## Principles of Genetics (BIOL2250)

Department of Biology
Memorial University of Newfoundland

In three point linkage problems, there are eight class or four pairs of gene combinations:
a) the parentals
b) 2 pairs of single crossovers
c) 1 pair of double crossover

If the total number of progeny is not large enough to produce recombination sets involving closely linked genes one or more classes may be missing from the given information, especially the double crossovers set.

Step 1.  Organize the given classes into allele combinations
Sometimes the information of progeny classes are given as descriptions and not allele combinations.  To simplify the calculations, allele abbreviations are used.

Step 2. Match pairs of allele combinations
If the allele combinations are not correctly paired with their inverse allele combinations ( + + + with a b c and a + c with + b +), they must be paired.

Step 3.  Calculate the percentages of each allele pair
Calculate the percentage of total prtogeny of each pair of allele combinations.

Step 4.  Classification of each pair
If the genes are linked (only one large class pair), the largest class pair contains the parental combinations.  The smallest class pair represents the double crossover set and the other two pairs are the two single crossover combinations.  To double check, the numbers for each pair should be close.

Step 5.  Deterining gene order (find the middle gene)
Gene order does not depend upon right to left ordering (a b c = c b a).  Compare the parentals to the double crossover pairs.  Only the middle gene will be affected.

Step 6. Find map distances
a) Find the frequency (percentage of the total) of the single crossover pairs that represents recombination between one gene and the middle gene.  Add the frequency of the double crossover class.  The total percentage is equal to the map ditance between these two genes.
b) Repeat for the other gene compared to the middle gene.

Step 7. Draw the linkage map
With the information from above draw the map including the genes and map  distances.

Step 8.  Calculate the coefficient of coincidence
expected double crossovers (Edco) = [recombination frequency in region 1 (map units / 100)] X  [recombination frequency in region 2 (map units / 100)]
coefficient of coincidence
c.o.c = observed double crossovers  (Odco)/expected double crossovers (Edco)

Step 9.  Calculate the Interference
I = 1-c.o.c.

## Example of steps involved in solving linkage problems:

 Step 1 Step 2 Step 3 Step 4 d a n   293 d a +     21 d + n  131 d + +    55  + + +  302 + + n    24 + a +  124 + a n     50 d a n   293 + + +  302  d + n  131 + a +  124  d + +    55 + a n     50  d a +     21 + + n    24 58.5   25.5   10.5   4.5 Parentals  Single Crossover  Single Crossover  Double Crossover

Step 5. Determining the order
The parentals compared to the double crossovers (d a n   vs  d a + and + + +   vs   + + n) indicates that n is in the middle.

Step 6.  Find the map distances
a) The distance from 'd' to 'n' is 10.5% + 4.5% = 15.0% or 15 map units.
b) The distance from 'n' to 'a' is 25.5% + 4.5% = 30.0% or 30 map units.

Step 7. Draw the linkage map

d               n                             a
---+---------------+-----------------------------+---
15 map units            30 map units

Step 8.  Calculate the coefficient of coincidence
expected double crossovers (Edco) = [recombination frequency in region 1 (map units / 100)] X  [recombination frequency in region 2 (map units / 100)]

c.o.c = observed double crossovers  (Odco)/expected double crossovers (Edco)
c.o.c = 0.045/(0.15 X 0.30) = 1

Step 9.  Calculate the Interference
I = 1 - c.o.c.
I= 1 - 1 = 0.0 or 0.0 %

copyright Brian E. Staveley 1987, 1989, 1994, 2001
email me at bestave@mun.ca