Contributions of individual taxa to overall morphological disparity

Two methods are discussed for assessing the contributions of subgroups to the morphological disparity of the larger group containing them. (1) Given an ordination of points representing specimens or species in morphological space, morphological disparity of the entire group is measured as the average squared distance of points from the centroid. The contribution that a subgroup makes to morphological disparity is measured as the average squared distance of its points from the overall centroid (not the subgroup centroid), weighted by the subgroup sample size relative to the total group sample size. Thus, morphological disparity of a group can be additively partitioned into the disparity components of its subgroups, and the relative contributions of these subgroups can be assessed quantitatively. (2) An alternative approach is to compare morphological disparity of a group to the disparity it would have if a certain subgroup were omitted. If the resulting disparity differs substantially from the original disparity, then the subgroup in question is considered to have a significant effect on morphological disparity. Because some subgroups are very centralized in morphological space, omitting them can cause an increase in morphological disparity when disparity is measured as the average dissimilarity among species. In general, relatively large subgroups that are located peripherally in morphospace make the greatest contributions to morphological disparity, and failure to sample smaller groups often has little effect on disparity estimates. The two methods are applied to morphological disparity in trilobites, partitioned at different levels in the taxonomic hierarchy. Results of the two methods are intuitively reasonable and largely in agreement, and point to the predominance of Early Cambrian olenelloids, Cambro-Ordovician Libristoma, Ordovician Asaphina and Cheirurina, Siluro-Devonian Phacopida and Phacopina, and Devonian Proetida.