Arline and Sidney Sachs
Marilyn Gelber asked what the chances of getting a matching segment of
105.5 cM with a second cousin. I estimated it is about 1% of the time.
My logic which is not simple:
Only half of the parent DNA is pass to each of the children. Between
sisters, they is a 75% chance that they get the matching DNA >from one or
both of their common parents. Then >from each grandparent, we will get on
average 25% of their DNA. Therefore second cousins should have around
4.7% (.75*.25*.25) on average common DNA. That means that second cousins
on average should share 159 cM (3400 * .047) of DNA. That DNA is not
random over the 22 chromosomes that are passed to the next generation. On
each chromosomes, segment of DNA are copy >from one parent for awhile and
then switch to the other parent. The point that this occurred is call a
crossover point. On average with each passing >from parent to child, there
are on average around 34 crossovers randomly over all of the DNA.
Therefore in three generations there are around 102 (34 * 3) crossovers.
Adding the 22 chromosomes, >from a parent we will have on average 124
segments >from the great-grandparents. This average about 15.5 (124 / 8)
segments for each with an average length about 27 cM (3400/124). This is
about one quarter the length of Marilyn Gelber longest segment with her
second cousin. Using Poisson, the chances of getting a segment four time
the average is about 1.5% of the time. Times this percentage by the
numbers of segments (124) times the percentage of common DNA (.047), on
average second cousins will have a common segments length of this length
about 1% of the time.