A two-locus test cross can reveal the gamete frequencies produced by a heterozygous parent.

Suppose the parent being tested is

$$AB/ab$$

and it is crossed with a tester homozygous recessive at both loci:

$$ab/ab.$$

The tester produces only $ab$ gametes. Therefore each offspring genotype directly identifies the gamete contributed by the heterozygous parent.

For example:

Because the heterozygote is in coupling phase, $AB$ and $ab$ are parental gamete types, while $Ab$ and $aB$ are recombinant.

Recombination frequency

The recombination frequency, often written $r$, is

$$r=\frac{\text{number of recombinant offspring}}{\text{total offspring}}.$$

Equivalently, multiply by $100%$ to report a percentage.

Worked example

A test cross produces:

• $AB$: 418 offspring
• $ab$: 402 offspring
• $Ab$: 92 offspring
• $aB$: 88 offspring

The recombinant count is

$$92+88=180,$$

and the total is

$$418+402+92+88=1000.$$

Therefore

$$r=\frac{180}{1000}=0.18,$$

or

$$18%.$$

The parental classes are much more frequent than the recombinant classes, so the loci show linkage.

Reciprocal recombinant classes should be considered together

A crossover between the same two loci creates reciprocal recombinant chromatid types. In a large unbiased sample, the two recombinant classes are therefore often similar in frequency, though sampling variation can make their observed counts unequal.

The same is true for the two parental classes.

Recombination frequency is an observed transmission statistic

The value $r=0.18$ means that 18% of the scored gametes were recombinant for these two loci. It does not mean that exactly 18% of meiotic cells experienced one crossover between the loci, because a meiosis can contain zero, one or multiple crossover events and different chromatids can participate.

The test cross translates hidden gamete production into countable offspring classes, making recombination frequency experimentally measurable.