DNA - Can you enlighten?

Dear Todd,

Like many, DNA is a very mysterious world to me. The discussion at the moment is very interesting. There is one aspect I wonder about, but more wonder whether I am wrong.

A person gets 50% of DNA from his/her father and 50% from his/her mother.

Todd A. Farmerie...

With the exception of the X and Y chromosomes and mtDNA, yes.

Now that 50% from the father, where did that come from? Does he pass on half of _his_ father and half of _his_ mother? So that the grandchild would have 25% from each grandparent?

Todd A. Farmerie...

Each chromosome pair remixes with each generation, so _statistically_
25% comes from each grandparent, compared to _exactly_ 50% (one of the
pair of chromosomes) coming from each parent.

I read somewhere that a person could have an ancestor, many generations ago, and not have any DNA from that ancestor, is that correct?

Todd A. Farmerie...

Absolutely. With each generation the amount from each ancestor is
divided by (statistically) 1/2. You have about 3,000,000,000 base pairs
in your DNA. Even were it to be exactly 50% and the DNA could actually
be subdivided with single-nucleotide resolution (both of these
assumptions are invalid, but for the sake of argument . . . ), by 32
generations you would have 4,000,000,000 ancestors, and some could not
possibly be represented. In fact, the point is reached much earlier,
because it is not exactly 50%, but statistically 50% and some lineage
will have drawn the short straw, and further, some regions of the DNA
are more prone to recombination than others, so you do not really have
nucleotide-level resolution in this redivision process. (Keep in mind,
too, that most [greater than 99.9%] of this DNA is identical among all
humans, so who it came from is rather immaterial.)

With the mtDNA, all of it comes from the maternal line. (There are a
few documented cases of paternal inheritance, but these are extremely
rare, and there has been no observed mixing of maternal and paternal -
just all or nothing). The Y is (virtually) entirely male-line derived
(an extremely small portion, usually ignored in such discussions, mixes
with a similar portion of the X, just like discussed above).

As to the X, a male gets his entirely from his mother, a female gets one
from each. This means that of a womans Xs, one is a statistical 50/50
mix from her maternal grandparents, while the other is 100% from her
paternal grandmother (the paternal grandfather passed his Y to the
father, and no X comes from him [except for the small portion that can
remix with the Y]). Thus the patralineal line, as well as any line with
two successive males, contribute nothing to the X. Other lines
contribute an amount reduced by 50% (statistically) for each maternal
generation (not reduced for each paternal generation), such that the
matralineal line, the lowest of those represented is simply 1/2
multiplied by itself for the number of generations involved, while the
highest represented lineage is one that alternates
male-female-male-female, and the X contribution is 1/2 times itself for
half the number of generations. THus:

For most DNA, where z - the percent contribution and n - the number of
generations, it is:

z=(1/2)^n * 100%

For the X, where m - the number of female generations:

z=(1/2)^m * 100% OR z=0 when two or more successive males occur

For the matrilineal line, m=n:

z=(1/2)^n * 100%

for the alternating line, m=n/2:

z=(1/2)^n/2 * 100%

(you asked . . . .)

I think, I am not the only one wondering about this.
Look forward to hearing from you.
Leo van de Pas