Double crossovers do not occur as often as one would expect, particularly if the distance between markers is fairly short. In theory, the probability of having a double crossover between any three markers is the probability of the two single crossovers. Consider the following map, showing percent recombination.

lz     10.7      su      14.8      gl

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The theoretical probability of a DCO would be (.107)(.148) = .0158 or 1.58%. In the population of 740 individuals that this map was based on, this would give (.0158)(740) = 11.69, or rounding up, 12 DCOs.

However, in an experiment where the actual frequency of double crossovers was calculated, it was found to be 6/740 = .008 or 0.8%.  The term "coefficient of coincidence" describes the ratio of observed to expected double crossovers. In this case it would be: c of c = 6/12 = .50 or 50%. This means that only half as many DCOs were observed as would be expected if crossovers in one interval had no effect on crossovers in the next interval. Obviously, having a crossover in one interval did interfere with having a crossover in the next interval.

The term "interference" describes the following relationship:

1 - coefficient of coincidence. Thus, for these data, the interference is 1 - 0.5 = 0.5. Interference usually increases as the distance between two markers becomes smaller, until a point where double crossing over does not occur. In this case, the coefficient of coincidence = 0 and interference = 1. This distance is usually about 10 % recombination. When the distance between two markers is greater than 45 % recombination, then the coefficient of coincidence = 1 and interference is 0. In other words, you would see (i) complete interference at 10% recombination and below, (ii) no interference at 45 % recombination and above, and (iii) steadily decreasing values of interference as you went from 10 to 45 % recombination.

What are the implications?
In medium density genome map construction, you are usually dealing with average distances in the 5 to 10 cM range, so interference should be complete and there should be very few double crossovers between markers.  Relative to % recombination and cM,  at about 10% recombination and below, the % recombination value = cM; from 10% and upward, the cM value will be larger than the % recombination value. The reason is that in making the % recombination to cM conversion, you try to take into account an average number of DCOs. As we've shown, DCOs can give you "parental" combinations of markers and thus cause you to underestimate the number of crossover events that actually occurred.    For example, consider the following percentages of recombination and the corresponding Kosambi cM values:

Kosambi cM = (0.25)ln ((1+ 2(observed recombination)/1-2 (observed recombination)).