m having trouble understanding LOD scores could someone help

\'m having trouble understanding LOD scores, could someone help me work through this question?

Suppose there are two families who have affected individuals showing similar clinical symptoms. Segregation of the disease in Family A gives LOD scores in excess of +4 (over the range of = 0 to = 0.1) with a series of genetic markers that are clustered together on chromosome 2. However, with these same genetic markers, segregation of the disease in Family B gives LOD scores of –2 or below (over the range of = 0 to = 0.1). Give a likely explanation for this apparent discrepancy. Fully explain how this conclusion is reached.

Solution

lod score is calculated in 2 methods

1)when progeny size is small

assume certain genetic distance between two genes (0 and 0.1) let distance r=0.1

assume that you have 13 individuals out of which 2 are recombinant.the probability of recombination are 1-r=1-0.1=0.9

track each genotype then 1-r/2=0.9/2=0.45.the probability of recombination is r/2=0.1/2=0.05

probability of two genes are linked id(0.45)^11)*(0.5^2)

probability of non linked=0.25^(r+nr)=0.25^13

now log of oddds=probality of linked genes/non linked genes=(0.45)^11*(0.5^2)/(0.25)^13=25.7

The lod score will be log10(25.7)=1.41

repeat this processfor r=0,0.01,0.02,0.03,0.05,0.the highest value of lod score get youthe correct answer