# Punnett and His Square

Thus for Punnett, Mendel’s math became the Punnett square

Math:    (1/4 RR   +  1/2Rr   +  1/4 rr)

In the diagram, Punnett designated the gametes made in the male and female parents with single letters. The diagram shows that when the gametes combine, the offspring (inside the squares) again have the genes in pairs in their cells.  Accounting for the random union of gametes is accomplished with the four squares in the diagram.  Two squares give the same Rr result, one the RR genotype (pointed out by the arrow) and one rr. Both the algebra and diagram approaches provide the same prediction. Crossing an Rr with an Rr will produce three genotypes, RR, Rr and rr. They will be produced in a ratio based on the principle of segregation.

Therefore, Punnett’s diagram clarified for many biologists what Mendel was telling them in his published article. This was a challenging idea to understand because he was asking biologists to use something they could not see (genes) and explain something they could see (traits in peas or some other living organism).

Because Mendel recognized he was proposing a very different idea with the segregation principle, he was likely motivated to share the most convincing evidence possible.  Mendel conducted additional experiments.  One experiment was to test the hypothesis that there were two different kinds of F2s which expressed the dominant trait and these two types were being made by the F1s in predictable fractions.  How would Mendel show that F2s which had the same phenotype did not always have the same genotype?

Mendel tested the breeding behavior of the F2s.  Mendel harvested all the selfed seed produced by his F2s and grew progeny rows of F3s.  His segregation principle predicted that of the dominant F2s, there should be two that are heterozygous for every one homozygote made (on average).  The results of this experiment are summarized in Data Table 2.  Did Mendel’s data support the hypothesis?

 F2 type Mixed rows True Breeding Ratio Round seed 372 193 1.93 to 1 Yellow cotyledon 353 166 2.13 to 1 Gray seed coat 64 36 1.78 to 1 Inflated pod 71 29 2.45 to 1 Green pod 60 40 1.50 to 1 Axial flower 67 33 2.03 to 1 Tall plant 72 28 2.57 to 1
Average ratio heterozygote F2 to homozygote F2 was 2.06 to 1

Mendel’s data from rows of F3s that all came from F2s with the dominant trait supported his hypothesis.  There were always two kinds of rows (true breeding and mixed) and the rows were in a 2:1 ratio.  This fits with the principle of segregation.

The genes controlling the monogenic traits behaved in predictable ways.

By publishing these results in a scientific journal, Mendel allowed other scientists to learn from his work. This story reveals the real power of publishing research in the “permanent” scientific literature. The power of publication does not mean you were right with your science. The real power is that other scientists can find your paper, read it, think about your ideas, and then test them.  In Mendel’s case, he was already dead when his fellow biologists discovered that his new ideas to explain the biology of peas were not only correct, but universal in their application.