Archive for History of Exact Sciences

, Volume 66, Issue 4, pp 359–396 | Cite as

The analytic geometry of genetics: part I: the structure, function, and early evolution of Punnett squares

  • W. C. Wimsatt


A square tabular array was introduced by R. C. Punnett in (1907) to visualize systematically and economically the combination of gametes to make genotypes according to Mendel’s theory. This mode of representation evolved and rapidly became standardized as the canonical way of representing like problems in genetics. Its advantages over other contemporary methods are discussed, as are ways in which it evolved to increase its power and efficiency, and responded to changing theoretical perspectives. It provided a natural visual decomposition of a complex problem into a number of inter-related stages. This explains its computational and conceptual power, for one could simply “read off” answers to a wide variety of questions simply from the “right” visual representation of the problem, and represent multiple problems, and multiple layers of problems in the same diagram. I relate it to prior work on the evolution of Weismann diagrams by Griesemer and Wimsatt (What Philosophy of Biology Is, Martinus-Nijhoff, the Hague, 1989), and discuss a crucial change in how it was interpreted that midwifed its success.


Cultural Evolution Adaptive Radiation Analytic Geometry Tabular Array Mendelian Genetic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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I. Sources for Punnett squares and other diagrams

  1. Babcock, E.B., and R.E.Clausen. 1918. Genetics in relation to agriculture. New York: McGraw-Hill.Google Scholar
  2. Bateson, W., R.C. Punnett, and E. Saunders. 1906. Experimental studies in the physiology of heredity (report to the Evolution Committee of the Royal Society, III), 2–11. London: The Royal Society [p.152-161 in Bateson’s collected papers].Google Scholar
  3. Bateson, W.W. (1913, third impression with additions, 2 earlier printings in 1909). Mendel’s principles of heredity. London: Cambridge University Press.Google Scholar
  4. Baur Erwin. (1914) Einführung in die experimentelle vererbungslehre. Verlag von der Gebruder Borntraeger, BerlinGoogle Scholar
  5. Callebaut W. (1993) Taking the naturalistic turn: Or how real philosophy of science is done. University of Chicago Press, ChicagoGoogle Scholar
  6. Castle, William E. 1916. Genetics and eugenics. Cambridge: Harvard (4 editions through 1930).Google Scholar
  7. Conklin, E. 1915. Heredity and environment. Princeton: Princeton University Press (5 editions through 1923).Google Scholar
  8. Crew F.A.E. (1925) Animal genetics: An introduction to the science of animal breeding. Oliver and Boyd, LondonGoogle Scholar
  9. Darbishire A.D. (1911) Breeding and the Mendelian discovery. Cassell and Co., LondonGoogle Scholar
  10. Darlington, C.D., and K. Mather. 1949. The elements of genetics. London: Allen and Unwin (reprinted 1969 by Schocken Books, New York).Google Scholar
  11. Dendy A. (1912) Outlines of evolutionary biology. Appleton, New YorkCrossRefGoogle Scholar
  12. Gilbert S. (1985) Principles of embryology. Sunderland, SinauerGoogle Scholar
  13. Hassell M.P. (1978) The dynamics of arthropod predator-prey systems. Princeton University Press, PrincetonzbMATHGoogle Scholar
  14. Herbert S. (1910) The first principles of heredity. A & C Black, LondonGoogle Scholar
  15. Hogben L. (1946) An introduction to mathematical genetics. Norton, New YorkGoogle Scholar
  16. Mendel, G. 1866. Experiments in Plant-Hybridization (English trans: 1902). Cambridge: Harvard University Press.Google Scholar
  17. Morgan, T.H. 1913, 1914. Heredity and sex, 2nd ed. New York: Columbia University Press (pagination from 1914 ed.).Google Scholar
  18. Morgan T.H. (1916) A critique of the theory of evolution. Princeton University Press, PrincetonGoogle Scholar
  19. Morgan, T.H., A.H. Sturtevant, H.J. Muller, and C.B. Bridges. 1915. The mechanism of mendelian heredity. New York: Henry Holt and Co.Google Scholar
  20. Punnett R.C. (1907) Mendelism. 2nd ed. MacMillan and Co., LondonzbMATHGoogle Scholar
  21. Punnett, R.C. 1911. Mendelism, 3rd ed. London: MacMillan and Co. (5 editions through 1927).Google Scholar
  22. Schank, J.C., and T.J. Koehnle. 2007. Modeling complex biobehavioral systems. In Modeling Biology: Structures, Behaviors, Evolution ed. M.D. Laubichler, and G.B. Muller, 219–244. Cambridge, MA: MIT Press.Google Scholar
  23. Sinnott E., Dunn L.C. (1939) Principles of genetics, 3rd ed. McGraw-Hill, New YorkGoogle Scholar
  24. Sinnott, E., L.C. Dunn, and T. Dobzhansky. 1950. Principles of genetics, 4th ed. New York: McGraw-Hill.Google Scholar
  25. Sturtevant, A.H., and G. Beadle. 1939. An introduction to genetics. Philadelphia: W. B. Saunders.Google Scholar
  26. Walter, H. 1913. Genetics, 1st ed. New York: MacMillan (1913, 1917 reprint).Google Scholar
  27. Wilson, E.B. 1896. The cell in development and inheritance. London: Macmillan Co.Google Scholar
  28. Wilson E.B. (1925) The cell in development and heredity, 3rd ed. MacMillan, New YorkGoogle Scholar
  29. Wilson James. (1916) A manual of Mendelism. A.&C. Black, LondonGoogle Scholar
  30. Wimsatt, W.C. 1987. False Models as means to Truer Theories. In Neutral Models in Biology ed. M. Nitecki, and A. Hoffman, 23–55. London: Oxford University Press.Google Scholar
  31. Wimsatt, W.C., and J.C. Schank. 1993. Modelling—A Primer (or: the crafty art of making, exploring, extending, transforming, tweaking, bending, disassembling, questioning, and breaking models). Now public domain through BioQUEST library of strategic simulations.Google Scholar
  32. Wimsatt, W.C. 2007. Re-Engineering Philosophy for Limited Beings: Piecewise Approximations to Reality. Cambridge: Harvard University Press.Google Scholar

II. Other references

  1. Allchin, D. 1991. Resolving disagreement in science: The Ox-Phos controversy, 1961–1978, Ph.D. dissertation, Committee on the Conceptual Foundations of Science, The University of Chicago.Google Scholar
  2. Basalla G. (1988) The evolution of technology. Cambridge University Press, CambridgeGoogle Scholar
  3. Boyd R., Richerson P (1985) Culture and the evolutionary process. University of Chicago Press, ChicagoGoogle Scholar
  4. Carlson, E.A. 1967. The gene: A critical history. Philadelphia: W. B. Saunders.Google Scholar
  5. Clarke A., Fujimura J. (1992) The right tool f or the job. Princeton University Press., PrincetonGoogle Scholar
  6. Coleman W.L. (1970) Conservative thought in science: the case of William Bateson. Centaurus 15: 228–314CrossRefGoogle Scholar
  7. Darden L. (1991) Theory construction in science: Strategies from Mendelian genetics. Oxford University Press, OxfordGoogle Scholar
  8. Darlington, C.D. 1937. Recent advances in cytology. Philadelphia: The Blakiston Co. (reprinted, 1988, by The Garland Publishing Co., New York).Google Scholar
  9. Gould, S.J., and R.C. Lewontin. 1979. The Spandrels of San Marco and the Panglossian Paradigm. Proceedings of the Royal Society of London, B 205: 581–598.Google Scholar
  10. Griesemer, J.R. 1994. Image and argument: Towards a visual logic of weismannism. Unpublished talk, conference on visualization in science, Galveston Medical Center, Galveston TX, April 30, 1994.Google Scholar
  11. Griesemer, J.R., and W.C. Wimsatt. 1989. Picturing Weismannism: A case study in conceptual evolution. What Philosophy of Biology Is (essays for David Hull), ed. M. Ruse, 75–137. The Hague: Martinus-Nijhoff.Google Scholar
  12. Hull D. (1988) The processes of science. University of Chicago Press, ChicagoGoogle Scholar
  13. Kohler R. (1994) Lords of the fly. University of Chicago Press, ChicagoGoogle Scholar
  14. Levins, R., and R.C. Lewontin. 1985. The dialectical biologist. Cambridge: Harvard University Press.Google Scholar
  15. Provine, W. 1971. The origins of theoretical population genetics. Chicago: University of Chicago Press.Google Scholar
  16. Putnam, H. 1975. The meaning of ‘meaning’. In Minnesota studies in the philosophy of science, vol. 7, ed. K. Gunderson. Minneapolis: University of Minnesota Press.Google Scholar
  17. Tufte E. (1983) The quantitative display of visual information. Graphics Press, New HavenGoogle Scholar
  18. von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press.Google Scholar
  19. Wimsatt, W.C. 1981. Robustness, reliability and overdetermination. In Scientific inquiry and the social sciences, ed. M. Brewer, and B. Collins, 124–163. San Francisco: Jossey-Bass.Google Scholar
  20. Wimsatt, W.C. 1987. False models as means to truer theories. In Neutral models in biology, ed. M. Nitecki, and A. Hoffman, 23–55. London: Oxford University Press.Google Scholar
  21. Wimsatt, W.C. 1991. Taming the dimensions–visualizations in science. In PSA-1990, vol. 2, ed. M. Forbes, L. Wessels, and A. Fine, 111–135. East Lansing: The Philosophy of Science Association.Google Scholar
  22. Wimsatt, W.C. 1992. Golden generalities and co-opted anomalies: Haldane vs. Muller and the Drosophila group on the theory and practice of linkage mapping. In Fisher, Haldane, Muller, and Wright: Founders of the modern mathematical theory of evolution, ed. S. Sarkar, 107–166. Dordrecht: Martinus-Nijhoff.Google Scholar
  23. Wimsatt, W.C. 1999. Genes, memes, and cultural inheritance, invited contribution for April 1999Biology and Philosophy special issue on influence of R. C. Lewontin. 14: 279–310.Google Scholar
  24. Wimsatt, W.C. 2001. Generative entrenchment and the developmental systems approach to evolutionary processes. In Cycles of contingency:Developmental systems and evolution, ed. S. Oyama, R. Gray, and P. Griffiths, 219–237. Cambridge: MIT Press.Google Scholar
  25. Wimsatt, W.C., and J.R. Griesemer. 2007. Reproducing entrenchments to scaffold culture: The central role of development in cultural evolution. InIntegrating evolution and development, ed. R. Sansom, and R. Brandon, 227–324. Cambridge: MIT Press.Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Philosophy, Conceptual Foundations of Science, and Evolutionary BiologyUniversity of ChicagoChicagoUSA

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