Percent Recombinant Genotypes versus Map Distance

The observed recombination fraction between two loci is an estimate of one-half the number of chiasma or crossover events between two loci. This is because crossing over occurs at the four-strand stage and for single crossover events, only two of the four strands participate in the recombination. Two non-sister chromatids participate in the cross-over and the other two chromatids do not exchange chromosome segments. Each crossover event produces two recombinant genotypes and two parental types.

The observed proportion of recombinant genotypes is not an accurate estimate of one-half the number of crossover events because of double-crossovers. If we knew how many recombinant genotypes were the result of single crossovers and how many recombinant genotypes were the result of double crossover events, we could count the recombinants that were the result of a single crossover event once and then add to this twice the number of recombinants due to double crossover events. This sum would represent the total number of crossover events between two loci. The physical map distance between two loci is proportional to the total number of crossover events that occurred between the two loci.

The average of two-strand, three-strand, and four-strand double- crossovers is fifty percent recombination. Single crossovers also result in fifty percent recombinant and fifty percent non-recombinant genotypes. The difference between single and double crossovers is that the single crossovers represent one event while double crossovers represent two events. When the physical mapping distance in Centimorgans is estimated from the observed proportion of recombinant gentotypes, the distance between loci is underestimated. The reason that the physical distance is underestimated is that double-crossovers only result in fifty percent recombinant genotypes the same as single- crossover events. Since we cannot determine the number of double- crossovers, we count each pair of recombinant genotypes as one crossover event. The failure to count recombinant genotypes caused by double- crossover events as two crossover events results in an under-estimation of the map distance.

The greater the proportion of recombinant genotypes, the greater the map distance between the two loci of interest. This is because the probability of a crossover event is assummed to be constant at each point on the chromosome. Therefore the longer the distance between two loci, the higher the probability of a crossover occurring between any two points on the chromosome. As the physical distance between two loci increases beyond 10 Centimorgans, the probability of double crossover events between two loci increases. For very short physical distances between two loci, the probability of double crossovers is small enough that the physical distance can be accurately estimated based on the assumption that all recombinant genotypes are the result of single crossover events.