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Quantification of shape by use of Fourier analysis: the Mississippian blastoid genus Pentremites

Published online by Cambridge University Press:  08 April 2016

Johnny Arlton Waters
Johnny Arlton Waters*
Affiliation:
Department of Geology, West Georgia College, Carrollton, Georgia 30117
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Abstract

Psychological evidence suggests that the visual outline of an object is the most important character for discriminating differences in external morphology. External morphology is an important taxonomic character in describing living and fossil species, for example, the blastoid Pentremites. Comparison of different views of the same specimen utilizing Fourier series suggests that the skeleton of Pentremites commonly is not rotationally symmetrical and that the asymmetry is not associated with any specific ray. Analysis of a growth series indicates that the amplitudes of the second and third harmonics are significantly correlated with growth, which is demonstrated to be anisometric. Definable changes in the lateral outline can be attributed to changes in harmonic amplitudes and a wide range of morphological forms comparable to known taxa can be generated by systematically varying the amplitudes of the first four harmonics. The population used in this study probably represents Pentremites robustus Lyon and is from Bangor Limestone in the abandoned Moulton Quarry, Lawrence County, Alabama.

Type
Research Article
Information
Paleobiology , Volume 3 , Issue 3 , Summer 1977 , pp. 288 - 299
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Anstey, R. L. and Delmet, D. A. 1972. Genetic meaning of zooecial chamber shapes in fossil bryozoans: Fourier analysis. Science. 177:1000–1002.Google Scholar
Anstey, R. L. and Delmet, D. A. 1973. Fourier analysis of zooecial shapes in fossil bryozoans. Geol. Soc. Am. Bull. 84:1753–1763.Google Scholar
Bliss, C. I. 1948. Periodic regression in biology and climatology. Conn. Agric. Exper. Stat. Bull. 615:55 pp.Google Scholar
Breimer, A. and Macurda, D. B. Jr. 1972. The phylogeny of the fissiculate blastoids. Koninkl. Nederl. Akad. van Weten Verh. Afd. Nat. Eerste Reeks. Deel 26(3) 390 p.Google Scholar
Christopher, R. A. and Waters, J. A. 1974. Fourier series as a quantitative descriptor of miospore shape. J. Paleontol. 48:697–709.Google Scholar
Delmet, D. A. and Anstey, R. L. 1974. Fourier series of morphological plasticity within an Ordovician bryozoan colony. J. Paleontol. 48:217–226.Google Scholar
Galloway, J. J. and Kaska, H. V. 1957. Genus Pentremites and its species. Geol. Soc. Am. Mem. 69:104 pp.Google Scholar
Hayward, L. C. 1960. A Study of Cyclic Phenomena Using the Classical Fourier Analysis with Appropriate Statistical Methods. 61 pp. MS Thesis, Univ. Calif.; Los Angeles, Calif.Google Scholar
Horowitz, A. S. 1956. Fauna of the Glen Dean Limestone (Chester) in Indiana and Northern Kentucky. 450 pp. Ph.D. Thesis. Indiana Univ.; Bloomington, Ind.Google Scholar
Kaesler, R. L. and Waters, J. A. 1972. Fourier analysis of the ostracode margin. Geol. Soc. Am. Bull. 83:1169–1178.Google Scholar
Li, J. C. R. 1964. Statistical Inference 1. 658 pp. Edward Bros., Inc.; Ann Arbor, Mich.Google Scholar
Lu, K. H. 1965. Harmonic analysis of the human face. Biometrics. 21:491–505.Google Scholar
Macurda, D. B. Jr. 1966. The ontogeny of the Mississippian blastoid Orophocrinus. J. Paleontol. 40:92–124.Google Scholar
Macurda, D. B. Jr. 1975. The Pentremites (Blastoidea) of the Burlington limestone (Mississippian). J. Paleontol. 49:346–373.Google Scholar
Raup, D. M. 1966. Geometric analysis of the shell coiling: general problems. J. Paleontol. 40:1178–1190.Google Scholar
Raup, D. M. 1967. Geometric analysis of shell coiling: coiling in ammonoids. J. Paleontol. 41:43–65.Google Scholar
Raup, D. M. and Stanley, S. M. 1971. Principles of Paleontology. 388 pp. W. H. Freeman; San Francisco, Calif.Google Scholar
Rodriguez, J. 1960. Invertebrate Fauna of the Golconda Formation (Middle Chester) of Southern Indiana and Illinois. 259 pp. Ph.D. Thesis, Indiana Univ.; Bloomington, Ind.Google Scholar
Steel, R. G. D. and Torrie, J. H. 1960. Principles and Procedures of Statistics. 481 pp. McGraw-Hill; New York.Google Scholar
Younker, J. K. 1971. Evaluation of the Utility of Two Dimensional Fourier Shape Analysis for the Study of Ostracode Carapaces. 62 pp. M.S. Thesis, Mich. State Univ.; E. Lansing, Mich.Google Scholar
Zahn, C. T. and Roskies, R. Z. 1972. Fourier descriptors for plane closed curves. IEEE Trans. on Computers C-21(3):269–282.Google Scholar