RAREFACTION ANALYSIS OF MORPHOLOGICAL AND TAXONOMIC DIVERSITY

Our assessment of morphological diversity is influenced by morphological extremes and therefore depends on sample size (taxonomic richness). Rarefaction predicts the morphological diversity that would probably be observed in a sample of reduced size, thereby allowing both compensation for differences in sample size that may be strictly preservational, and analysis of diversity structure, that is, the relationship between morphological and taxonomic diversity. Middle and Late Cambrian trilobites exhibit a diversity structure characterized by many variations on a few morphological themes. In contrast, Middle and Late Ordovician trilobites occupy a larger range of morphospace per unit of species richness. Diversity structure in the Devonian is similar to that in the Middle and Late Ordovician, but the magnitude of morphological diversity is lower in the Devonian, as many fewer species are observed. For blastoids, different aspects of morphological diversity (range of morphospace occupied, number of character states possessed, and number of different regions in morphospace occupied) exhibit different relationships to taxonomic richness. In all cases Permian blastoids are characterized by a diversity structure in which morphological diversity per unit of taxonomic richness is greater than for Devonian blastoids. Changes in morphological diversity in fissiculate blastoids appear to reflect evolution of continuous variation in thecal morphology more than changes in the number of character states. Saunders and Swan's data on Namurian ammonoids illustrate some significant differences in diversity structure among stratigraphic levels, but many apparent differences in morphological diversity are consistent with the possibility that they reflect the sampling of different numbers of species from the same underlying diversity structure. Rarefaction curves are also presented for idealized increases and decreases in diversity, and these are compared to some of the observed changes in trilobites, blastoids, and ammonoids.