Shape Transformations

Shape Changes in Biology

Puffer to Mola mola figure

D'Arcy Thompson's classic fish transformation

An early attempt to quantitatively describe the mechanism of shape change was published by D'Arcy Thompson in a landmark book that all students of shape change should read (Thompson, 1917) . The particular image that inspires most who see it is illustrated above - the puffer to Mola mola transformation. While ellegant and visually simple, this graphical technique has never been explicitly described such that an experimentalist could repeat it. Some 60 odd years later another scientist made an effort to formalize the technique into a procedure he called 'bioorthogonal analysis' (Bookstein, 1980). The mathematics behind this approach were daunting to the average biologist and thus the method remained fallow in the mainstream of biological shape study. Then, in 1981, a technique was published for alligning and comparing homologous sets of landmark-coordinates (Siegel, 1981, 1982). The technique was explained in relatively simple ways but the most important advance, to the average biologist, was that a computer algorithm to compute the allignments was also published. This date was also significant in being close to the beginning of the Personal Computer (PC) Era. This allowed biologists to follow the published algorithm of Siegel and start studying shape-change this way. I started my interest in this approach at that time. It was obvious to me that the approach was perfect for studying the shapes of planar structures such as insect wings. The field has burgeoned since then and made great strides towards making the math approachable by the biologist (Bookstein, 1991). (For the latest information on this technology visit the SUNY Stony Brook Morphometrics Page.)

Human/Chimp dichotomy

In the late '70s and early '80s the evolution of shape was embroiled in controversy about the validity of newly developed techniques, some developed ad hoc by non-biometricians. Some of the topics were also controversial. In particular, a study was published out of the Allan Wilson laboratory claiming a rapid morphological evolution of the shapes of the humanoid line of evolution compared to a measured slow evolution of the frogs (Cherry, Case and Wilson, 1978). A figure comparing human to chimpanzee illustrates the dramatic change in shape/proportions for a species pair whose DNA similarity is closer than almost all recorded sibling mamalian species.

The desire to explain the apparent rapid evolution of the hominoids led to a paper (Wyles, Kunkel & Wilson, 1983) which ascribes the rapid morphological evolution to large brains. A large brain is a trait associated with vocal communication in groups. Thus the hominoids, the song birds and marine mammals each communicate within their own species. They all need larger brains with which to carry on this communication and the attendant processing of information which other mammals are not endowed with and do not benefit from. The communication and learning of information from one-another enlargens the interface of the individual with the environment. This increases the rate of evolution (including morphological evolution) and has been given the name "behavioral drive". In effect, the evolution of a larger brain and communication skills leads to an autocatalytic increased rate of evolution.

Another current interest in studying shape change focuses on insect wings (Abbasi et al., 2009) and the ability to discriminate shape differences between the sexes, populations, and species. Of greater interest is the potential to enlargen this approach to 3-dimensional objects.

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Abbasi, R., M. Mashhadihan, M. Abbasi, B. Kiabi (2009). Geometric morphometric study of populations of the social wasp, Polistes dominulus (Christ, 1791) from Zanjan province, north-west Iran. New Zealand Journal of Zoology 36: 41-46. Abstract

Benson, R. H., R. E. Chapman, and A. F. Siegel. 1983. On the measurement of morphology and its change. Paleobiology 8:328-339.

Bookstein, F. L. 1977. The study of shape transformation after D'Arcy Thompson. Math. Biosciences 34: 177-219.

Bookstein, F. L. 1980. When one form is between two others: an application of biorthogonal analysis. Amer. Zool. 20:627-641.

Bookstein, F. L. 1981. Coordinate systems and morphogenesis. In: "Morphogenesis and Pattern Formation" T. G. Connelly, L. L. Brinkley, and B. M. Carlson, Eds., Raven Press, New York, pp. 265-287.

Bookstein, F. L. 1984. A statistical method for biological shape comparisons. J. Theor. Biol. 107:475-520.

Bookstein, F. L. 1985. Morphometrics in evolutionary biology: The geometry of size and shape change, with examples from fishes. Acad. Nat. Sci., Phila., 277.

Bookstein, F. L. 1986. Size and shape spaces for landmark data in two dimensions (with discussion). Statist. Sci. 1:181-242.

Bookstein, F. L. 1987. Random walk and the existence of evolutionary rates. Paleobiology 13:446-464.

Bookstein, F. L., and R. A. Reyment. 1989. Microevolution of Miocene Brizalina (Foraminifera) studied by canonical variate analysis and analysis of landmarks. Bull. Math. Biol. 51:657-679.

Bookstein, F. L., and P. D. Sampson. 1990. Statistical models for geometric components of shape change. Communs. Statist. Theory Meth. 19:1939-1972.

Bookstein, F. L. 1991. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge U. Press, Cambridge, UK. pp435.

Bookstein, F. L. 1997.   Landmark methods for forms without landmarks: Localizing group differences in outline shape.   Medical Image Analysis 1:225--243.

Cherry, L. M., S. M. Case, J. G. Kunkel, and A. C. Wilson. 1979. Comparisons of frogs, humans, and chimpanzees. Science 204:435.

Cherry, L. M., S. M. Case, J. G. Kunkel, J. S. Wyles, and A. C. Wilson. 1982. Body shape metrics and organismal evolution. Evolution 36: 914-933.

Cherry, L. M., S. M. Case, and A. C. Wilson. 1978. Frog perspective on the morphometric difference between humans and chimpanzees. Science 200: 209- 211.

Kunkel, J. G., L. M. Cherry, S. M. Case, and A. C. Wilson. 1980. M-statistics and morphometric divergence. Science 208: 1060-1061.

Rohlf, F. J. 1990. Rotational fit (Procrustes) Methods. Chapter 10 Pp. 227-236 in Rohlf and Bookstein Procedings of the Michigan morphometrics workshop.(Blue Book).

Rohlf, F. J. 2000. Geometric morphometrics in systematics. Chapter in N. Macleod and P. Forey (eds.) Morphology, shape and phylogenetics. Taylor&Francis: London.

Sampson, P. D., and A. F. Siegel. 1985. The measure of 'size' independent of 'shape' for multivariate lognormal populations. J. Am. Statist. Ass. 80:910-914.

Siegel, A. F. 1981. Geometric data analysis: An interactive graphics program for shape comparison. Modern Data Analysis, R. L. Launer and A. F. Siegel eds. Academic Press 103-122.

Siegel, A. F., and R. H. Benson. 1982. A robust comparison of biological shapes. Biometrics 38:341-350.

Smith, D.R., B.J. Crespi & F.L. Bookstein (1997)   Fluctuating asymmetry in the honey bee, Apis mellifera: effects of ploidy and hybridization.   Journal of Evolutionary Biology, 10, 551-574.

Thompson, D'Arcy W. 1917. On growth and form. Cambridge University Press. 793 p.

Wyles, J. S., J. G. Kunkel, and A. C. Wilson. 1983. Birds, behavior and anatomical evolution. Proc. Natl. Acad. Sci. USA 80:4394-4397.

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Page maintained by Joe Kunkel, Copyright(c) 1995. Created: 95/10/28 Updated: 97/02/16