Mendel's law of independent assortment says that alleles of different genes sort into gametes independently. You saw why in How Meiosis Makes Variation: each pair of homologous chromosomes lines up either way in metaphase I. But that only works for genes on different chromosomes. Genes that sit near each other on the same chromosome travel together.
Key idea
Linked genes are on the same chromosome and tend to be inherited together. In a test cross of a dihybrid, they give mostly parental types (the combinations the parent received) and a few recombinants, made when crossing over swaps segments between homologs.
Why it works
Suppose a fly got the chromosome carrying A and B from one parent and the chromosome carrying a and b from the other. If the genes are on that one chromosome, its gametes carry AB or ab, just as they came in, unless a crossover happens between the two genes in prophase I. Then a chromatid can carry Ab or aB. Crossovers between two close genes are rare, so recombinants are few. If the genes were on different chromosomes, all four gametes would be equally common: 1 : 1 : 1 : 1.
Worked examples
Worked example: Spotting linkage
A fly heterozygous for gray body (G) and long wings (L), which received G and L from one parent, is test-crossed to a black, short-winged fly (gg ll). The 1,000 offspring: gray long 420, black short 410, gray short 85, black long 85. Are the genes linked?
- If unlinked, each class would be about 250 (1 : 1 : 1 : 1).
- Gray long and black short are the parental combinations: 830 of 1,000.
- Gray short and black long are recombinants: 170 of 1,000.
- The big excess of parental types means the genes are linked.
Answer: Yes, linked. (A chi-square test against 1 : 1 : 1 : 1 would give a huge χ², far above 7.81.)
Worked example: Which are the parental types?
A plant got the chromosome with A and b from one parent and the one with a and B from the other. In a test cross, which offspring classes should be most common if the genes are linked?
- Parental types match the combinations on the parent's two chromosomes: Ab and aB.
- Recombinants are the new combinations: AB and ab.
Answer: The Ab and aB phenotype classes. Parental means "as the parent received them", not "dominant-dominant".
Common mistake
Expecting 1 : 1 : 1 : 1 from every dihybrid test cross. That ratio needs genes on different chromosomes (or very far apart on one). When two classes are far more common than the other two, suspect linkage; when you count, the two big classes are the parental types.
You can test linkage formally with chi-square: the null hypothesis is independent assortment (1 : 1 : 1 : 1 in a test cross).