Statistical Science

A Statistical Model to Explain the Mendel–Fisher Controversy

Ana M. Pires and João A. Branco

Full-text: Open access

Abstract

In 1866 Gregor Mendel published a seminal paper containing the foundations of modern genetics. In 1936 Ronald Fisher published a statistical analysis of Mendel’s data concluding that “the data of most, if not all, of the experiments have been falsified so as to agree closely with Mendel’s expectations.” The accusation gave rise to a controversy which has reached the present time. There are reasonable grounds to assume that a certain unconscious bias was systematically introduced in Mendel’s experimentation. Based on this assumption, a probability model that fits Mendel’s data and does not offend Fisher’s analysis is given. This reconciliation model may well be the end of the Mendel–Fisher controversy.

Article information

Source
Statist. Sci. Volume 25, Number 4 (2010), 545-565.

Dates
First available in Project Euclid: 14 March 2011

Permanent link to this document
http://projecteuclid.org/euclid.ss/1300108237

Digital Object Identifier
doi:10.1214/10-STS342

Mathematical Reviews number (MathSciNet)
MR2807770

Citation

Pires, Ana M.; Branco, João A. A Statistical Model to Explain the Mendel–Fisher Controversy. Statist. Sci. 25 (2010), no. 4, 545--565. doi:10.1214/10-STS342. http://projecteuclid.org/euclid.ss/1300108237.


Export citation

References

  • Bateson, W. (1902). Mendel’s Principles of Heredity, a Defense, 1st ed. Cambridge Univ. Press, London.
  • Bateson, W. (1909). Mendel’s Principles of Heredity, a Defense, 2nd ed. Cambridge Univ. Press, London.
  • Bowler, P. J. (1989). The Mendelian Revolution. Athlone, London.
  • Dawkins, R. (1995). River out of Eden: A Darwinian View of Life. Perseus Books Group, New York.
  • De Beer, G. (1964). Mendel, Darwin and Fisher (1865–1965). Notes and Records Roy. Soc. London 19 192–226.
  • Di Trocchio, F. (1991). Mendel’s experiments: A reinterpretation. J. Hist. Biol. 24 485–519.
  • Dobzhansky, T. (1967). Looking back at Mendel’s discovery. Science 156 1588–1589.
  • Easterling, R. G. (1976). Goodness of fit and parameter estimation. Technometrics 18 1–9.
  • Edwards, A. W. F. (1986a). Are Mendel’s results really too close? Biol. Rev. 61 295–312. Also reproduced in Franklin et al. (2008).
  • Edwards, A. W. F. (1986b). More on the too-good-to-be true paradox and Gregor Mendel. J. Hered. 77 138.
  • Fairbanks, D. J. and Rytting, B. (2001). Mendelian controversies: A botanical and historical review. Am. J. Bot. 88 737–752. [Also reproduced in Franklin et al. (2008).]
  • Fairbanks, D. J. and Schaalje, B. (2007). The tetrad-pollen model fails to explain the bias in Mendel’s pea (Pisum sativum) experiments. Genetics 177 2531–2534.
  • Fisher, R. A. (1936). Has Mendel’s work been rediscovered? Ann. of Sci. 1 115–137. [Also reproduced in Franklin et al. (2008).]
  • Franklin, A., Edwards, A. W. F., Fairbanks, D. J., Hartl, D. L. and Seidenfeld T. (2008). Ending the Mendel–Fisher Controversy. Univ. Pittsburgh Press, Pittsburgh.
  • Hald, A. (1998). A History of Mathematical Statistics. Wiley, New York.
  • Hartl, D. L. and Fairbanks, D. J. (2007). Mud sticks: On the alleged falsification of Mendel’s data. Genetics 175 975–979.
  • Leonard, T. (1977). A Bayesian approach to some multinomial estimation and pretesting problems. J. Amer. Statist. Assoc. 72 869–874.
  • Massey, F. J. (1951). The Kolmogorov–Smirnov test for goodness of fit. J. Amer. Statist. Assoc. 46 68–78.
  • Meijer, O. (1983). The essence of Mendel’s discovery. In Gregor Mendel and the Foundation of Genetics (V. Orel and A. Matalová, eds.) 123–172. Mendelianum of the Moravian Museum, Brno, Czechoslovakia.
  • Mendel, G. (1866). Versuche über plflanzenhybriden verhandlungen des naturforschenden vereines in Brünn. In Bd. IV für das Jahr, 1865 78–116. [The first english translation, entitled “Experiments in plant hybridization,” published in Bateson (1909) is also reproduced in Franklin et al. (Fra2008).]
  • Nissani, M. and Hoefler-Nissani, D. M. (1992). Experimental studies of belief-dependence of observations and of resistance to conceptual change. Cognition Instruct. 9 97–111.
  • Novitski, C. E. (1995). Another look at some of Mendel’s results. J. Hered. 86 62–66.
  • Olby, R. (1984). Origin of Mendelism, 2nd ed. Univ. Chicago Press, Chicago.
  • Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arised from random sampling. Philos. Mag. 50 157–175.
  • Piegorsch, W. W. (1983). The questions of fit in the Gregor Mendel controversy. Comm. Statist. Theory Methods 12 2289–2304.
  • Pilgrim, I. (1984). The too-good-to-be-true paradox and Gregor Mendel. J. Hered. 75 501–502.
  • Pilgrim, I. (1986). A solution to the too-good-to-be-true paradox and Gregor Mendel. J. Hered. 77 218–220.
  • R Development Core Team (2008). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
  • Robertson, T. (1978). Testing for and against an order restriction on multinomial parameters. J. Amer. Statist. Assoc. 73 197–202.
  • Root-Bernstein, R. S. (1983). Mendel and methodology. Hist. Sci. 21 275–295.
  • Rosenthal, R. (1976). Experimenter Effects in Behavioural Research. Irvington, New York.
  • Seidenfeld, T. (1998). P’s in a pod: Some recipes for cooking Mendel’s data. PhilSci Archive, Department of History and Philosophy of Science and Department of Philosophy, Univ. Pittsburgh. [Also reproduced in Franklin et al. (Fra2008).]
  • Stigler, S. M. (2008). CSI: Mendel. Book review. Am. Sci. 96 425–426.
  • Thagard, P. (1988). Computational Philosophy of Science. MIT Press, Cambridge, MA.
  • Weiling, F. (1986). What about R.A. Fisher’s statement of the “Too Good” data of J. G. Mendel’s Pisum paper? J. Hered. 77 281–283.
  • Weldon, W. R. F. (1902). Mendel’s law of alternative inheritance in peas. Biometrika 1 228–254.