How does the 9:3:3:1 ratio demonstrate independent assortment?

The 9:3:3:1 ratio demonstrates the law of independent assortment by showing that the inheritance of one trait does not influence the inheritance of another.1

When Gregor Mendel crossed pea plants differing in two traits—such as seed color (yellow vs. green) and seed surface (round vs. wrinkled)—he observed that the F1 generation displayed only the dominant phenotypes. When these hybrids were self-pollinated, the resulting F2 generation produced four phenotypic classes in a 9:3:3:1 ratio.1

This ratio confirms that the segregation of the color alleles occurs independently of the segregation of the seed surface alleles. This outcome is expected if the hybrid plants produce equal numbers of four distinct types of gametes, representing all possible combinations of the parental genes. The random union of these gametes results in the 9:3:3:1 distribution, proving that genes for different traits are transmitted independently of one another.12