The main part of the Punnett's scientific life was scientific collaboration with William Bateson; the two established genetics at Cambridge. Together with William Bateson, Punnett discovered gene linkage in sweet peas Lathyrus odoratus. Moreover, Punnett analyzed various ratios occurring in Mendelian inheritance and introduced Punnett's square, which helped to define the number and variety of genetic combinations by showing how zygotes are made by combinations of gametes.
The graphic method developed by Punnett simplified the dificult cases, the squares being formed by simply arranging paternal gamets in rows and maternal gamets in columns.
Neither Bateson nor Punnett have accepted the chromosomal explanation of linkage when observing coupling and repulsions phenomena in sweet pea.
Punnett has developed breeding experiments, in both animals and plants, mostly working on the genetics of sweet pea, poultry and maize.