AP® Biology · Unit 5 · Topic 5.3
Independent Assortment and Dihybrid Crosses
Independent assortment means alleles for different genes sort into gametes independently of each other, so a dihybrid cross of two heterozygotes gives phenotypes in a 9:3:3:1 ratio. Because the genes are independent, you can find any combined probability just by multiplying the separate probabilities for each gene.
Mendel's law of independent assortment says genes on different chromosomes (or far apart on the same one) get distributed into gametes without influencing each other. A plant that is RrYy makes four kinds of gametes in equal proportion: RY, Ry, rY, and ry. Cross two RrYy parents and you can lay out all 16 combinations in a Punnett square, one gamete type from each parent along each edge. Sorting the 16 boxes by phenotype gives 9 round-yellow, 3 round-green, 3 wrinkled-yellow, and 1 wrinkled-green: the 9:3:3:1 ratio.
You don't need the full 16-box grid to get there. Each gene segregates on its own into a 3:1 ratio of dominant to recessive phenotype. Since the genes assort independently, the combined probability of any phenotype combination is just the product of the two separate ratios: (3/4 round + 1/4 wrinkled) times (3/4 yellow + 1/4 green) expands to 9/16, 3/16, 3/16, 1/16. This product rule scales to any number of genes: for AaBbCc x AaBbCc, the chance of aabbCc is P(aa) x P(bb) x P(Cc) = 1/4 x 1/4 x 1/2 = 1/32, no giant Punnett square required.
This sits right next to test crosses and pedigree analysis in the unit, because the 9:3:3:1 expectation is the baseline that chi-square tests check real data against. A test cross, crossing an unknown genotype with a homozygous recessive, is a different tool: it reveals whether an individual is homozygous or heterozygous dominant, not the ratio from two known heterozygotes.
Key terms
- Independent assortment
- The principle that alleles of different genes separate into gametes independently of one another.
- Dihybrid cross
- A cross tracking two genes at once, typically between two double heterozygotes like RrYy x RrYy.
- Product rule
- The probability of two independent events both occurring equals the product of their individual probabilities.
- Test cross
- A cross between an individual of unknown genotype and a homozygous recessive individual, used to reveal hidden alleles.
- Phenotypic ratio
- The proportion of offspring showing each observable trait combination, such as 9:3:3:1 in a dihybrid cross.
Watch it explained
- How it worksWalk me through building a 16 box Punnett square for a RrYy by RrYy cross.
- How it worksHow does multiplying two separate 3 to 1 ratios reproduce the 9 to 3 to 3 to 1 result?
- Worked exampleFind the fraction of offspring that are round and green from a RrYy by RrYy cross.
- Worked exampleFind the chance of an aabbCc offspring from an AaBbCc by AaBbCc cross using the product rule.
- Common mistakeWhy isn't a test cross the same thing as crossing two heterozygotes?
Check yourself
End of topic.