Trihybrid Cross Punnett Square Calculator

A trihybrid cross tracks three loci at once, and its arithmetic follows directly from the law of independent assortment. An individual heterozygous at n loci produces 2 to the n gamete types, so AaBbCc yields eight: ABC, ABc, AbC, Abc, aBC, aBc, abC, and abc. Crossing two such parents fills an 8 by 8 grid of 64 equally likely cells, containing 3 to the n = 27 distinct genotypes and, under complete dominance, 2 to the n = 8 phenotype classes in the ratio 27:9:9:9:3:3:3:1. That series is simply the expansion of (3 + 1) cubed, which is why the multiplication rule is faster than the grid: the chance of aabbcc is one quarter cubed, or 1 in 64, and the chance of showing all three dominant traits is three quarters cubed, or 27 in 64. The grid is only valid when the three genes assort independently, which in practice means they sit on different chromosomes or are separated by more than about 50 centimorgans. Linked loci inflate the parental gamete classes and deflate the recombinants, so observed counts drift toward the two parental phenotypes. Testing a trihybrid ratio uses a chi-squared statistic with 7 degrees of freedom, giving a critical value of 14.07 at p = 0.05, and the smallest class is only 1 in 64, so detecting a deviation reliably requires several hundred offspring rather than a few dozen. Epistasis between loci, differential gamete or zygote viability, sex linkage, and incomplete penetrance all distort the expected counts as well.

Gregor Mendel presented his pea experiments to the Natural History Society of Brunn in 1865 and published them in 1866. Beyond the familiar one-character and two-character crosses, he explicitly carried out trifactorial experiments on Pisum sativum, following combinations of his seven characters such as seed shape, cotyledon colour, and seed-coat colour simultaneously, and reported that the classes appeared in the proportions predicted by treating each character independently. That result was the empirical basis for what later became the law of independent assortment. His work went largely unread until 1900, when Hugo de Vries, Carl Correns, and Erich von Tschermak independently reported similar segregation, and William Bateson promoted an English translation in 1902. The physical explanation followed quickly. Walter Sutton and Theodor Boveri argued in 1902 and 1903 that chromosomes pair and separate in meiosis in exactly the way Mendel's factors behaved, and Reginald Punnett popularized the checkerboard diagram around 1905 as a way of enumerating gamete combinations without algebra. Independent assortment then met its limit: Bateson and Punnett's sweet pea data, and Thomas Hunt Morgan's Drosophila crosses from 1910 onward, showed that genes on the same chromosome travel together, and Alfred Sturtevant's 1913 linkage map turned recombination frequency into map distance. Mendel's own seven characters, later mapped to four of the pea's seven chromosome pairs, happened to be far enough apart to assort freely.