1
MAPPING FUNCTION 1/27/09
As you learned in class, as the map distance between two linked genes increases, the
probability of multiple crossovers between them increases too. Thus, the observed
frequency of crossover recombination between the two genes will underestimate the true
map distance between them if the two genes are quite far apart. To correct for these
underestimates/errors, the great geneticist, J.B.S. Haldane developed a mapping function
(i.e., an equation to correct for these underestimates due to multiple crossovers). His
mapping function relies on the Poisson equation, so you should refer back to the Poisson
web handout (available at our course web site).
Once again, the Poisson equation is:
e
m
m
x
x
xP
−
=
!
)(
,
where m is the mean number of events for a defined unit of space or time (e.g., crossovers
per meiosis); x is the number of successes (e.g., specific number of actual crossovers),
and e is the natural base (2.717271727…..).
We are interested in the special case of having x = 0 (or no crossovers). Plugging x = 0
into the above equation reduces it to:
P (0) = (m
0
/ 0!) e
-m
= e
-m
.
If e
-m
refers to the probability of having no crossover, then (1 – e
-m
) is the probability of
having one or more crossovers. Haldane noted that this probability is the one that
underlies the frequency of recombination (RF). That is, one or more crossovers
contribute to the recombination frequency. He formalized this in his following equation.
RF = 0.5 (1 – e
-m
)
.
The 0.5 is for the fact that any crossover affects only two of the four chromatids of a
tetrad as we noted in class.
As an example, let’s say that the observed recombination frequency is 27.5% (0.275).
Then, plugging this into Haldane’s equation, we get:
0.275 = 0.5 (1 – e
-m
)
.
Rearranging this equation, we can solve for e
-m
.
e
-m
= 1 – (2 x 0.275) = 0.45
.
