Abstract
A stratigraphically oriented series of the Miocene foraminiferal speciesBrizalina mandoroveensis from Ikang, Cameroon, was analyzed both by conventional multivariate morphometric procedures and by the tensor biometric method of Bookstein (1986;Statist. Sci. 1, 181–142), a method which analyzes sets of landmark points rather than specific variables of shape or size. The conventional analysis used five size-measures upon 170 specimens from five stratigraphic levels; the tensor analysis encompassed six landmarks (12 coordinates) upon 50 specimens. Whereas certain features appeared in both analyses, such as the separation between levels one and five, the techniques did not always agree with respect to the interpretation of those findings or about most details in the sequence of mean phenotypes. The canonical variate analysis bases its ordination upon a general size factor (the meaning of which is obscured by the foreshortening of within-group variation which is built into the technique). The tensor analysis locates a similar ordination using mainly features of shape.
Similar content being viewed by others
Literature
Bookstein, F. L. 1978.The Measurement of Biological Shape and Shape Change. Lect. Notes Biomath., Vol. 24.
—. 1982. “Foundations of Morphometrics.”Ann. Rev. Ecol. Systematics 13, 451–470.
—. 1986. “Size and Shape Spaces for Landmark Data in Two Dimensions.”Statist. Sci. 1, 181–242.
—. 1989a. “Comment on D. G. Kendall A Survey of the Statistical Theory of Shape.”Statist. Sci.,4, 99–105.
—. 1989b. “Principal Warps: Thin-Plate Splines and the Decomposition of Deformations.”IEEE Trans. Patt. Anal. Mach. Intel.,11, 567–585.
Bookstein, F. L. 1990.Morphometric Tools for Landmark Data. Cambridge University Press, accepted for publication.
Bookstein, F. L. and P. Sampson. 1987. Statistical Models for Geometric Components of Shape Change”. Proceedings of the Section on Statistical Graphics: Annual Meeting of the American Statistical Association, pp. 18–27.
Bookstein, F. L. and P. Sampson. 1989. “Statistical Models for Geometric Components of Shape Change”.J. Am. Statist. Assoc., submitted.
Bookstein, F. L., B. Chernoff, R. Elder, J. Humphries, G. Smith and R. Strauss. 1985.Morphometrics in Evolutionary Biology. Special Publication No. 15. Academy of Natural Sciences of Philadelphia.
Brower, J. C. and J. Veinus. 1978. “Multivariate Analysis of Allometry Using Point Coordinates.”J. Paleontol. 52, 1037–1053.
Brower, J. C. and J. Veinus. 1978. “Multivariate Analysis of Allometry Using Point Coordinates.”J. Paleontol. 52, 1037–1053.
Eldredge, N. and S. J. Gould. 1972. “Punctuated Equilibria: An Alternative to Phyletic Gradualism.” InModels in Paleobiology, T. Schopf (Ed.), pp. 82–115. San Francisco: Freeman Cooper.
Goodall, C. R. 1983. “The Statistical Analysis of Growth in Two Dimensions.” Doctoral Dissertation, Department of Statistics, Harvard University.
Goodall, C. R. 1989. “WLS Estimators and Tests for Shape Differences in Landmark Data.”J. R. Statist. Soc., submitted.
Hopkins, J. W. 1966. “Some Considerations in Multivariate Allometry.”Biometrics 22, 747–760.
Mardia, K. V. and I. L. Dryden. 1989. “The Statistical Analysis of Shape Data.”Adv. appl. Probability, in press.
Reyment, R. A. 1980.Morphometric Methods in Biostratigraphy. London: Academic Press.
— 1982. “Phenotypic Evolution in a Cretaceous Foraminifer.”Evolution 36, 1182–1199.
— 1983. “Phenotypic Evolution in Microfossils.”Evol. Biol. 16, 209–254.
—, R. E. Blackith and N. A. Campbell. 1984.Multivariate Morphometrics (2nd edn). London: Academic Press.
Rohlf, F. J. and D. Slice. 1989. “Methods for Comparison of Sets of Landmarks.”Systematic Zool., submitted.
Siegel, A. F. and R. H. Benson. 1982. “A Robust Comparison of Biological Shapes.”Biometrics 38, 341–350.
Skalak, R., G. Dasgupta, M. Moss, E. Otten, P. Dullemeijer and H. Vilmann. 1982. “Analytical Description of Growth.”J. theor. Biol. 94, 555–577.
Sneath, P. H. A. 1967. “Trend-Surface Analysis of Transformation Grids.”J. Zool. 151, 65–122.
Strauss, R. F. and F. L. Bookstein. 1982. “The Truss: Body Form Reconstructions in Morphometrics.”Systematic Zool. 31, 113–135.
Thompson, D'A. W. 1961.On Growth and Form (abridged edn), J.T. Bonner (Ed.). Cambridge University Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bookstein, F.L., Reyment, R.A. Microevolution in MioceneBrizalina (foraminifera) studied by canonical variate analysis and analysis of landmarks. Bltn Mathcal Biology 51, 657–679 (1989). https://doi.org/10.1007/BF02459654
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02459654