## Equations for estimation of recombination fraction

between a marker and a translocation breakpoint

**Kosterin, O.E., Pukhnacheva, N.V.,**
Gorel, F.L. and Berdnikov, V.A. |
Institute of Cytology & Genetics
Novosibirsk 630090 Russia |

**W**e present here equations for estimation
of recombination fraction between a marker and a translocation breakpoint, followed by
pollen fertility versus semisterility, in F_{2} progenies
with the maximum likelihood method.

If a lethal is linked to a recessive allele *a* of a marker, then the maximum
likelihood estimation p of the recombination fraction and its standard deviation s will be
determined by the following formulae:

1. A marker is codominant. There exist six phenotypic classes with respect to the marker
and pollen fertility. Let us introduce the following designations: N, the total number of
progeny; A, the sum of three major classes: homozygotes for the marker with fertile pollen
and heterozygote with semisterile pollen; B, the sum of three minor classes: heterozygote
with fertile pollen and homozygotes with semisterile pollen.

Solution of the maximum likelihood equation leads to the following formulae for
estimations of recombination fraction* p* and its standard deviation *s*:

2. The marker is dominant. Let us designate the four phenotypic classes
existing as follows: A, dominant fertile; B, recessive fertile; C, dominant semisterile;
D, recessive semisterile. The estimation p can be found by numerical solution of the
equation

**- 2A / (1 + 2p - 2p**^{2})
+ 2B / (1 - 2p + 2p^{2}) + C / (1 - p
+ p^{2}) - D / (p - p^{2}) = 0

while the standard deviation is

*
*