An Example

r estimated from observed recombination = 0.30.

r = 1/2(1 - e) = 0.30
1 - e = 0.60
0.4 = e^-2d
ln(0.4) =-2d
-ln(0.4) = 2d
-(-0.916) = 2d
d = 0.458

l is the mean number of crossover events. Each crossover results in 50% recombination. Then l/2 = m.
m = recombination fraction

** The observed recombination percent was 0.3, the actual relative frequency of recombinant types is 0.458. The adjusted recombination percent is multiplied by two to equal the crossover percent. This is because each crossover event results in 50% non-parental gametes. The map is 45.8cM.

Haldane's mapping function converts the relationship of the sum fo two intervals to the sum of the total interval into a linear relationship.

r does not equal r + r

m = m + m

pg 20. Liu, B.H. Statistical Genomics.