Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T20:56:07.571Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlandmark classification in paleobiology: computational geometry as a tool for species discrimination

Published online by Cambridge University Press:  18 May 2016

Joshua Mike ,
Colin D. Sumrall ,
Vasileios Maroulas  and
Fernando Schwartz
Joshua Mike
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, U.S.A. E-mail: [email protected], [email protected], [email protected]
Colin D. Sumrall
Affiliation:
Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, Tennessee 37996, U.S.A. E-mail: [email protected]
Vasileios Maroulas
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, U.S.A. E-mail: [email protected], [email protected], [email protected]
Fernando Schwartz
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, U.S.A. E-mail: [email protected], [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

One important and sometimes contentious challenge in paleobiology is discriminating between species, which is increasingly accomplished by comparing specimen shape. While lengths and proportions are needed to achieve this task, finer geometric information, such as concavity, convexity, and curvature, plays a crucial role in the undertaking. Nonetheless, standard morphometric methodologies such as landmark analysis are not able to capture in a quantitative way these features and other important fine-scale geometric notions.

Here we develop and implement state-of-the-art techniques from the emerging field of computational geometry to tackle this problem with the Mississippian blastoid Pentremites. We adapt a previously known computational framework to produce a measure of dissimilarity between shapes. More precisely, we compute “distances” between pairs of 3D surface scans of specimens by comparing a mix of global and fine-scale geometric measurements. This process uses the 3D scan of a specimen as a whole piece of data incorporating complete geometric information about the shape; as a result, scans used must accurately reflect the geometry of whole, undamaged, undeformed specimens. Using this information we are able to represent these data in clusters and ultimately reproduce and refine results obtained in previous work on species discrimination. Our methodology is landmark free, and therefore faster and less prone to human error than previous landmark-based methodologies.

Type
Methods in Paleobiology
Information
Paleobiology , Volume 42 , Issue 4 , November 2016 , pp. 696 - 706
Copyright
Copyright © 2016 The Paleontological Society. All rights reserved 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Atwood, J. W., and Sumrall, C. D.. 2012. Morphometric investigation of the Pentremites fauna from the Glen Dean Formation, Kentucky. Journal of Paleontology 86:813–828.CrossRefGoogle Scholar
Bookstein, F. L., Gunz, P., Mitteroecker, P., Prossinger, H., Schaefer, K., and Seidler, H.. 2003. Cranial integration in Homo: singular warps analysis of the midsagittal plane in ontogeny and evolution. Journal of Human Evolution 44:167–187.Google Scholar
Budd, A. F., Johnson, K. G., and Potts, D. C.. 1994. Recognizing morphospecies in colonial reef corals, I. Landmark-based methods. Paleobiology 20:484–505.Google Scholar
Cox, T. F., and Cox, M. A. A.. 2001. Multidimensional scaling. Chapman and Hall, Boca Raton, Fla.Google Scholar
Ferreira, L., and Hitchcock, D. B.. 2009. A comparison of hierarchical methods for clustering functional data. Communications in Statistics Simulation and Computation 38:1925–1949.Google Scholar
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.Google Scholar
Frost, S. R., Marcus, L. F., Bookstein, F. L., Reddy, D. P., and Delson, E.. 2003. Cranial allometry, phylogeography, and systematics of large-bodied papionins (Primates: Cercopithecinae) inferred from geometric morphometric analysis of landmark data. Anatomical Record Part A 275:1048–1072.Google Scholar
Galloway, J. J., and Kaska, H. V.. 1957. Genus Pentremites and its species. Geological Society of America Memoir 69:1–114.CrossRefGoogle Scholar
Lieberman, D. E., Carlo, J., de León, M. P., and Zollikofer, C. P.. 2007. A geometric morphometric analysis of heterochrony in the cranium of chimpanzees and bonobos. Journal of Human Evolution 52:647–662.Google Scholar
Lipman, Y., Al-Aifari, R., and Daubechies, I.. 2013. The continuous Procrustes distance between two surfaces. Communications on Pure and Applied Mathematics 66:934–964.Google Scholar
Macurda, D. B. Jr. 1966. The ontogeny of the Mississippian blastoid Orophocrinus . Journal of Paleontology 40:92–124.Google Scholar
Macurda, D. B. Jr. 1975. The Pentremites (Blastoidea) of the Burlington Limestone (Mississippian). Journal of Paleontology 49:346–373.Google Scholar
Maderbacher, M., Bauer, C., Herler, J., Postl, L., Makasa, L., and Sturmbauer, C.. 2008. Assessment of traditional versus geometric morphometrics for discriminating populations of the Tropheus moorii species complex (Teleostei: Cichlidae), a Lake Tanganyika model for allopatric speciation. Journal of Zoological Systematics and Evolutionary Research 46:153–161.CrossRefGoogle Scholar
Mitteroecker, P., Gunz, P., Weber, G. W., and Bookstein, F. L.. 2004. Regional dissociated heterochrony in multivariate analysis. Annals of Anatomy–Anatomischer Anzeiger 186:463–470.CrossRefGoogle ScholarPubMed
Mitteroecker, P., Gunz, P., and Bookstein, F. L.. 2005. Heterochrony and geometric morphometrics: a comparison of cranial growth in Pan paniscus versus Pan troglodytes . Evolution and Development 7:244–258.Google Scholar
Piras, P., Marcolini, F., Raia, P., Curcio, M., and Kotsakis, T.. 2010. Ecophenotypic variation and phylogenetic inheritance in first lower molar shape of extant Italian populations of Microtus (Terricola) savii (Rodentia). Biological Journal of the Linnean Society 99:632–647.Google Scholar
Reyment, R. A., Bookstein, F. L., McKenzie, K. G., and Majoran, S.. 1988. Ecophenotypic variation in Mutilus pumilus (Ostracoda) from Australia, studied by canonical variate analysis and tensor biometrics. Journal of Micropalaeontology 7:11–20.Google Scholar
Rohlf, F. J. 1998. On applications of geometric morphometrics to studies of ontogeny and phylogeny. Systematic Biology 47:147–158.CrossRefGoogle ScholarPubMed
Sheets, H. D., Kim, K., and Mitchell, C. E.. 2004. A combined landmark and outline-based approach to ontogenetic shape change in the Ordovician trilobite Triarthrus becki . Pp. 67–82 in A.M.T. Elewa, ed. Morphometrics: applications in biology and paleontology. Springer Verlag, Berlin.CrossRefGoogle Scholar
Sokal, R. R., and Rohlf, F. J.. 2012. Biometry: the principles and practices of statistics in biological research, 4th ed. Freeman, New York.Google Scholar
Tan, P., Steinbach, M., and Kumar, V.. 2005. Introduction to data mining. Addison-Wesley, Boston.Google Scholar
Villemant, C., Simbolotti, G., and Kenis, M.. 2007. Discrimination of Eubazus (Hymenoptera, Braconidae) sibling species using geometric morphometrics analysis of wing venation. Systematic Entomology 32:625–634.Google Scholar
Waters, J. A., Horowitz, A. S., and Macurda, D. B.. 1985. Ontogeny and phylogeny of the Carboniferous blastoids Pentremites . Journal of Paleontology 59:701–712.Google Scholar
Wilk, J., and Bieler, R.. 2009. Ecophenotypic variation in the Flat Tree Oyster, Isognomon alatus (Bivalvia: Isognomonidae), across a tidal microhabitat gradient. Marine Biology Research 5:155–163.Google Scholar
Zelditch, M. L., Swiderski, D. L., and Sheets, H. D.. 2012. Geometric morphometrics for biologists: a primer. Academic, London.Google Scholar
Zollikofer, C. P. E., and Ponce De León, M. S.. 2004. Kinematics of cranial ontogeny: heterotopy, heterochrony, and geometric morphometric analysis of growth models. Journal of Experimental Zoology Part B 302:322–334.Google Scholar