Crossovers in neighboring chromosome intervals are not always statistically independent. In many organisms, one crossover changes the probability that another crossover will occur nearby. This phenomenon is called crossover interference.

A three-point cross can test for this effect by comparing the observed number of double crossovers with the number expected if crossovers in the two intervals were independent.

Suppose the recombination fractions for adjacent intervals are

$$r_{AB}=0.17$$

and

$$r_{BC}=0.154.$$

If crossover outcomes in the two intervals were independent, the expected fraction of double-crossover gametes would be approximately

$$r_{AB}r_{BC}=(0.17)(0.154)=0.02618.$$

For $1000$ scored offspring, the expected number of double crossovers would therefore be

$$1000(0.02618)\approx26.2.$$

Suppose the observed double-crossover classes contain only

$$12+10=22$$

offspring.

Coefficient of coincidence

The coefficient of coincidence compares observed and expected double crossovers:

$$\text{coefficient of coincidence} =\frac{\text{observed DCO}}{\text{expected DCO}}.$$

Here,

$$\frac{22}{26.2}\approx0.84.$$

Interference

Interference is commonly defined as

$$I=1-\text{coefficient of coincidence}.$$

Thus

$$I\approx1-0.84=0.16.$$

A positive value means fewer double crossovers occurred than would be expected from independent interval behavior. In this example, interference is about $0.16$, or $16%$ by this measure.

Interpreting the sign

• $I>0$: double crossovers are suppressed relative to independence;
• $I=0$: the observed double-crossover frequency matches the independent expectation;
• $I<0$: double crossovers are more frequent than the independent expectation.

The approximation uses recombination fractions as estimates of crossover occurrence in sufficiently short intervals. For long intervals, hidden multiple crossovers make this simple treatment less reliable.

Interference adds an important refinement to genetic maps: crossover positions are not necessarily generated by an independent random process along the chromosome. A genetic map therefore describes observed recombination behavior, including biological regulation of where crossovers occur.