MAPPING MODEL
When modeling recombination as a Poisson process (and neglecting crossover
interference) the recombination fraction r between two loci is related to the distance
between them by:
(1)
  clog(1 2r)
(LIU 1998)
When c = -1/2 this equation results in (HALDANE 1919) mapping function

(2)
r
1
1 e2 

2
and describes the probability of one or more crossover events occurring between two loci
 separated by physical distance .
A related function describes the expected frequency of haploids having no
apparent recombination between loci at distance :
(3)
h( ) 

1
4
1 e 3 
2

This value is equivalent to the expected frequency of haploids in which two loci
 separated by a physical distance  share the alleles of one of the parents.
Assuming that recombination rate is uniform over a chromosome, the distance
between two loci can be rescaled to an average recombination rate  so that:
(4)
h() 

1
 4 
1 e 3 
2

The expected frequency of haploids for which a locus at a physical position xi on
 chromosome j has the same parent as the locus at position  is then given by:
(5)

x 
4 i

1 
h(x i )  1 e 3  j 

2 
The scaled microarray data for polymorphic features can be fit to this function,
and the parameters  and  can be estimated numerically for each chromosome by
likelihood maximization. If all haploids in a pool share some trait, the maximum
likelihood estimate of  estimates the physical location of the cosegregating locus.