinoid order Spatangoida during the Cretaceous. We compare pat terns at the genus and species levels, with time subdivision into subepochs and into stages, and with morphological sampling based on landmarks, traditional morphometries, and discrete char acters. In terms of temporal scale, similarity of disparity pattern accrues despite a change in tem poral resolution, and a general deceleration in morphological diversification is apparent. Different morphometric methods also produce similar signals. Both the landmark analysis and the discrete character analysis suggest relatively high early disparity, whereas the analysis based on traditional morphometries records a much lower value. This difference appears to reflect primarily the mea surement of different aspects of overall morphology. Disparity patterns are similar at both the ge nus and species levels. Moreover, inclusion or exclusion of the sister order Holasteroida and the stem group Disasteroida in the sampled morphospace did not affect proportional changes in spa tangoid disparity. Similar results were found for spatangoid subclades visa -vis spatangoids as a whole. The relative robustness of these patterns implies that the choice of temporal scale, morpho metric scheme, and taxonomic level may not affect broad trends in disparity and the representation of large-scale morphospace structure.

Does shape matter? Morphological diversity and differential survivorship among Triassic ammonoid genera

“…Most of the correlations in Tables II and III showed only small changes in Spearman's r, and the amounts of variance in explained by the distance from the centroid typically changed by only 1 -2%. This result provides further support for the findings of Ciampaglio et al (2001) and Villier and Eble (2004) that found little change in disparity results with changes in time slice size. The problem of using absolute numerical ages was also addressed through Figures 2 and 3.…”

Morphological Disparity: An Attempt to Widen and to Formalize the Concept

“…Due to this, estimates calculated for morphospaces defined for different datasets may not be compatible directly. To remove this effect, several corrected estimates of morphospace volume are introduced (Ciampaglio et al, 2001;Villier & Eble 2004;Wills 2001;Zelditch et al, 2004). One of them is a relative volume calculated to exclude effect of traits number and dimension, another is a unite (or specific) volume calculated to exclude effect of number of objects.…”

“…The latter might be of special interest, as it allows to reflect also supposed fractal properties of the entire morphospace and its subspaces. The total morphospace volume and partial volumes of its subspaces are currently being analyzed by various dispersion-based or distance-based methods (Eble, 2000;Faleev et al, 2003;Foote, 1996Foote, , 1997Van Valen, 1974;Villier & Eble, 2004;Zelditch et al, 2004). The main (but not principal) difference is that dispersion-based methods imply a priory decomposition of the entire sample dispersion into within-and between-group dispersions, while distancebased methods are free of such precondition, which provides some specific merits (see below).…”

“…This approach makes it possible to analyze both volumes of morphospace and its subspaces and their overlaps. Several techniques of calculations are in use (Ciampaglio et al, 2001;Foote, 1997;Villier & Eble, 2004;Zelditch et al, 2004). In the most simple case (Foote, 1997;Zelditch et al, 2004), the distances among objects and a centroid are calculated for each elementary subspace separately to give an estimation of the latter's partial volume, and then the total morphospace volume is calculated as a sum of all the elementary ones (see notes on its insufficiency above).…”

“…It allows to evaluate statistical significance of differences between any pair of morphospaces /subspaces by their volume estimates (Zelditch et al, 2004). However, more popular is a non-parametric approach that employs various resampling methods (Pavlimov & Nanova, 2009;Villier & Eble, 2004;Zelditch et al, 2004). They imply bringing some stochastic component in the original data matrix and subsequent analyses of thus generated matrices by standard algorithms.…”