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PATTERNS AND PROCESSES IN MORPHOSPACE: GEOMETRIC MORPHOMETRICS OF THREE-DIMENSIONAL OBJECTS

Published online by Cambridge University Press:  27 April 2017

P. David Polly  and
Gary J. Motz
P. David Polly
Affiliation:
Departments of Geological Sciences, Biology, and Anthropology, Indiana University, 1001 E. 10th Street, Bloomington, Indiana 47405, USA 〈pdpolly@indiana.edu〉
Gary J. Motz
Affiliation:
Department of Geological Sciences and Center for Biological Research Collections, Indiana University, 1001 E. 10th Street, Bloomington, Indiana 47405, USA 〈garymotz@indiana.edu〉
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Abstract

Focusing on geometric morphometrics (GMM), we review methods for acquiring morphometric data from 3-D objects (including fossils), algorithms for producing shape variables and morphospaces, the mathematical properties of shape space, especially how they relate to morphogenetic and evolutionary factors, and issues posed by working with fossil objects. We use the Raupian shell-coiling equations to illustrate the complexity of the relationship between such factors and GMM morphospaces. The complexity of these issues re-emphasize what are arguably the two most important recommendations for GMM studies: 1) always use multivariate methods and all of the morphospace axes in an analysis; and 2) always anticipate the possibility that the factors of interest can have complex, nonlinear relationships with shape.

Type
Research Article
Information
The Paleontological Society Papers , Volume 22: Virtual Paleontology , September 2016 , pp. 71 - 99
Copyright
Copyright © 2017, The Paleontological Society 

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References

Ackermann, R.R., and Cheverud, J.M., 2000, Phenotypic covariance structure in tamarins (genus Saguinus): a comparison of variation patterns using matrix correlation and common principal component analysis: American Journal of Physical Anthropology, v. 111, p. 489–501.Google Scholar
Adams, D.C., 2013, Quantifying and comparing phylogenetic evolutionary rates for shape and other high-dimensional phenotypic data: Systematic Biology, v. 63, p. 166–177.Google Scholar
Adams, D.C., 2014a, A generalized K statistic for estimating phylogenetic signal from shape and other high-dimensional multivariate data: Systematic Biology, v. 63, p. 685–697.CrossRefGoogle ScholarPubMed
Adams, D.C., 2014b, A method for assessing phylogenetic least squares models for shape and other high-dimensional multivariate data: Evolution, v. 68, p. 2675–2688.Google Scholar
Adams, D.C., and Collyer, M.L., 2009, A general framework for the analysis of phenotypic trajectories in evolutionary studies: Evolution, v. 63, p. 1143–1154.Google Scholar
Adams, D.C., and Collyer, M.L., 2015, Permutation tests for phylogenetic comparative analyses of high-dimensional shape data: What you shuffle matters: Evolution, v. 69, p. 823–829.CrossRefGoogle ScholarPubMed
Adams, D.C., and Otarola-Castillo, E., 2013, Geomorph: an R package for the collection and analysis of geometric morphometric shape data: Methods in Ecology and Evolution, v. 4, p. 393–399, DOI: 10.1111/2041-210X.12035.CrossRefGoogle Scholar
Adams, D.C., Rohlf, F.J., and Slice, D.E., 2004, Geometric morphometrics: Ten years of progress following the ‘revolution’: Hystrix. v. 71, p. 5–16, DOI: 10.1080/11250000409356545.Google Scholar
Adams, D.C., Rohlf, F.J., and Slice, D.E., 2013, A field comes of age: Geometric morphometrics in the 21st century: Hystrix, v. 24, p. 7–14, DOI: 10.4404/hystrix-24.1-6283.Google Scholar
Angielczyk, K.D., and Sheets, H.D., 2007, Investigation of simulated tectonic deformation in fossils using geometric morphometrics: Paleobiology, v. 33, p. 125–148.CrossRefGoogle Scholar
Arnold, S.J., Pfrender, M.E., and Jones, A.G., 2001, The adaptive landscape as a conceptual bridge between micro- and macroevolution: Genetica, v. 112/113, p. 9–32.Google Scholar
Bastir, M., Rosas, A., and O’Higgins, P., 2006, Craniofacial levels and the morphological maturation of the human skull: Journal of Anatomy, v. 209, p. 637–654.Google Scholar
Bookstein, F.L., 1989, Principal warps: Thin-plate splines and the decomposition of deformations: IEEE Transactions in Pattern Analysis and Machine Intelligence, v. 11, p. 567–585.Google Scholar
Bookstein, F.L., 1991, Morphometric Tools for Landmark Data: Cambridge, UK, Cambridge University Press, 435 p.Google Scholar
Bookstein, F.L., 1997, Landmark methods for forms without landmarks: Morphometrics of group differences in outline shape: Medical Image Analysis, v. 1, p. 225–243, DOI: 10.1016/S1361-8415(97)85012-8.Google Scholar
Bookstein, F.L., 2013, Random walk as a null model for high-dimensional morphometrics of fossil series: Geometrical considerations: Paleobiology, v. 39, p. 52–74, DOI: 10.1666/0094-8373-39.1.52.Google Scholar
Bookstein, F.L., 2016, The inappropriate symmetries of multivariate statistical analysis in geometric morphometrics: Evolutionary Biology, v. 43, no. 3, p. 277–313, DOI: 10.1007/s11692-016-9382-7.Google Scholar
Bookstein, F.L., Chernoff, B., Elder, R., Humphries, J., Smith, G., and Strauss, R., 1985, Morphometrics in Evolutionary Biology: Philadelphia, Academy of Natural Sciences of Philadelpia, Special Publication, v. 15, 277 p.Google Scholar
Bookstein, F.L., Gunz, P., Mitteroecker, P., Prossinger, H., Schaeffer, K., and Seidler, H., 2003, Cranial integration in Homo: Singular warps analysis of the midsagittal plane in ontogeny and evolution: Journal of Human Evolution, v. 44, p. 167–187.CrossRefGoogle ScholarPubMed
Boyd, A., and Motani, R., 2008, Three-dimensional re-evaluation of the deformation removal technique based on ‘jigsaw puzzling’: Palaeontologia Electronica, no. 11.2.7A, p. 1–7. http://palaeo-electronica.org/2008_2/131/131.pdf (accessed July 2016).Google Scholar
Butler, M.A., and King, A.A., 2004, Phylogenetic comparative analysis: A modeling approach for adaptive evolution: American Naturalist, v. 164, p. 683–695.Google Scholar
Cardini, A., and Loy, A., eds., 2013, Virtual Morphology and Evolutionary Morphometrics in the New Millenium: Hystrix, v. 24, p. 1–140.Google Scholar
Caumul, R., and Polly, P.D., 2005, Phylogenetic and environmental components of morphological variation: Skull, mandible, and molar shape in marmots (Marmota, Rodentia): Evolution, v. 59, p. 2460–2472.Google Scholar
Chapman, R.E., 1990, Conventional Procrustes approaches, in Rohlf, F.J., and Bookstein, F.L., eds., Proceedings of the Michigan Morphometrics Workshop: Ann Arbor, Michigan, University of Michigan Museum of Zoology, p. 251–267.Google Scholar
Cheverud, J.M., 1982, Phenotypic, genetic, and environmental morphological integration in the cranium: Evolution, v. 36, p. 499–516.Google Scholar
Cignoni, P., Callieri, M., Corsini, M., Dellepiane, M., Ganovelli, F., and Ranzuglia, G., 2008, MeshLab: An open-source mesh processing tool, in Scarano, V., De Chiara, R., and Erra, U., eds., Eurographics Italian Chapter Conference: Geneva, Austria, Eurographics Association, p. 129–136.Google Scholar
Claude, J., 2008, Morphometrics with R: New York, Springer, 317 p.Google Scholar
Collins, B.M.J., 2014, Three-dimensional Bookstein shape coordinates and functional morphology of passive suspension feeding in Composita (Brachiopoda, Athyridida) [Master’s thesis]: Edmonton, Alberta, Canada, The University of Alberta, 92 p.Google Scholar
Collyer, M.L., and Adams, D.C., 2007, Analysis of two-state multivariate phenotypic change in ecological studies: Ecology, v. 88, p. 683–692.CrossRefGoogle ScholarPubMed
Collyer, M.L., and Adams, D.C., 2013, Phenotypic trajectory analysis: Comparison of shape change patterns in evolution and ecology: Hystrix, v. 24, p. 75–83.Google Scholar
Costa, A.G., 2010, A geometric morphometric assessment of plan shape in bone and stone Acheulean bifaces from the middle Pleistocene site of Castel di Guido, Latium, Italy, in Lycett, S., and Chauhan, P., eds., New Perspectives on Old Stones: New York, Springer, p. 23–41.Google Scholar
Dryden, I.L., and Mardia, K.V., 1998, Statistical Shape Analysis: Chichester, UK, John Wiley and Sons, 347 p.Google Scholar
Felsenstein, J., 1985, Phylogenies and the comparative method: American Naturalist, v. 125, p. 1–15.Google Scholar
Felsenstein, J., 2012, A comparative method for both discrete and continuous characters using the threshold model: American Naturalist, v. 179, p. 145–156.CrossRefGoogle ScholarPubMed
Figueirido, B., Palmqvist, P., and Pérez-Claros, J.A., 2009, Ecomorphological correlates of craniodental variation in bears and paleobiological implications for extinct taxa: An approach based on geometric morphometrics: Journal of Zoology, v. 277, p. 70–80.Google Scholar
Garland, T. Jr., Harvey, P.H., and Ives, A.R., 1992, Procedures for the analysis of comparative data using phylogenetically independent contrasts: Systematic Biology, v. 41, p. 18–32.CrossRefGoogle Scholar
Gerber, S., 2014, Not all roads can be taken: Development induces anisotropic accessibility in morphospace: Evolution and Development, v. 16, p. 373–381, DOI: 10.1111/ede.12098.Google Scholar
Gerber, S., and Hopkins, M.J., 2011, Mosaic heterochrony and evolutionary modularity: The trilobite genus Zacanthopsis as a case study: Evolution, v. 65, p. 3241–3252, DOI: 10.1111/j.1558-5646.2011.01363.x.Google Scholar
Gerber, S., Neige, P., and Eble, G.J., 2007, Combining ontogenetic and evolutionary scales of morphological disparity: A study of early Jurassic ammonites: Evolution and Development, v. 9, p. 472–482.Google Scholar
Gingerich, P.D., 1993, Quantification and comparison of evolutionary rates: American Journal of Science, v. 293, p. 453–478.CrossRefGoogle Scholar
Gingerich, P.D., 2009, Rates of evolution: Annual Review of Ecology, Evolution, and Systematics, v. 40, p. 657–675.Google Scholar
Gómez-Robles, A., and Polly, P.D., 2012, Morphological integration in the hominin dentition: Evolutionary, developmental, and functional factors: Evolution, v. 66, p. 1024–1043, DOI: 10.1111/j.1558-5646.2011.01508.x.Google Scholar
Gómez-Robles, A., Bermúdez De Castro, J.M., Arsuaga, J.-L., Carbonell, E., and Polly, P.D., 2013, No known hominin species matches the expected dental morphology of the last common ancestor of Neanderthals and modern humans: Proceedings of the National Academy of Sciences, USA, v. 110, p. 18196–18201, DOI: 10.1073/pnas.1302653110.Google Scholar
Goswami, A., and Polly, P.D., 2010a, Methods for studying morphological integration, modularity and covariance evolution, in Alroy, J., and Hunt, G., eds., Quantitative Methods in Paleobiology: Paleontological Society Papers, v. 16, p. 213–243.Google Scholar
Goswami, A., and Polly, P.D., 2010b, The influence of character correlations of phylogenetic analyses: A case study of the carnivoran cranium, in Goswami, A., and Friscia, A., eds., Carnivoran Evolution: New Views on Phylogeny, Form, and Function: Cambridge, UK, Cambridge University Press, p. 141–164.CrossRefGoogle Scholar
Gower, J.C., 1971, Statistical methods of comparing different multivariate analyses of the same data, in Hodson, F.R., Kendall, D.G., and Tautu, P., eds., Mathematics in the Archaeological and Historical Sciences: Edinburgh, Scotland, Edinburgh University Press, p. 138–149.Google Scholar
Gower, J.C., 1975, Generalized Procrustes analysis: Psychometrika, v. 40, p. 33–50, DOI: 10.1007/BF02291478.Google Scholar
Grafen, A., 1989, The phylogenetic regression: Philosophical Transactions of the Royal Society, Series B, v. 326, p. 119–157.Google ScholarPubMed
Gunz, P., 2005, Statistical and geometric reconstruction of hominid crania: Reconstructing australopithecine ontogeny [Ph.D. Thesis]: Vienna, Austria, University of Vienna, 255 p.Google Scholar
Gunz, P., and Mitteroecker, P., 2013, Semilandmarks: A method for quantifying curves and surfaces: Hystrix, v. 24, p. 103–109, DOI: 10.4404/hystrix-24.1-6292.Google Scholar
Gunz, P., Mitteroecker, P., and Bookstein, F.L., 2005, Semilandmarks in three dimensions, in Slice, D.E., ed., Modern Morphometrics in Physical Anthropology: New York, Kluwer, p. 73–93.Google Scholar
Gunz, P., Mitteroecker, P., Neubauer, S., Weber, G.W., and Bookstein, F.L., 2009, Principles for the virtual reconstruction of hominin crania: Journal of Human Evolution, v. 57, p. 48–62.CrossRefGoogle ScholarPubMed
Hammer, Ø., and Harper, D.A.T., 2006, Paleontological Data Analysis: Oxford, UK, Wiley-Blackwell, 368 p.Google Scholar
Hammer, Ø., Harper, D.A.T., and Ryan, P.D., 2001, PAST: Paleontological statistics software package for education and data analysis: Palaeontologia Electronica, v. 4, no. 1, art. 4A, 9 p. http://palaeo-electronica.org/2001_1/past/issue1_01.htm.Google Scholar
Harmon, L.J., Losos, J.B., Davies, T.J., Gillespie, R.G., Gittleman, J.L., Jennings, W.B., Kozak, K.H., McPeek, M.A., Moreno-Roark, F., Near, T.J., and Purvis, A., 2010, Early bursts of body size and shape evolution are rare in comparative data: Evolution, v. 64, p. 2385–2396.Google ScholarPubMed
Harvey, P.H., and Pagel, M.D., 1991, The Comparative Method in Evolutionary Biology: Oxford, UK, Oxford University Press, 239 p.CrossRefGoogle Scholar
Head, J.J., and Polly, P.D., 2015, Evolution of the snake body form reveals homoplasy in amniote Hox gene function: Nature, v. 520, p. 86–89, DOI: 10.1038/nature14042.Google Scholar
Hughes, N.C., and Jell, P.A., 1992, A statistical/computer graphic technique for assessing variation in tectonically deformed fossils and its application to Cambrian trilobites from Kashmir: Lethaia, v. 25, p. 317–330.Google Scholar
Hunt, G., 2007a, Evolutionary divergence in directions of high phenotypic variance in the ostracode genus Poseidonamicus : Evolution, v. 61, p. 1560–1576, DOI: 10.1111/j.1558-5646.2007.00129.x.CrossRefGoogle ScholarPubMed
Hunt, G., 2007b, The relative importance of directional change, random walks, and stasis in the evolution of fossil lineages: Proceedings of the National Academy of Sciences, USA, v. 104, p. 18404–18408.Google Scholar
Hunt, G., and Rabosky, D.L., 2010, Phenotypic evolution in fossil species: Pattern and process. Annual Review of Earth and Planetary Science, v. 42, p. 421–441, DOI: 10.1146/annurev-earth-040809-152524.CrossRefGoogle Scholar
Kim, K., Sheets, H.D., Haney, R.A., and Mitchell, C.E., 2002, Morphometric analysis of ontogeny and allometry of the Middle Ordovician trilobite Triarthrus becki : Paleobiology, v. 28, p. 364–377, DOI: 10.1666/0094-8373(2002)028<0364:MAOOAA>2.0.CO;2.Google Scholar
Klingenberg, C.P., 2011, MorphoJ: An integrated software package for geometric morphometrics: Molecular Ecology Resources, v. 11, p. 353–357, DOI: 10.1111/j.1755-0998.2010.02924.CrossRefGoogle ScholarPubMed
Klingenberg, C.P., 2013, Visualization in geometric morphometrics: How to read and how to make graphs showing shape changes: Hystrix, v. 24, p. 15–24, DOI: 10.4404/hystrix-24.1-7691.Google Scholar
Klingenberg, C.P., and Gidaszewski, N.A., 2010, Testing and quantifying phylogenetic signals and homoplasy in morphometric data: Systematic Biology, v. 59, p. 245–261.Google Scholar
Klingenberg, C.P., and Marugán-Lobón, J., 2013, Evolutionary covariation in geometric morphometric data: Analyzing integration, modularity, and allometry in a phylogenetic context: Systematic Biology, v. 62, p. 591–610, DOI: 10.1093/sysbio/syt025.Google Scholar
Kowalewski, M., and Novack-Gottshall, P., 2010, Resampling methods in paleontology, in Alroy, J., and Hunt, G., eds., Quantitative Methods in Paleobiology: Paleontological Society Papers, v. 16, p. 19–54.Google Scholar
Lebrun, R., 2014, ISE-MeshTools, a 3D interactive fossil reconstruction freeware, in 12th Annual Meeting of the European Association of Vertebrate Paleontologists, Torino, Italy, 11 June 2014: Torino, Italy, European Association of Vertebrate Paleontologists, p. 19.Google Scholar
Legendre, P., and Legendre, L., 1998, Numerical Ecology: Amsterdam, The Netherlands, Elsevier, 853 p.Google Scholar
Lohmann, G.P., 1983, Eigenshape analysis of microfossils: A general morphometric procedure for describing changes in shape: Mathematical Geology, v. 15, p. 659–672, DOI: 10.1007/BF01033230.CrossRefGoogle Scholar
MacLeod, N., 1999, Generalizing and extending the Eigenshape method of shape space visualization and analysis: Paleobiology, v. 25, p. 107–138.Google Scholar
MacLeod, N., 2002, Geometric morphometrics and geological shape-classification systems: Earth-Science Reviews, v. 59, p. 27–47.Google Scholar
MacLeod, N., and Forey, P., eds., 2002, Morphology, Shape, and Phylogenetics: Abingdon, UK, Taylor and Francis, 318 p.Google Scholar
MacLeod, N., and Rose, K.D., 1993, Inferring locomotor behavior in Paleogene mammals via Eigenshape analysis: American Journal of Science, v. 293A, p. 300–355, DOI: 10.2475/ajs.293.A.300.Google Scholar
Manly, B.F.J., 2004, Randomization, Bootstrap, and Monte Carlo Methods in Biology: Cornwall, UK, Chapman and Hall, 480 p.Google Scholar
Marcus, L.F., Bello, E., and García-Valdecasas, A., eds., 1993, Contributions to Morphometrics: Madrid, Spain, Museo Nacional de Ciencias Naturales Monografias, 270 p.CrossRefGoogle Scholar
Marcus, L.F., Corti, M., Loy, A., Naylor, G., and Slice, D.E., eds., 1996, Advances in Morphometrics: New York, Plenum Press, 588 p.Google Scholar
Mardia, K.V., Bookstein, F.L., and Moreton, I.J., 2000, Statistical assessment of bilateral symmetry of shapes: Biometrika, v. 87, p. 285–300.Google Scholar
Marroig, G., Melo, D.A., and Garcia, G., 2012, Modularity, noise, and natural selection: Evolution, v. 66, p. 1506–1524.Google Scholar
Martins, E.P., and Hansen, T.F., 1997, Phylogenies and the comparative method: A general approach to incorporating phylogenetic information into the analysis of interspecific data: American Naturalist, v. 149, p. 646–667.Google Scholar
MATLAB 2015, MATLAB: Natick, Massachusetts, MathWorks, http://www.mathworks.com/products/matlab/?s_tid=hp_fp_ml.Google Scholar
McGhee, G.R., 1999, Theoretical Morphology: New York, Columbia University Press, 378 p.Google Scholar
McKinney, M.L., 1990, Classifying and analyzing evolutionary trends, in McNamara, K.J., ed., Evolutionary Trends: Tucson, Arizona, University of Arizona Press, p. 28–58.Google Scholar
Mitteroecker, P., and Gunz, P., 2009, Advances in geometric morphometrics: Evolutionary Biology, v. 36, p. 235–247.Google Scholar
Mitteroecker, P., Gunz, P., Bernhard, M., Schaefer, K., and Bookstein, F.L., 2004, Comparison of cranial ontogenetic trajectories among great apes and humans: Journal of Human Evolution, v. 46, p. 679–697, DOI: 10.1016/j.jhevol.2004.03.006.Google Scholar
Mitteroecker, P., and Hutteger, S.M., 2009, The concept of morphospaces in evolutionary and developmental biology: Mathematics and metaphors: Biological Theory, v. 4, p. 54–67, DOI: 10.1162/biot.2009.4.1.54.Google Scholar
Monteiro, L.R., 1999, Multivariate regression models for geometric morphometrics: The search for causal factors in the analysis of shape: Systematic Biology, v. 48, p. 192–199.Google Scholar
Monteiro, L.R., 2013, Morphometrics and the comparative method: Studying the evolution of biological shape: Hystrix, v. 24, p. 25–32.Google Scholar
Mooers, A.Ø., and Schluter, D., 1999, Reconstructing ancestor states with maximum likelihood: Support for one-and two-rate models: Systematic Biology, v. 48, p. 623–633.Google Scholar
Ogihara, N., Nakatsukasa, N., Nakano, Y., and Ishida, H., 2006, Computerized restoration of nonhomogeneous deformation of a fossil cranium based on bilateral symmetry: American Journal of Physical Anthropology, v. 130, p. 1–9.Google Scholar
Pagel, M., 1999, The maximum likelihood approach to reconstructing ancestral character states of discrete characters on phylogenies: Systematic Biology, v. 48, p. 612–622.CrossRefGoogle Scholar
Pagel, M., Meade, A., and Barker, D., 2004, Bayesian estimation of ancestral character states on phylogenies: Systematic Biology, v. 53, p. 673–684.Google Scholar
Perez, S.I., Bernal, V., and Gonzalez, P.N., 2006, Differences between sliding semilandmarks methods in geometric morphometrics, with an application to human craniofacial and dental development: Journal of Anatomy, v. 208, p. 769–784.CrossRefGoogle Scholar
Phillips, P.C., and Arnold, S.J., 1999, Hierarchical comparison of genetic variance-covariance matrices, I, Using the Flury hierarchy: Evolution, v. 53, p. 1506–1515.Google Scholar
Phillips, R., O’Higgins, P., Bookstein, F., Green, B., Gunnarson, H., Shady, Y., Dalge, V., Gowigati, R., and Ben Ali, O., 2010, EVAN Toolbox: European Virtual Anthropology Network—EVAN: Vienna, Austria, Evan Society, http://evan-society.org/node/42.Google Scholar
Pierce, S.E., Angielczyk, K.D., and Rayfield, E.J., 2009, Shape mechanics in thalattosuchian (Crocodylomorpha) skulls: Implications for feeding behaviour and niche partitioning: Journal of Anatomy, v. 215, p. 555–576, DOI: 10.1111/j.1469-7580.2009.01137.x.Google Scholar
Polly, P.D., 2001, Paleontology and the comparative method: Ancestral node reconstructions versus observed node values: American Naturalist, v. 157, p. 596–609.Google Scholar
Polly, P.D., 2004, On the simulation of morphological shape: Multivariate shape under selection and drift: Palaeontologia Electronica, v. 7, no. 2, art. 7A, 28 p. http://palaeo-electronica.org/2004_2/evo/issue2_04.htm.Google Scholar
Polly, P.D., 2005, Development and phenotypic correlations: The evolution of tooth shape in Sorex araneus : Evolution & Development, v. 7, p. 29–41, DOI: 10.1111/j.1525-142X.2005.05004.x.Google Scholar
Polly, P.D., 2008a, Developmental dynamics and G-matrices: Can morphometric spaces be used to model phenotypic evolution?: Evolutionary Biology, v. 35, p. 83–96, DOI: 10.1007/s11692-008-9020-0.Google Scholar
Polly, P.D., 2008b, Adaptive zones and the pinniped ankle: A 3D quantitative analysis of carnivoran tarsal evolution, in Sargis, E., and Dagosto, M., eds., Mammalian Evolutionary Morphology: A Tribute to Frederick S. Szalay: Dordrecht, The Netherlands, Springer, p. 165–194.Google Scholar
Polly, P.D., 2014, Phylogenetics for Mathematica, ver. 3.0: Bloomington, Indiana, Department of Geological Sciences, Indiana University.Google Scholar
Polly, P.D., 2016a, Geometric Morphometrics for Mathematica, ver. 12.0: Bloomington, Indiana, Department of Geological Sciences, Indiana University.Google Scholar
Polly, P.D., 2016b, Quantitative Paleontology for Mathematica, ver. 4.3: Bloomington, Indiana, Department of Geological Sciences, Indiana University.Google Scholar
Polly, P.D., Lawing, A.M., Fabre, A.C., and Goswami, A., 2013a, Phylogenetic principal components analysis and geometric morphometrics: Hystrix, v. 24, p. 33–41.Google Scholar
Polly, P.D., Polyakov, A.V., Ilyashenko, V.N., Onischenko, S.S., White, T.A., Bulatova, N.S., Pavlova, S., Borodin, P.M., and Searle, J.B., 2013b, Phenotypic variation across chromosomal hybrid zones of the common shrew (Sorex araneus) indicates reduced gene flow: PLoS ONE, v. 8, art. e67455, DOI: 10.1371/journal.pone.0067455.Google Scholar
R Core Team 2013, R: A language and environment for statistical computing: Vienna, Austria, R Foundation for Statistical Computing, http://www.R-project.org/.Google Scholar
Raup, D.M., 1961, The geometry of coiling in gastropods: Proceedings of the National Academy of Sciences, USA, v. 47, p. 602–609.Google Scholar
Raup, D.M., 1966, Geometric analysis of shell coiling: General problems: Journal of Paleontology, v. 40, p. 1178–1190.Google Scholar
Raup, D.M., and Michelson, A., 1965, Theoretical morphology of the coiled shell: Science, v. 147, p. 1294–1295.Google Scholar
Raup, D.M., 1977, Stochastic models in evolutionary paleontology, in Hallam, A., ed., Patterns of Evolution as Illustrated by the Fossil Record: Amsterdam, The Netherlands, Elsevier, p. 59–78.Google Scholar
Revell, L.J., 2009, Size correction and principal components for interspecific comparative studies: Evolution, v. 63, p. 3258–3268.Google Scholar
Revell, L.J., 2010, Phylogenetic signal and linear regression on species data: Methods in Ecology and Evolution, v. 1, p. 319–329, DOI: 10.1111/j.2041-210X.2010.00044.x.Google Scholar
Revell, L.J., and Collar, D.C., 2009, Phylogenetic analysis of the evolutionary correlation using likelihood: Evolution, v. 63 p. 1090–1100, DOI: 10.1I11/j.1558-5646.2009.00616.x.Google Scholar
Revell, L.J., Harmon, L.J., and Collar, D.C., 2008, Phylogenetic signal, evolutionary process, and rate: Systematic Biology, v. 57, p. 591–601.Google Scholar
Reyment, R.A., Blackith, R.E., and Campbell, N.A., 1984, Multivariate Morphometrics: London, Academic Press, 223 p.Google Scholar
Richtsmeier, J., and Lele, S., 1993, A coordinate-free approach to the analysis of growth patterns: Models and theoretical considerations: Biological Reviews, v. 68, p. 381–381.Google Scholar
Richtsmeier, J.T., Deleon, V.B., and Lele, S.R., 2002, The promise of geometric morphometrics: American Journal of Physical Anthropology, v. 119, p. 63–91.Google Scholar
Rohlf, F.J., 1986, Relationships among Eigenshape analysis, Fourier analysis, and analysis of coordinates: Mathematical Geology, v. 18, p. 845–854, DOI: 10.1007/BF00899747.Google Scholar
Rohlf, F.J., 1988, NTSYS-pc: Numerical Taxonomy System: Setauket, New York, Exeter Publishing, 43 p.Google Scholar
Rohlf, F.J., 1990, Rotational fit Procrustes methods: University of Michigan, Museum of Zoology Special Publications, v. 2, p. 227–236.Google Scholar
Rohlf, F.J., 1993, Relative warp analysis and an example of its application to mosquito wings, in Marcus, L.F., Bello, E., and Garcia-Valdecasas, A., eds., Contributions to Morphometrics: Madrid, Spain, Museo Nacional de Ciencias Naturales, p. 131–159.Google Scholar
Rohlf, F.J., 1999, Shape statistics: Procrustes superimpositions and tangent spaces: Journal of Classification, v. 16, p. 197–223, DOI: 10.1007/s003579900054.Google Scholar
Rohlf, F.J., 2001, Comparative methods for the analysis of continuous variables: Geometric interpretations: Evolution, v. 55, p. 2143–2160.Google Scholar
Rohlf, F.J., 2002, Geometric morphometrics and phylogeny, in MacLeod, N., and Forey, P., eds., Morphology, Shape, and Phylogenetics: Abingdon, UK, Taylor and Francis, p. 175–193.CrossRefGoogle Scholar
Rohlf, F.J., 2015, The TPS series of software: Hystrix, v. 26, p. 9–12, DOI: 10.4404/hystrix-26.1-11264.Google Scholar
Rohlf, F.J., and Bookstein, F.L., eds., 1990, Proceedings of the Michigan Morphometrics Workshop: Ann Arbor, Michigan, University of Michigan, Museum of Zoology, Special Publication 2: 380 p.Google Scholar
Rohlf, F.J., and Corti, M., 2000, Use of two-block partial least squares to study covariation in shape: Systematic Biology, v. 49, p. 740–753, DOI: 10.1080/106351500750049806.Google Scholar
Rohlf, F.J., and Slice, D., 1990, Extensions of the Procrustes method for the optimal superimposition of landmarks: Systematic Zoology, v. 39, p. 40–59, DOI: 10.2307/2992207.Google Scholar
Roopnarine, P.D., Byars, G., and Fitzgerald, P., 1999, Anagenetic evolution, stratophenetic patterns, and random walk models: Paleobiology, v. 25, p. 41–57.Google Scholar
Schindelin, J., Arganda-Carreras, I., Frise, E., Kaynig, V., Longair, M., Pietzsch, T., Preibisch, S., Rueden, C., Saalfeld, S., Schmid, B., Tinevez, J.-Y., White, D.J., Hartenstein, V., Eliceiri, K., Tomancak, P., and Cardona, A., 2012, FIJI: an open-source platform for biological-image analysis: Nature Methods, v. 9, p. 676–682, DOI: 10.1038/nmeth.2019.Google Scholar
Schlager, S., 2016, Morpho: calculations and visualisations related to geometric morphometrics: R package version 2.3.1.1: Freiburg, Germany, Stefan Schlager, https://CRAN.R-project.org/package=Morpho.Google Scholar
Schneider, C.A., Rasband, W.S., and Eliceiri, K.W., 2012, NIH Image to ImageJ: 25 years of image analysis: Nature Methods, v. 9, p. 671–675, DOI: 10.1038/nmeth.2089.Google Scholar
Schreiber, H.A., Roopnarine, P.D., and Carlson, S.D., 2014, Three-dimensional morphological variability of Recent rhynchonellide brachiopod crura: Paleobiology, v. 40, p. 640–658, DOI: 10.1666/13042.Google Scholar
Schunke, A.C., Bromiley, P.A., Tautz, D., and Thacker, N.A., 2012, TINA manual landmarking tool: Software for the precise digitization of 3D landmarks: Frontiers in Zoology, v. 9, art. 6, DOI: 10.1186/1742-9994-9-6.Google Scholar
Sheets, H.D., 2003, IMP-integrated morphometrics package: Buffalo, New York, Department of Physics, Canisius College.Google Scholar
Slater, G.J., Harmon, L.J., and Alfaro, M.E., 2012, Integrating fossils with molecular phylogenies improves inference of trait evolution: Evolution, v. 66, p. 3931–3944.Google Scholar
Slice, D.E., ed., 2005, Modern Morphometrics in Physical Anthropology: New York, Kluwer Academic, 384 p.Google Scholar
Slice, D.E., 2013, Morpheus et al., Java Edition: Tallahassee, Florida, Department of Scientific Computing, The Florida State University.Google Scholar
Strauss, R.E., Atanassov, M.N., and De Oliveira, J.A., 2003, Evaluation of the principal-component and expectation-maximization methods for estimating missing data in morphometric studies: Journal of Vertebrate Paleontology, v. 23, p. 284–296.Google Scholar
Sutton, M.D., Garwood, R.J., Siveter, David J., and Siveter, Derek J., 2012, Spiers and VAXML; A software toolkit for tomographic visualisation, and a format for virtual specimen interchange: Palaeontologia Electronica, v. 15, no. 2, art. 5T, 14 p http://palaeo-electronica.org/content/issue-2-2012-technical-articles/226-virtual-palaeontology-toolkit.Google Scholar
Thompson, D.W., 1917, On Growth and Form: Cambridge, UK, Cambridge University Press, 793 p.CrossRefGoogle Scholar
Via, S., and Lande, R., 1985, Genotype-environment interaction and the evolution of phenotypic plasticity: Evolution, v. 39, p. 505–522.Google Scholar
Viscosi, V., and Cardini, A., 2011, Leaf morphology, taxonomy and geometric morphometrics: A simplified protocol for beginners: PLoS ONE, v. 6, art. e25630, DOI: 10.1371/journal.pone.0025630.Google Scholar
Webster, M., and Sheets, H.D., 2010, A practical introduction to landmark-based geometric morphometrics, in Alroy, J., and Hunt, G., eds., Quantitative Methods in Paleobiology: The Paleontological Society Papers, v. 16, p. 163–188.Google Scholar
Wiley, D.F., Amenta, N., Alcantara, D.A., Ghosh, D., Kil, Y.J., Delson, E., Harcourt-Smith, W., Rohlf, F.J., St. John, K., and Hamann, B., 2005, Evolutionary morphing: Proceedings of 16th IEEE Visualization Conference (VIS 2005), Minneapolis, Minnesota, 23-28 October 2005: New York, Institute of Electrical and Electronics Engineers, p. 431–438, DOI: 10.1109/VISUAL.2005.1532826.Google Scholar
Wolfram, S., 2015, Wolfram Mathematica, ver. 10.1.0.0: Champaign, Illinois, Wolfram Research, http://www.wolfram.com/mathematica/.Google Scholar
Zelditch, M.L., Swiderski, D.L., Sheets, H.D., and Fink, W.L., 2012, Geometric Morphometrics for Biologists: A Primer: San Diego, California, Elsevier Academic Press, 488 p.Google Scholar
Zollikofer, C.P.E., and De León, M.S.P., 2005, Virtual Reconstruction: A Primer in Computer-Assisted Paleontology and Biomedicine: Hoboken, New Jersey, Wiley Interscience, 333 p.Google Scholar