D'Arcy Thompson was a biologist, a mathematician and a classicist. His writing was great literature as well as great science. He is primarily known for a single book — On Growth and Form — and indeed for a single chapter within it, on his 'theory of transformations', which shows how the differences between the forms of related species can be represented geometrically. This theory cries out for causal explanation, which is something the great man eschewed. Perhaps the time is close when comparative developmental genetics will be able to provide such an explanation.
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Raff, R. A., Arthur, W., Carroll, S. B., Coates, M. I. & Wray, G. Chronicling the birth of a discipline. Evol. Dev. 1, 1–2 (1999).
Raff, R. A. Evo–devo: the evolution of a new discipline. Nature Rev. Genet. 1, 74–79 (2000).
Arthur, W. The emerging conceptual framework of evolutionary developmental biology. Nature 415, 757–764 (2002).
Carroll, S. Endless Forms Most Beautiful: the New Science of Evo Devo and the Making of the Animal Kingdom (W. W. Norton, New York, 2005).
Holland, P. W. H. The future of evolutionary developmental biology. Nature 402, C41–C44 (1999).
Hall, B. K. Evolutionary Developmental Biology (Kluwer Academic, Dordrecht, 1999).
Gould, S. J. Ontogeny and Phylogeny (Harvard Univ. Press, Cambridge, Massachusetts, 1977).
McGinnis, W., Garber, R. L., Wirz, J., Kuroiwa, A. & Gehring, W. J. A homologous protein-coding sequence in Drosophila homeotic genes and its conservation in other metazoans. Cell 37, 403–408 (1984).
Scott, M. P. & Weiner, A. J. Structural relationships among genes that control development: sequence homology between the Antennapedia, Ultrabithorax and fushi tarazu loci of Drosophila. Proc. Natl Acad. Sci. USA 81, 4115–4119 (1984).
Thompson, D'A. W. On Growth and Form (Cambridge Univ. Press, Cambridge, 1917).
Huxley, J. S. Problems of Relative Growth (Methuen, London, 1932).
De Beer, G. R. Embryos and Ancestors (Clarendon, Oxford, 1940).
Goldschmidt, R. The Material Basis of Evolution (Yale Univ. Press, New Haven, 1940).
Waddington, C. H. The Strategy of the Genes (Allen & Unwin, London, 1957).
Thompson, R. D'A. D'Arcy Wentworth Thompson, The Scholar–Naturalist, 1860–1948 (Oxford Univ. Press, London, 1958).
Darwin, C. On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life (J. Murray, London, 1859).
Hennig, W. Phylogenetic Systematics (Univ. Illinois Press, Urbana, 1966).
Child, C. M. Patterns and Problems of Development (Chicago Univ. Press, Chicago, 1941).
Wolpert, L. Positional information and pattern formation. Curr. Top. Dev. Biol. 6, 183–224 (1971).
Meinhardt, H. Models of Biological Pattern Formation (Academic Press, London, 1982).
Bookstein, F. L. Morphometric Tools for Landmark Data: Geometry and Biology (Cambridge Univ. Press, Cambridge, 1991).
Klingenberg, C. P., Leamy, L. J., Routman, E. J. & Cheverud, J. M. Genetic architecture of mandible shape in mice: effects of quantitative trait loci analyzed by geometric morphometrics. Genetics 157, 785–802 (2001).
Sander, K. in Development and Evolution (eds Goodwin, B. C., Holder, H. & Wyllie, C. C.) 137–159 (Cambridge Univ. Press, Cambridge, 1983).
Richardson, M. K. Heterochrony and the phylotypic period. Dev. Biol. 172, 412–421 (1995).
Hafen, E. & Stocker, H. How are the sizes of cells, organs, and bodies controlled? PLoS Biol. 1, e86–e97 (2003).
Arthur, W. The Origin of Animal Body Plans: A Study in Evolutionary Developmental Biology (Cambridge Univ. Press, Cambridge, 1997).
Simpson, G. G. Tempo and Mode in Evolution (Columbia Univ. Press, New York, 1944).
Leroi, A. M. The scale independence of evolution. Evol. Dev. 2, 67–77 (2000).
I thank H. Arthur, U. Frank, G. McCormack and A. Panchen for scientific discussion and comments on the draft manuscript, and the library of Trinity College Dublin for the loan of copies of the first and second editions (1917 and 1942, respectively) of On Growth and Form.
The author declares no competing financial interests.
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Arthur, W. D'Arcy Thompson and the theory of transformations. Nat Rev Genet 7, 401–406 (2006). https://doi.org/10.1038/nrg1835
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