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

Abstract

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.

Phylogeny and tempo of diversification in the superradiation of spiny-rayed fishes

“…Morphological variation, or "disparity," within each of these time bins was calculated as the sum of variances on retained morphospace axes (multivariate variance). In contrast to other measures of disparity, multivariate variance has the desirable property of being relatively insensitive to variation in sample size (48). (Fig.…”

The origin and early radiation of dinosaurs

“…Statistical tests can then be used to determine if certain groups of organisms (usually binned either taxonomically or by time) have a greater diversity of morphologies than other groups. In statistical terms, morphological diversity can be quantified in many ways, but the two most common methods calculate range and variance statistics for the different bins (Wills et al, 1994;Ciampaglio et al, 2001). Range measures denote the entire spread of morphological variation (the size of morphospace occupied by the group), whereas variance measures indicate average dissimilarity among members of the group (the spread of the group in morphospace).…”

Dinosaur morphological diversity and the end-Cretaceous extinction

“…Quantitative analysis of morphological disparity-the variability in anatomical characters and body plans expressed by a group of organisms [23][24][25][26][27] -can also provide crucial insights into the evolutionary trajectory of dinosaurs during the latest Cretaceous. Disparity measures document changes in the anatomical diversity of clades, which may be a general proxy for the breadth of functional and ecological behaviour expressed, regardless of whether those clades had high or low species richness or faunal abundance.…”