Paleobiology, 42(4), 2016, pp. 696–706 DOI: 10.1017/pab.2016.19
Nonlandmark classification in paleobiology: computational geometry as a tool for species discrimination
Joshua Mike, Colin D. Sumrall, Vasileios Maroulas, and Fernando Schwartz
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 computa-
tional 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.
Joshua Mike, Vasileios Maroulas, and Fernando Schwartz. Department ofMathematics, University of Tennessee, Knoxville, Tennessee 37996, U.S.A. E-mail:
mike@math.utk.edu,
maroulas@math.utk.edu,
Fernando@math.utk.edu
Colin D. Sumrall. Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, Tennessee 37996, U.S.A. E-mail:
csumrall@utk.edu
Accepted: 25 March 2016 Published online: 18 May 2016 Data available from the Dryad Digital Repository:
http://dx.doi.org/10.5061/dryad.cg7b7
Introduction Shape has often been used along with
discrete morphologies to investigatemany ques- tions in biology and paleobiology, including species discrimination (Budd et al. 1994; Villemant et al. 2007; Maderbacher et al. 2008; Atwood and Sumrall 2012), ontogeny (Rohlf, 1998; Bookstein et al. 2003; Sheets et al. 2004) ecophenotypic variation (Reyment et al. 1988; Wilk and Bieler 2009; Piras et al. 2010), evolution via heterochrony (Mitteroecker et al. 2004, 2005; Lieberman et al. 2007), functional morphology (Zollikofer and Ponce De Léon 2004), phylogeo- graphy (Frost et al. 2003), and many others (Zelditch et al. 2012). Recent advances involving 3D landmark-based analysis have made marked improvements but nevertheless still rely on an expert handpicking a set of landmark points that represent the geometry of an entire object. The representation of shape by a relatively few
© 2016 The Paleontological Society. All rights reserved.
landmarksissubjectivebecause user-selected points are chosen for the ease of consistent identification by the user and not necessarily because they represent points with the greatest
varianceamonggroups.Additionally, important shape variation outside the landmarks, such as concavity versus convexity,will not be captured by these methods, limiting their usefulness in many situations. To mitigate these problems, we apply a
recent computational-geometry technique called continuous Procrustes distance, or CP distance (see Lipman et al. [2013]). This methodology determines dissimilarity, or distance, between pairs of 3D surface scans of specimens drawn from mixed populations of species. Form taxa are best separated by incorporating a particular combination of geometric features of the 3D scans (such as curvature and area density) into the CP-distance algorithm. The statistical
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