Three-Point Cross: Gene Order and Double Crossovers

A three-point cross follows three linked genes at once. It gives the gene order and the map distances in one experiment, and it catches double crossovers that a two-point cross undercounts.

The three rules

1. The two most common classes are the parentals (no crossover).
2. The two rarest classes are the double crossovers.
3. Compare a double crossover class to a parental class. The one gene that switched is the middle gene.

Worked example

A heterozygote A B C / a b c is test-crossed to a b c / a b c. The 1080 offspring:

Gene order. A b C differs from the parental A B C only at B, so B is in the middle. The order is A, B, C. (If the order is not given in the problem, the order you started with may be wrong; the double crossover test fixes it.)

Distance A to B. Count every offspring with a crossover between A and B, including double crossovers: 62 + 58 + 5 + 5 = 130. 130/1080 = 12.0%, so 12.0 map units.

Distance B to C. 38 + 42 + 5 + 5 = 90. 90/1080 = 8.3 map units.

Distance A to C. 12.0 + 8.3 = 20.4 map units. Counting only the offspring that look recombinant for A and C gives 200/1080 = 18.5%, which is too low, because a double crossover swaps the middle gene and leaves A and C in their parental combination. Add each double crossover twice (2 x 10 = 20) to get 220/1080 = 20.4%.

Coefficient of coincidence and interference

• Expected double crossovers = 0.120 x 0.083 x 1080, about 10.8.
• Observed = 10.
• Coefficient of coincidence = observed/expected, about 0.92.
• Interference = 1 - coincidence, about 0.08.

Positive interference means one crossover makes a nearby second crossover less likely, which is the usual case.

Why double crossovers are the rarest

A double crossover needs two independent events, so its frequency is roughly the product of the two single-crossover frequencies. Here that is about 1 percent, versus 8 to 12 percent for the single classes.

Common traps

• Picking the middle gene as the one that is most different from the parentals. It is the one that switched in the double crossover class.
• Leaving out the double crossovers when computing each interval. Each interval must include them.
• Using the three-point order you were given without checking. The data decide.
• Expecting distances to add exactly after a rough count. They add once double crossovers are counted in every interval they span.

One-minute recap

Parentals are most common, double crossovers are rarest, and the gene that flips in a double crossover is in the middle. Each interval counts its single crossovers plus all double crossovers. Distances then add, and coincidence compares observed to expected doubles. For the two-point basics, see the recombination frequency note.