In fact, by focusing only on common ancestry of DNA that gets inherited,all CA's found in genetic studies will be much older than the MRCA.

Our most recent female-female line ancestor is called "Mitochondrial Eve"since Mitochondrial DNA passes (almost) entirely through the female lineand so may be used to estimate a date for her.Contrary to a lot of confused discussion,e.g. [Ayala, 1995],Mitochondrial Eve's existence is not in doubt.We can work it out from our armchair.What is in dispute is the date,which has been estimated at 100,000 to 200,000 years ago.

Also contrary to much confused discussion by paleontologists,no date for Mitochondrial Eve implies any sort ofpopulation bottleneck at that time. Mitochondrial Eve would have co-existedwith huge numbers of male andfemale relations from whom we also descend.Indeed, [Ayala, 1995] points out thatour inheritance from Mitochondrial Evewould be only 1 part in 400,000 of our DNA.The rest we inherit from her contemporaries.But he still spends half the paper attacking the ideaof a small ancestral population - an idea that no one believes.

As a result of thinking about Y chromosome Adam, we can see that if we use surnames strictly in the male line forever into the future,then not only will all hereditary titles die out,but all surnames except one will die out too.

The world does not of course strictly follow that surname rule,but the West approximately does,and surnames do go extinct.Without a mechanism for generating entirely new surnames from scratch(not belonging to either parent)the diversity of surnames can only decline.Neil Frasernicely describes it as"a random walk - next to a cliff. The only force acting on the system is that once a name randomly stumbles to zero it is gone and can never recover."

Say for one gene, your father's two copies are AB,your mother's are CD.You could end up with AC, your sibling could end up with BD.For this gene only,there is no genetic evidence of your recent common ancestry.

If there are n events at which to choose betweenyour father's grandfather copy and grandmother copy,the probability of you inheriting from himnone of your grandfather's DNA (*)is:

(*) If you are your father's daughter.If his son, you must inherit the Y chromosome.We will ignore the special cases of themale-male and female-female lines.Admittedly these are hard to ignore with grandparents,since they are 2 of only 4 lines,but these 2 special lines can be ignored as we go back 10 generations or more.

[Chang, 1999, author's reply]discusses this extreme case.I'm not sure if n=23 here(the no. of chromosomes).Then the probability of all grandmother,none from grandfather, would be(1/2)23= 1 in 223= 1 in 8.4 million.

If we allow for crossover, the probability of all grandmother,none from grandfather, is:

If n=23,(1/4)23= 1 in 246= 1 in 70 trillion.

Q. Is n=23?

If n=23probability (3/4)23 = 1 in 747.

How does crossover affect this?If one great-grandparent is c,your father has 3/4 chance of getting either c,or c crossed with d.He then has 3/4 chance of passing this on,either as is or crossed over.So you have (3/4)2 = 0.56 chance of inheriting some c,or 1 - (3/4)2 = 0.44 chance of inheriting none.So we get chance of inheriting no DNAfrom a great-grandparent is:

If n=23probability (0.44)23= 1 in 181 million.

Q. Is n=23?

If n=23, the probability depends on t.This is equal to 1/2 for:1-(1/2)t-1 = 0.971/2t-1 = 0.032t-1 = 33.7t-1 = 5In other words, more than 6 generations back,the prob. of inheriting no DNA at all from one of yourancestors is more than 1/2.

But what about crossover?With crossover, the probability of inheriting none of the DNAof an ancestor at generation t is:

If n=23, the probability depends on t.This is equal to 1/2 for:(3/4)t-1 = 0.03t-1 = 12In other words, more than 13 generations back,the prob. of inheriting no DNA at all from one of yourancestors is more than 1/2.Note that at 13 generations back (c. 1500s - 1600s) you have8192 ancestors.

Q. Is n=23?

For small n, it is easier (more probable) to not inherit from an ancestor.With a single event (n=1), it could easily lose that event.With a large number of events, it is unlikely it losesthem all.For large n, it is harder to not inheritfrom an ancestor.As n goes to infinity, you must have inherited some DNAfrom the ancestor.

We can see that above, for any finite t,as n goes to infinity,the probability of not inheriting goes to zero.

For an MRCA 30 generations ago,you need 230 people = 1 billion peopleto be sure that their samples of1 part in 230 of the ancestor's DNAmust overlap.

As I say, I need to do more reading on this.I'm sure this has been discussed before.There is some discussion of this in[Wiuf and Hein, 1999].

So the "real" CAs (the CA1s) outnumber the CAs of a gene (the CA4s),but do they vastly outnumber them?As genome size tends to infinity(i.e. n goes to infinity)it becomes impossible for an actual ancestor (CA1) not to be at leasta partial genetic ancestor (CA2) as well.So the difference between CA1 and CA2 breaks down.

I used to say on this page:

but now we can see this is not so.(At least I put in "(I think)" in the correct place!)The difference between CA2 and CA3 does not break down.For any finite n, you are getting a larger inheritance from the ancestoralright,but it is still only 1 part in 2t,so for any 2 descendants it is quite possible that their samplesdo not overlap (for any reasonable size t).The probability of overlap depends on t, not on n.

For instance, [O'Connell, 1995] is confused about Mitochondrial Eve's relation to the fossil record- no date for Mitochondrial Eve, no matter how recent,could possibly contradict the fossil record studied by the paleontologists.This is based on the error of assuming that Mitochondrial Eve is important(see above).

One could even say that genealogy is the pursuit of statistical artefacts.

Link:
Common ancestors of all humans (using genetics)

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