Mendel also followed two traits at once, such as seed shape (R round, r wrinkled) and seed color (Y yellow, y green). A cross of two RrYy plants is a dihybrid cross. It rests on the product rule and on independent assortment.
Key idea
A gamete carries one allele of each gene. RrYy makes four kinds of gametes, RY, Ry, rY and ry, in equal numbers. RrYy × RrYy fills a 16-box square with a 9 : 3 : 3 : 1 phenotype ratio.
Why it works
Because the genes sort independently, each gene gives its usual 3 : 1. Combine them with the product rule: both dominant ¾ × ¾ = 9/16; dominant shape and green ¾ × ¼ = 3/16; wrinkled and yellow ¼ × ¾ = 3/16; both recessive ¼ × ¼ = 1/16. Those are 9 : 3 : 3 : 1.
Worked example: Writing gametes
List the gametes of AaBb, and of AABb.
- Pair each allele of gene A with each allele of gene B, like FOIL.
- AaBb: A with B, A with b, a with B, a with b.
- AABb: A with B, A with b (both A alleles are the same).
Answer: AaBb: AB, Ab, aB, ab. AABb: AB, Ab.
Worked example: Counting offspring
From RrYy × RrYy, 320 seeds are grown. About how many are wrinkled and yellow?
- Wrinkled: ¼. Yellow: ¾.
- Wrinkled and yellow: ¼ × ¾ = 3/16.
- 3/16 of 320 = 60.
Answer: About 60.
Worked example: A test cross with two genes
RrYy × rryy. What is the phenotype ratio?
- RrYy makes RY, Ry, rY, ry, each ¼; rryy makes only ry.
- Offspring: RrYy, Rryy, rrYy, rryy, each ¼.
Answer: 1 : 1 : 1 : 1 (round yellow : round green : wrinkled yellow : wrinkled green).
Common mistake
The most common mistake is writing gametes such as Aa or Bb: two alleles of the same gene. Meiosis separates the two alleles of each gene, so a gamete never has both. Check every gamete: it must have exactly one letter for each gene.
The 9 : 3 : 3 : 1 rule needs genes on different chromosomes. Genes close together on the same chromosome tend to travel together; that is linkage, a topic for later study.