The Gregor Mendel Controversy: Early Issues of Goodness-of-Fit and Recent Issues of Genetic Linkage

Mendel J. G. , “Experiments on plant hybrids”, The origins of genetics: A Mendel source book, ed. by Stern C. and Sherwood E. (San Francisco, 1966), 1–48.

See Weinstein A. , “How unknown was Mendel's paper?”, Journal of the history of biology, x (1977), 341–64.

See Provine W. B. , The origins of theoretical population genetics (Chicago, 1971).

Fisher R. A. , “Has Mendel's work been rediscovered?”, Annals of science, i (1936), 115–37.

Fisher actually reported a value of 0.99993 (ibid., 131), an error that probably crept in due to a lack of precision in the algorithm or computing machine he used at the time.

The theoretical X² variable with N degrees of freedom is a sum of squared, Gaussian (bellshaped) random variables. Thus if two X² variables, one with N and one with M degrees of freedom, are added together, the resulting random variable has a X² distribution with N+M degrees of freedom. If we were to test the goodness-of-fit of two or more independent events producing categorical data, we could use this additive property to report the result in one statistic: The sum. Fisher used this additive property to report the fit of Mendel's data by decomposing it into pertinent sub-divisions.

Fisher , op. cit. (ref. 4), 131. Also see Corces A. and Monaghan F. , “More about Mendel's experiments: Where is the bias?”, Journal of heredity, lxxvi (1985), 384.

Fisher's, and other, statistical questions are detailed in Piegorsch W. W. , “The questions of fit in the Gregor Mendel controversy”, Communications in statistics – theory and methods, xii (1983), 2289–304.

Zirkle C. , “Some oddities in the delayed discovery of Mendelism”, Journal of heredity, lv (1964), 65–72.

Fisher , op. cit. (ref. 4), 132.

Wright S. , “Mendel's ratios”, in Stern and Sherwood (eds), op. cit. (ref. 1), 173–5.

Root-Bernstein R. S. , “Mendel and methodology”, History of science, xxi (1983), 275–95. Also see Campbell M. , “Explanations of Mendel's results”, Centaurus, xx (1976), 159–74.

Weiling F. , “Hat J. G. Mendel bei seinen Versuchen ‘zu genau’ gearbeitet? Der X²-test und seine Bedeutung fuer die Beurteilung genetischer Spaltungsverhaeltnisse”, Der Zuechter, xxxvi (1966), 359–65. Also see idem, “Mendel's ‘too good’ data in Pisum experiments”, Folia Mendeliana, vi (1970), 75–77.

Blakley G. R. , “Darwinian natural selection acting within populations”, Journal of theoretical biology, xvii (1966), 252–81.

Gustafsson Å. , “The life of Gregor Johann Mendel – Tragic or not?”, Hereditas, lxii (1969), 239–58.

Dobzhansky T. , “Looking back at Mendel's discovery”, Science, clvi (1967), 1588–9.

Pearl R. , Introduction to medical biometrics and statistics (Philadelphia, 1940), 85–90.

Bateson W. , Mendel's principles of heredity (Cambridge, 1913), 8.

Root-Bernstein , op. cit. (ref. 12), 289.

Olby R. C. , Origins of Mendelism (London, 1966).

van der Waerden B. L. , “Mendel's experiments”, Centaurus, xii (1968), 275–8.

Orel V. , “Will the story on ‘too good’ results of Mendel's data continue?”, Bioscience, xviii (1968), 776–8.

In fact, so were Corren's 1900 and Darbishire's 1908–9 results. See Weiling , op. cit. (ref. 13).

Piegorsch , op. cit. (ref. 8), 2299–300.

Fisher , op. cit. (ref. 4), 133.

Douglas L. and Novitski E. , “What chance did Mendel's experiments give him of noticing linkage?”, Heredity, xxxviii (1977), 253–7. Also see ref. 36.

Lamprecht H. , Die neue Genenkarte von Pisum, und warum Mendel in seinen Erbsenkreuzungen keine Genenkoppelung gefunden hat (Graz, 1968).

Blixt S. , “Why didn't Gregor Mendel find linkage?”, Nature, cclvi (1975), 206.

Mendel , op. cit. (ref. 1), 22.

ibid., 7.

Douglas and Novitski , op. cit. (ref. 26), 255.

Novitski E. and Blixt S. , “Mendel, linkage, and synteny”, Bioscience, xxviii (1978), 34–35.

Douglas and Novitski , op. cit. (ref. 26), 256.

Novitski and Blixt , op. cit. (ref. 32), 34.

Ibid.

Nilsson E. , Traedsgardaerter (Stockholm, 1951).

Adapted from Blixt S. Marx G. A. , and Murfet I. C. , “Descriptive list of genes for Pisum”, Pisum newsletter, x (1978), 80–101.