The One Marker

The probability that at least one marker is located within a 2d cM genome segment is:

P = 1 - (1-2d/L)ⁿ
Let L = 20M and d = 10cM
P = 1 - (1-(20/2000))ⁿ = 1 - (1-0.01)¹⁰⁰

Suppose we have data from 100 markers, then n =100.

P = 1 - (1-(20/2000))¹⁰⁰ = 1 - 0.37 = 63%

63% is the probability that at least one of the 100 marker is within a 20cM segment of the genome.

Lui states that "In practical experiments, the number of marker needed may be much less than the predicted number, if previous information and screening procedures are used. The predictions are most useful for genomes with little information."

Number of Progeny Required for Minimum Confidence Interval.
pg 192 Statistical Genomics

N >  (3.92)²
N >  c²I(Q)

Where c is the target maximum range for a 95% confidence interval, I(Q) is the expected information content per individual as Q is varied. Information content per observation for various types of progeny is provided on pg. 180 (Table 6.16).