The AI Journal

Gregor Mendel’s 1866 paper reports pea-breeding counts across seven traits, run in ratios that should cluster around 3:1 for dominant to recessive offspring if his theory of discrete, independently inherited factors was correct. In 1936 the statistician Ronald Fisher pooled Mendel’s results and ran a chi-square test against that expectation. The aggregate fit was not merely good; it was good at a probability of less than one in ten thousand. Honest counting, repeated across the scale of Mendel’s programme, should drift further from the predicted ratio far more often than this. Fisher’s number is the seed of a century-long argument that is now usually summarised as settled: Fisher accused Mendel of fraud, and later scholarship cleared his name. Both halves of that sentence misdescribe what actually happened, and the misdescription has let the real puzzle sit unanswered while everyone argues about a charge nobody filed.

Fisher did not accuse Mendel of fraud. His 1936 paper is explicit that the aggregate agreement is implausible on the assumption of honest, unadjusted reporting, and he raises the possibility that the data were brought closer to expectation somewhere between the counting and the publication. But he assigns that possible adjustment, if it occurred, more readily to an assistant or gardener acting on Mendel’s behalf than to Mendel himself, whom he describes with evident professional respect as a careful and serious experimenter. This is a narrower and more cautious claim than “the data were cooked,” and a still narrower one than “Mendel cooked them.” Fisher was, by 1936, one of the chief architects of the modern synthesis that put Mendelian inheritance at the centre of evolutionary biology; he had every institutional reason to want the founding data to hold up, and his paper reads as a statistician troubled by a number rather than a critic looking for a scandal. Somewhere in the retelling, a hedge about an anonymous gardener’s possible unconscious tidying became a straightforward accusation against the man whose name is on the paper. That compression is doing a great deal of work in how the dispute gets taught.

The defence built up against the compressed version is substantial, and largely sound on its own narrow terms. Novitski’s 2004 paper in Genetics revisits the specific statistical choices behind Fisher’s aggregate chi-square — how trials were pooled, what the effective degrees of freedom should be — and shows the implausibility is less extreme than Fisher’s headline figure implies once those choices are scrutinised, though it remains real. Fairbanks and Rytting’s 2001 review in the American Journal of Botany surveys several of Mendel’s disputed data sets and proposes that classification of borderline plants — judging by eye which of two close phenotypes a given pea displayed — would tend, entirely without intent, to resolve ambiguous cases in the direction the experimenter already expected. Franklin, Edwards, Fairbanks, Hartl and Seidenfeld’s 2008 book-length reassessment, bringing a statistician, a geneticist and historians of science to the same material, concludes after extensive review that no evidence supports deliberate fabrication by Mendel. Taken together, this is a serious and largely successful defence against the charge that Mendel lied.

It is a defence against a charge that was barely made and that was never, in Fisher’s own text, the interesting part of his finding. Suppose every word of it is granted: suppose Mendel never altered a count, never discarded an inconvenient plant, never nudged a borderline classification. The chi-square anomaly does not go away. It was never a claim about Mendel’s character; it was a claim about the shape of the published numbers, and that shape is still there, agreeing with theoretical expectation to a degree that random sampling should not reliably produce. Exonerating the man answers a question about motive. It leaves untouched the question about mechanism: given that nobody lied, why do the numbers look like someone did?

A specific answer to that question has existed since 2010 and gets cited far less than the character debate it does not participate in. Pires and Branco, writing in Statistical Science, build an explicit model in which no single number in Mendel’s records needs to be altered for the aggregate fit to come out exactly this implausible. Their mechanism is a selective stopping and repetition rule: across a research programme that ran for the better part of a decade, a trial whose early counts drifted from the expected ratio was more likely to be extended, repeated, or supplemented with further plants than one whose early counts already matched. Confirming runs get banked; surprising runs get a second look. Applied consistently over years of breeding seasons, this produces precisely the kind of chi-square compression Fisher detected, built entirely out of genuine, unaltered counts selectively retained. The model makes a specific prediction rather than a plausible-sounding story: trials that happened to confirm the expected ratio early should show smaller final sample sizes than trials that initially drifted and were evidently extended, and this pattern is checkable directly against the sample sizes Mendel actually reported trait by trait. It has held up under that check, yet the standard account of the controversy still runs from Fisher’s 1936 paper straight to the fraud rebuttals, as though the dispute were only ever about Mendel’s honesty.

The strongest objection to treating this as a tidy resolution is that it may not be one. Deciding, even unconsciously, that a confirming trial is finished while a deviating one needs another look is itself a form of bias toward the expected answer — arguably the very thing the fraud charge was reaching for, just described in the vocabulary of stopping rules instead of the vocabulary of cheating. If that is right, the Pires–Branco account has not replaced the accusation so much as given it a more clinical name, and the defenders who insist on “no fraud” are drawing a line that this mechanism quietly erases.

The line is worth drawing anyway, because fabrication and selective retention are not the same failure, even when they produce similar-looking data. Fabrication invents a number that was never observed. Selective stopping reports only numbers that were genuinely observed, filtered by which observations prompted a second trial — a practice that was, in Mendel’s era and for a long time afterward, an unremarked feature of how experiments were run rather than a personal lapse singled out in one man’s notebook. The claim worth defending is not that Mendel’s data are untainted by any bias whatsoever; it is narrower than that, and more useful: that nothing in the record requires invented numbers, and that a specific, testable account of how real ones could produce this exact anomaly has been sitting in the literature since 2010, unabsorbed by a controversy still organised around whether one dead naturalist lied.

What should have closed the matter did not, because the dispute had already calcified around the wrong question: a referendum on Mendel’s character rather than a mechanism in his data. The chi-square anomaly Fisher calculated in 1936 is exactly as implausible today as it was then. What has changed is that a model exists which reproduces it from ordinary, nameable experimental behaviour, and the textbooks keep citing Fisher’s paper to argue about an accusation it does not contain.