Poisson Distribution

We have previously shown that a Poisson distribution has the form: e(1, m, m/2!, m/3!, m/4!... m/i!)

Events(X)	P(x)
0	e
1	e(m)
2	em/2
3	em/3
4	em/4

Let l = mean number of crossover events. The probability of zero crossover events is e^-l. The probability of at least one crossover event is:

1 - e^-l = 1 - p(zero crossover events)

p(at least one crossover event) = 1 - e

2r = 1 - e^-l
r = 1/2(1-e^-l)

2r = 1-e^-l
e^-l = 1-2r
ln(e^-l) = ln(1-2r)
-l = ln(1-2r)
l = -ln(1-2r)

The distance = l/2, because l is the probability of a crossover. Distance is measured in recombinantion units.

p = 1/2(1 - e)
p = 1/2(1 - e^-l)

d = 1/2(-ln(1-2r))

The actual map distance is on the horizontal axis. The observed recombination is on the vertical axis. p is the observed relative frequency of recombination in % (verticle axis). d is the actual physical distance between two loci in Morgans.

* Map distances are given in centiMorgans and the recombination fraction is given in percent.

The recombination frequency = 1/2(1 - e^-2d) = r.
d = actual recombination, r = observed recombination because only 50% of crossover events result in a non-parental type. 2d is the mean number of crossover events. Each crossover event results in 50% recombination. d = l/2, l = mean # of crossover events. l = 2d.