What is Mendel's Law of Independent Assortment?
Mendel's law of independent assortment states: "During gamete formation, the segregation of alleles for one gene is independent of the segregation of alleles for another gene."
Every gene in the genome of a diploid organism has two copies, called a gene pair. When the organism reproduces, the pair splits up into separate gametes. Which member of the pair that an offspring gets is random. This is Mendel's first law of inheritance, or the law of segregation.
But what happens when you have two gene pairs? Or more?
With one gene, call it A, when you cross an individual with a genotype of AA to an individual with aa, their offspring will all be Aa. Cross the offspring to each other, and the grandoffspring will always have a genotype ratio of 1:2:1 - 1 part AA (dominant homozygotes), 2 parts Aa (heterozygotes), and 1 part aa (recessive homozygotes). These generally appear as three quarters phenotype A and one quarter phenotype a - a 3:1 ratio (assuming neither A nor a codes for lethal defects).
Now suppose you have two genes, A and B. When you cross an individual of AABB to an individual of aabb, their offspring will all be AaBb. The grandoffspring will generally have a phenotype ratio of 9:3:3:1. That's 9 parts A and B, 3 parts A and b, 3 parts a and B, and 1 part a and b.
Where does the 9:3:3:1 ratio come from?
The genotypes behind it are every possible combination of As and as with Bs and bs, in the ratios of the Punnett square to the left. The math turns out to be two separate 1:2:1 ratios (or 3:1 phenotype ratios) - one for A and one for B - that are just stacked on top of each other.
According to Mendel's law of independent assortment, also known as the second law of inheritance, how one gene pair segregates into the gametes is completely independent of how the other gene pair segregates.