4.2 Dihybrid Crosses, Linkage and Recombination

A dihybrid cross follows two loci. For loci on different chromosomes, homologous-pair orientations at meiosis I are independent. An $AaBb$ individual makes $AB$, $Ab$, $aB$ and $ab$ gametes equally, assuming equal survival. Crossing two double heterozygotes gives 9:3:3:1 phenotypes under complete dominance.

Humans have far more genes than chromosomes, so many loci share a chromosome. Such loci are linked and form one linkage group. Alleles on the same DNA molecule tend to enter a gamete together, producing more parental combinations than recombinant combinations.

Writing only $AaBb$ loses physical information. In coupling, $AB/ab$ places AB together; in repulsion, $Ab/aB$ places Ab together. Without crossing over, coupling produces AB and ab gametes, while repulsion produces Ab and aB. The same alleles can therefore give very different ratios.

During prophase I, non-sister chromatids can exchange corresponding DNA at a chiasma. A crossover between the loci creates two reciprocal recombinant chromatids while two remain parental. Crossovers outside the interval do not recombine the loci, so close loci generate few recombinants.

In a test cross, the recessive tester exposes gametes from the heterozygote. Recombinant percentage estimates map distance; 1% recombination is one centimorgan. Hotspots mean map distance is not a uniform base-pair ruler.

Observed recombination does not exceed 50%. At large separations, multiple crossovers can restore parental combinations and the four classes approach equality. Near 50%, data do not reveal linkage: loci may be on different chromosomes or far apart on one. Morgan used such deviations in fruit flies to connect genes with chromosomes.

For $AB/ab$, a test cross against $ab/ab$ labels AB and ab offspring as parental and Ab and aB as recombinant. For $Ab/aB$, those labels reverse. 'Parental' refers to allele combinations on the heterozygote's original homologues, not automatically to dominant or common phenotypes. Phase must be inferred from the two largest reciprocal offspring classes when a sufficiently large test-cross dataset is provided.

A double heterozygote at unlinked loci creates four gamete types at 25% each. A linked double heterozygote with 12% recombination creates recombinant gametes at about 6% each and parental gametes at about 44% each. The reciprocal classes within each pair should be similar because one crossover produces both products, though sampling causes small numerical differences.

A dihybrid test cross is especially revealing because the tester's recessive alleles do not hide the tested gamete. By contrast, crossing two double heterozygotes merges several gamete combinations into the same phenotype, making linkage harder to diagnose. Experimental design matters: choose a cross whose observable offspring retain the information needed to distinguish hypotheses.

Mendel's law of independent assortment is best treated as a conditional model, not an exceptionless statement. It works for loci on different chromosomes and for loci sufficiently far apart to behave as unlinked. Morgan's anomalous fruit-fly ratios did not discard segregation; they added chromosome position and crossing over to explain when assortment predictions fail.

Map distances from several gene pairs can be combined to infer order. If A–B is 5 cM, B–C is 8 cM and A–C is about 13 cM, B plausibly lies between A and C. If A–C were about 3 cM instead, A and C would lie on the same side of B. Three-point test crosses are more powerful because double crossovers can be detected rather than mistaken for parental chromatids.