Factcheck study shows that Mendel’s statistics add up

The famous experiments of the 19th century Moravian friar Gregor Mendel set down universal laws that still underpin the field of genetics. The term Mendelian inheritance, describes how characteristics are passed from one generation to the next, and in biology has a status like Newtonian mechanics in physics.

There has been much discussion of how Mendel got this right at a time when, it seems, everyone else thought differently about inheritance. One idea was that Mendel developed a theory of inheritance from first principles and then set out to gather data to support this idea. So, a controversy arose after the statistician and geneticist Sir Ronald Fisher scrutinised these experiments in the 1930s and criticised Mendel’s interpretation suggesting his results were “too good to be true”; a better fit to the theoretical expectation than should be expected.

Now a study has launched a staunch defence of Mendel against the charge of statistical bias, perhaps bringing this debate to a conclusion.

John Innes Centre researcher Dr Noel Ellis and author of the study says:

“Mendel’s work has received a lot of attention since the 150th anniversary of his 1865 lectures and 1866 paper, while an earlier book ‘Ending the Mendel Fisher Controversy’, seems to have missed some important biological clues. Altogether this has left some lingering doubts about the probity of Mendel’s work, which we hope this paper have finally dispelled.”

Mendel famously selected garden pea (Pisum sativum) for his main experiments because the plants and seeds have a wide range of clearly distinguished traits and are convenient for crossing experiments. Over eight years and involving at least 28,000 pea plants and their offspring, Mendel produced clear results from which he made and tested quantitative predictions, an approach which was exceptional in biology at that time. He explained the frequency with which each trait appeared in the offspring as a consequence of the random cellular events at fertilization.

In a fresh examination of Mendel’s experiments, the researchers describe the range of pea varieties available in Mendel’s time and show that these could readily provide all the material Mendel needed for his experiments; the traits he chose to follow were the basis of the way seed types were organised in catalogues at the time.

Key findings of the new analysis were:

  • Analysis of all Mendel’s segregation ratios does not support the suggestion that they differ remarkably from expectation.
  • Fisher’s calculations assume independent segregation, but two of the traits, stem length and pod shape, may be genetically linked, so they shouldn’t be assumed to segregate independently.
  • Fisher assumed Mendel’s results were a random selection of his data – but Mendel himself made it clear that the results he presented were not a random selection of the data he collected, saying for example: “[the] first ten members from both experiment series may serve as an illustration.”
  • Fisher assumed Mendel’s experiments were conducted in the order they were presented in Mendel’s 1866 paper. But the new study shows that this is not necessarily the case.
  • Fisher failed to recognise that the survival rate of Mendel’s seedlings made one of his key assumptions very unlikely.
  • Fishers calculations do not consider deviation from expected genotype frequencies in individual seed batches or any error in genotyping based on observed phenotypes.

The paper concludes: “Statistical criticism of Mendel’s data has been a pernicious feature of discussions of his work and has done great damage to the reputation of one of history’s most insightful biological scientists. We find Mendel’s 1866 paper is exemplary both in terms of its presentation and in its interpretation of numerical data.”

Dr Ellis says: “We were surprised that Fisher and Edwards, though great statisticians, got it wrong. But not at all surprised that Mendel was right.”

Mendel never received recognition for his work in his lifetime. It was only 40 years after his death that his theory of inheritance became the foundation of the new science of “genetics”, a phrase coined by William Bateson the first director of the John Innes Centre.

Collaborators for this study were Dr Peter van Dijk from Keygene, Dr Julie Hofer from the John Innes Centre and Dr Martin Swain at IBERS, Aberystwyth.

The full study: Mendel’s pea crosses: varieties, traits and statistics appears in the journal Hereditas.

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