NONLANDMARK CLASSIFICATION IN PALEOBIOLOGY Traditional landmark analysis has advan-
tages in two areas over CP-analysis. First, type 1 landmarks, as used in the Atwood et al. (2012) study, are points that have anatomical homology between specimens. Whereas calculated geometric “feature points” may change position between species, the type 1 landmarks represent identical points, allow- ing for different types of questions to be addressed; however, as mentioned above, landmarks could be used as the feature points for CP distance in a future study. Second, landmarks used for the Atwood
et al. (2012) study require preservation of only the A ambulacrum and adjacent interambula- cra for any given specimen. Specimens could be analyzed with confidence even if other portions of the theca were missing or covered with matrix. The CP-distance method, as presently used, requires complete preservation of thecal surfaces preserved three dimension- ally and without significant adhering matrix. Our forthcoming work will address both of these issues.
Conclusion
We compare a novel computational- geometry methodology based on continuous Procrustes distance with the standard method of discrete Procrustes distance for tackling the problem of species discrimination on Pentremites. Our results show that the CP- distance methodology is not only (slightly) superior at resolving the issue but also sig- nificantly reduces processing time and vulner- ability to human error. Specifically, advantages appear in the separa-
tion of P. tulipiformis species from the cluster containing the P. fredericki and P. spicatus species. In contrast, Atwood and Sumrall (2012) clusters afew P. fredericki as P. tulipiformis,and the respective clusters are visually mixed. We attribute this advantage to the CP-distance calculation taking into consideration curvature measurements,which reflect the concavity of the specimens’ plates. This differs significantly from the output that can be obtained using DP distance alone; in that methodology, concavity is measured only as a subtle change in the position of a couple of landmarks.
705
This phenomenon is vastly amplified when large regions of the sample are concave and eventually adds up to a large difference in the resulting CP distance. As a consequence, we are effectively able to separate species that are concave from those that are not. In addition, we determined the sensitivity of
the CP-distance methodology to varying resolutions of scans. We found a threshold of approximately 1000 points per scan, under which the reliability of the method begins to wither. Nevertheless, we showed that even at the lowest resolution levels there is informa- tion to be gained. Because of the relatively low cost and short time involved in performing low-resolution scans, our technique opens the door for future researchers in the area to produce several low-cost, preliminary studies; this would allow them to choose where to invest their in-depth efforts more effectively.
Acknowledgments The authors would like to thank two anony-
mous reviewers for their comments, which substantially improved the manuscript. Special thanks to J. A. Waters at the Appalachian State University for very helpful conversations and B. Allen at the University of Tennessee, Knoxville, for suggestions and discussions.
References
Atwood, J. W., and C. D. Sumrall. 2012. Morphometric investiga- tion of the Pentremites fauna from the Glen Dean Formation, Kentucky. Journal of Paleontology 86:813–828.
Bookstein, F. L., P. Gunz, P.Mitteroecker,H. Prossinger,K. Schaefer, and H. Seidler. 2003. Cranial integration in Homo:singularwarps analysis of the midsagittal plane in ontogeny and evolution. Journal ofHuman Evolution 44:167–187.
Budd, A. F., K. G. Johnson, and D. C. Potts. 1994. Recognizing morphospecies in colonial reef corals, I. Landmark-based methods. Paleobiology 20:484–505.
Cox, T. F., and M. A. A. Cox. 2001. Multidimensional scaling. Chapman and Hall, Boca Raton, Fla.
Ferreira, L., and D. B. Hitchcock.
2009.Acomparison of hierarchical methods for clustering functional data. Communications in Statistics Simulation and Computation 38:1925–1949.
Foote, M. 1991. Morphological and taxonomic diversity in clade’s history: the blastoid record and stochastic simulations. Contributions from the Museum of Paleontology, University of Michigan 28:101–140.
Frost, S. R., L. F. Marcus, F. L. Bookstein, D. P. Reddy, and E. Delson. 2003. Cranial allometry, phylogeography, and systema- tics of large-bodied papionins (Primates: Cercopithecinae) inferred from geometric morphometric analysis of landmark data. Anatomical Record Part A 275:1048–1072.
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