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Every genetics chapter uses the Punnett square, and most students never ask who Punnett was. He was a Cambridge zoologist who helped build genetics in the years after Mendel's work was rediscovered in 1900. His square makes ratios easy to see. The same research group also produced the sweet pea data that showed when the square's simple answer is wrong. This post covers both, with the real numbers.
Who was Reginald Punnett?
The Royal Society's biographical memoir by F. A. E. Crew records that Reginald Crundall Punnett was born at Tonbridge in Kent on 20 June 1875. A detailed account by the statistician A. W. F. Edwards in the journal Genetics (2012) fills in his career. Punnett wrote the first genetics textbook, Mendelism, in 1905. He worked closely with William Bateson from 1904, and in 1912 he became the first Arthur Balfour Professor of Genetics at Cambridge. He was elected to the Royal Society the same year. He founded the Journal of Genetics with Bateson, asked the mathematician G. H. Hardy the question that led to Hardy's 1908 paper on Mendelian proportions in a mixed population, and developed a way of sexing day-old chicks from sex-linked feather colours. He retired in 1940 and died on 3 January 1967.
Where did the square come from?
Edwards writes that the square "seems to have been a development of 1905, too late for the first edition of his Mendelism (May 1905)," and that the first published diagrams appeared in 1906. Bateson acknowledged the debt in print: "For the introduction of this system, which greatly simplifies difficult cases, I am indebted to Mr. Punnett." The second edition of Mendelism (1907) used the square, and the third (1911) called it the "chessboard" method.
In a separate history, Edwards (2012) in Studies in History and Philosophy points out that Mendel's own paper contained a similar square diagram. The NCERT Class 12 chapter Principles of Inheritance and Variation describes it as "a graphical representation to calculate the probability of all possible genotypes of offspring in a genetic cross."
How do you use the square for a dihybrid cross?
Write the four gamete types of each parent along the top and side, fill the 16 boxes, and count. For two genes, each with complete dominance, an F₁ × F₁ cross gives the familiar 9:3:3:1. Each box has the same chance, 1/16, because each gamete type has the same chance, 1/4. That assumption is where trouble starts. Our post on solving genetics problems step by step covers the routine method.
What did the sweet peas show?
Bateson, Saunders and Punnett crossed sweet peas that differed in flower colour and pollen shape. Edwards (2012) reproduces their F₂ counts from the Royal Society's Report III (1906). Among the coloured plants:
Purple, long pollen: 1,528
Purple, round pollen: 106
Red, long pollen: 117
Red, round pollen: 381
Total: 2,132 plants.
Worked check. Take each gene alone first.
Purple : red = (1,528 + 106) : (117 + 381) = 1,634 : 498, about 3.3 : 1.
Long : round = (1,528 + 117) : (106 + 381) = 1,645 : 487, about 3.4 : 1.
Each gene on its own is close to 3:1. Now test the square's 9:3:3:1 prediction for the combinations: 2,132 × 9/16 = 1,199; 2,132 × 3/16 = 400 for each of the two middle classes; 2,132 × 1/16 = 133.
The observed numbers are nowhere near: 1,528 against 1,199, 106 and 117 against about 400, and 381 against 133. The parental combinations are far too common. Bateson and Punnett called this "partial coupling".
How did they fit the data?
Edwards explains that Bateson and Punnett found the numbers fitted if gametes were made in the ratio 7 BL : 1 Bl : 1 bL : 7 bl, where B gives purple and L long pollen. A square with 16 gametes on each side has 256 boxes, and it gives 177 : 15 : 15 : 49.
You can check the 49: round pollen and red flowers need bl from both parents, and 7 × 7 = 49. Scaled to 2,132 plants, the expected numbers become 1,474, 125, 125 and 408, close to what they counted.
They did not explain coupling with chromosomes; Edwards notes that they resisted that explanation for years. T. H. Morgan's fruit fly work supplied it, and NCERT describes how Morgan coined the terms linkage and recombination. Our post on linkage and crossing over covers how this is examined.
Common mistakes:
Using 9:3:3:1 for genes that are linked. Read the question for "linked" or "same chromosome".
Checking only the combined ratio. Test each gene alone first; a 3:1 there shows each gene is segregating normally.
Giving every box the same weight when gametes are unequal. Multiply gamete frequencies instead.
If you get stuck setting up crosses like these, the Fermi Problem Library has a step-by-step solver that explains the reasoning.
What can a student take from Punnett?
A good diagram is a tool for thinking. The square made hard cases simple enough to check.
Know the assumptions behind your tool. The same group found where it fails.
Look at real numbers. The coupling was visible only because they counted thousands of plants.
Redo the sweet pea check from the numbers above, without looking, and confirm each gene alone is close to 3:1.
