BSCI 1511L Statistics Manual: Calculation of recombination frequencies

Note: The term "frequency" can refer to either absolute frequency or relative frequency. Review the definitions of relative and absolute frequencies in sections 1.1 through 1.3 of the statistics manual. 

Linkage analysis of this type was first performed by Bridges and Olbrycht (1926).  Using the notation above, they pointed out that +mf and w++ phenotypes represent single cross-overs between w and m and that ++f and wm+ phenotypes represent single cross-overs between m and f.  It must be remembered, however, that double cross-overs also represent recombination events both between w and m, and between m and f.  These cases must be included when calculating either of the recombination frequencies.  Therefore, the frequency of crossing-over between w and m is equal to the sum of the relative frequencies of single and double crossover outcomes:

                         (+mf)              +  (w++) + (+m+) + (w+f)         or  (+mf) + (w++) + (+m+) + (w+f)

                        total of all flies  total        total       total                            total of all flies

where each value in parentheses is the absolute frequency (count) of flies in the category.  Likewise, the frequency crossing-over between m and f is equal to:

                         (wm+) + (++f) + (+m+) + (w+f)           or  (wm+) + (++f) + (+m+) + (w+f)

                         total      total       total      total                        total of all flies

So far, we have referred to these calculated values as recombination frequencies.  A relative frequency represents the fraction of the time that something happens and can be expressed as either a decimal fraction (ranging between 0 and 1) or as a percent.  Because crossing-over is more likely the further apart loci are spaced physically on the chromosome, map distances or actual physical distances between loci on the chromosomes are proportional to their recombination frequencies.  For this reason, recombination frequencies are used as a unit of distance along a chromosome.  The unit of chromosome map distance is called a morgan (M), in honor of the early geneticist Thomas Hunt Morgan, and is equivalent to a decimal recombination frequency.  More commonly, map distances are expressed as centimorgans (cM), which would then be equivalent to a recombination frequency expressed as a percent. 

If two loci are not on the same chromosome, then they will assort randomly.  If we incorrectly thought that two loci were linked and performed the same kind of crosses as we did here, we would get a 1:1:1:1 ratio of phenotypes.  The two groups that we would conclude were "recombinant" phenotypes would have a frequency of ¼ + ¼  or 50%.  So unlinked loci that assort randomly behave just like linked loci that are 50 cM apart.  Linked loci that are more than 50 cM apart recombine as often as they remain together and therefore behave as if they were on separate chromosomes.  This means that the mapping method that we used in this experiment is not effective for determining the distance between two loci on a chromosome that are more than 50 cM apart. 

However, map distances between widely spaced loci can be calculated by summing the distances between intervening loci.  For example, the map distance between w and f is equal to the distance between w and m plus the distance between m and f.  With enough this kind of information, we could map the distance between many gene loci.  This has been done for Drosophila (Table 1; the X chromosome is also called chromosome 1) and a few other organisms. 

Table 1. Drosophila melanogaster linkage map.  Distances are expressed in cM.

Fig. 1  Organization of types of Drosophila melanogaster chromosomes.  The chromosomes are to scale with megabase-pair references oriented as in the National Center for Biotechnology Information (NCBI) database. Note that only one of each kind of chromosomes is shown here - the total number of chromosomes in an individual is eight (i.e. 2N=8).  Males have an X and a Y chromosome and two each of chromosomes 2 through 4.  Females have two X chromosomes and two each of chromosomes 2 through 4. 

Table 1 was derived long ago using the tools of classic Mendelian genetics.  Since that time, the entire genome of D. melanogaster has been sequenced and is now available on the Internet via the NCBI web site. 

Figure 1 (previously shown in the Drosophila I experiment) shows the relative sizes of the chromosomes and the locations of their centromeres.  The centimorgan distances are approximate and estimated by comparing the map distances in Table 1 with bp numbers in the NCBI database. 

You can jump directly to the Drosophila melanogaster genomeby clicking here.  From the genome view entry page, click on the cartoon of the X chromosome.  This will take you to the map view of the X chromosome.  To find a locus on the chromosome, type the name in the Search box at the top of the screen.  Then click on the Find in This View button.