Detecting changes in morphospace occupation patterns in the fossil record: characterization and analysis of measures of disparity

Recently, there has been much interest in detecting and measuring patterns of change in disparity. Although most studies have used one or two measures of disparity to quantify and characterize the occupation of morphospace, multiple measures may be necessary to fully detect changes in patterns of morphospace occupation. Also, the ability to detect morphological trends and occupation patterns within morphospace depends on using the appropriate measure(s) of disparity. In this study, seven measures were used to determine and characterize sensitivity to sample size of the data, number of morphological characters, percentage of missing data, and changes in morphospace occupation pattern. These consist of five distance measures—sum of univariate variances, total range, mean distance, principal coordinate analysis volume, average pairwise dissimilarity—and two non-distance measures—participation ratio and number of unique pairwise character combinations. Evaluation of each measure with respect to sensitivity to sample size, number of morphological characters, and percentage of missing data was accomplished by using both simulated and Ordovician crinoid data. For simulated data, each measure of disparity was evaluated for its response to changes of morphospace occupation pattern, and with respect to simulated random and nonrandom extinction events. Changes in disparity were also measured within the Crinoidea across the Permian extinction event. Although all measures vary in sensitivity with respect to species sample size, number of morphological characters, and percentage of missing data, the non-distance measures overall produce the lowest estimates of variance (in bootstrap analyses). The non-distance measures appear to be relatively insensitive to changes in morphospace occupation pattern. All measures, except average pairwise dissimilarity, detect changes in occupation pattern in simulated nonrandom extinction events, but all measures, except number of unique pairwise character combinations and principal coordinate analysis volume, are relatively insensitive to changes in pattern in simulated random extinction events. The distance measures report similar changes in disparity over the Permian extinction event, whereas the non-distance measures differ. This study suggests that each measure of disparity is designed for different purposes, and that by using a combination of techniques a clearer picture of disparity should emerge.