Dihybrid Cross Punnett Square Calculator

A dihybrid cross follows two loci at once. A parent heterozygous at both, such as AaBb, produces four gamete types in equal proportion, AB, Ab, aB and ab, because the alleles at unlinked loci segregate independently during meiosis. Crossing two such parents gives a 4 by 4 grid whose 16 cells enumerate equally likely fertilizations, and the familiar 9:3:3:1 phenotypic ratio is nothing more than the product of two independent 3:1 monohybrid ratios. The genotypic breakdown is finer, giving nine distinct genotypes in the proportions 1:2:1:2:4:2:1:2:1, with the double heterozygote AaBb the single most common outcome at 4 in 16. A test cross against a doubly recessive aabb parent collapses the grid to a 1:1:1:1 result, which is useful precisely because the offspring phenotypes read out the gamete types of the unknown parent directly. The ratio holds only under a specific set of conditions: independent assortment, complete dominance at both loci, equal viability of all genotypes, and a sample large enough for proportions to emerge. Each condition has a characteristic failure mode. Genes sitting close together on the same chromosome are linked and yield an excess of parental combinations. Epistasis, where one locus masks the other, converts 9:3:3:1 into 9:7, 12:3:1, 9:3:4, 13:3 or 15:1 depending on the interaction. Incomplete dominance makes all nine genotypes phenotypically distinct. Lethal alleles delete classes outright. It is also worth stressing that the square states probabilities, not an actual set of 16 offspring; real progeny counts deviate by chance, and the proper check is a chi-square goodness-of-fit test against 9:3:3:1 with three degrees of freedom and a critical value of 7.815.

Gregor Mendel, an Augustinian friar at the monastery in Brno, carried out his pea crosses between roughly 1856 and 1863, presented the results to the Natural History Society of Bruenn in 1865, and published them as Versuche ueber Pflanzen-Hybriden in 1866. He tracked seven characters, and the decisive two-character experiment crossed plants differing in both seed shape and seed colour. Among 556 seeds from the F2 generation he counted 315 round yellow, 108 round green, 101 wrinkled yellow and 32 wrinkled green, close enough to 9:3:3:1 to establish that the two characters were transmitted independently of one another. The paper attracted almost no attention for over three decades until Hugo de Vries, Carl Correns and Erich von Tschermak independently rediscovered the principles in 1900. The grid diagram itself is not Mendel's. It was introduced by Reginald Punnett at Cambridge in the first decade of the twentieth century as a teaching device, developed alongside William Bateson, who coined the word genetics in 1906. There is a neat irony in the pairing, because in 1905 Bateson and Punnett published sweet pea data in which flower colour and pollen grain shape plainly did not assort independently, producing an excess of the parental combinations they described as coupling. They could not explain it. The resolution came from Thomas Hunt Morgan's group a few years later in the form of genetic linkage, so the dihybrid square is simultaneously the classic demonstration of independent assortment and the tool that first exposed its limits.