Once Can Be Enough by Allan Franklin & Ronald Laymon

Author:Allan Franklin & Ronald Laymon
Language: eng
Format: epub
ISBN: 9783030625658
Publisher: Springer International Publishing

5.3 “Too Good to Be True”

In 1936 R.A. Fisher, the distinguished British geneticist and statistician, reanalyzed Mendel’s data and concluded, on the basis of χ2 analysis, that Mendel’s data fit his hypotheses too well (Fisher 1936). They were “too good to be true.” Fisher obtained a value of χ2 = 41.6056 for Mendel’s 84 experiments. A fit this good between data and theory has a probability of 0.00007, a highly unlikely event. Given his admiration for Mendel’s work, Fischer suggested that Mendel’s data had been falsified by a well-intentioned, unnamed assistant. Fisher’s χ2 analysis, however, attracted little attention until around 1965, the centenary of the publication of Mendel’s paper. This led to an avalanche of commentary that has been extensively reviewed in Franklin et al. (2008, pp. 1–77) which also contains reprints of several of the most important papers in that deluge.

Here we will focus attention on what we consider in retrospect to be the most salient responses to Fischer’s conclusion that Mendel’s data were “too good to be true.” We do this to indicate in a telling and concise manner the nature of the problems with systematic uncertainty and possible confounding causes that Mendel—in large part unknowingly—had to deal with. Once Mendel’s work had been rediscovered these problems would in turn provide an ongoing challenge for the development of the science of genetics.

In short, there are two basic approaches to dealing with what has become known as the Mendelian Paradox, that is, the conflict between Mendel’s beautifully conceived experimental scheme and the surprising agreement between his data and his hypotheses. First, that Mendel somehow, perhaps unknowingly and inadvertently, biased his experimental procedures by improperly culling suspect progeny from his test samples. Second, that the expression of the Mendelian factors was corrupted by confounding causes which meant that Mendel’s experimental samples were not extracted from a population where those factors satisfied the binomial distribution. In other words, Fisher’s χ2 analysis was inapplicable because Mendel’s peas were either not independently distributed within self-fertilizing pods or because of some confounding cause were not randomly expressed.

We begin our review with the second approach because, in the present context, it best sets the stage for a consideration of the first approach. Teddy Seidenfeld considered such a confounding process based on what he refers to as the Correlated Pollen Model15:Suppose that within the pea-flower for hybrids, 10 egg cells form according an i.i.d. [independent and identically distributed] “fair” (binomial) distribution. However, approximating the speculated, checkerboard pattern that pollen have on the anther, suppose that exactly 5 of every 10 pollen cells arriving at the egg cells are dominant. Last, assume that, with equal probability, 2 of these 10 zygotes spontaneously abort, leaving 8 peas/pod. The result is a model where pollen cells are negatively correlated within a pod (Seidenfeld in Franklin et al. (2008, p. 233).

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