Multiple Lines of Descention

Prince Charles is descended in 99 different ways from William the Silent, and thousands of ways from charlemagne. it is called ancestral collapse. you have more ancestors living 1000 years ago then there were people in the world so they start doubling up

Thanks. I had not heard the term Ancestral Collapse.

Neither had I. Sounds made up. Probably isn't but it sounds that way! But like you I am connected to historical people several way , through several line. Example. King Henry the 2ND of England. I come down through William Longspree and King John. Also more recently three sisters married two brothers and another of my relatives. Then their children inter married cousins and then the thrid gen. did the same things. It can get messy but interesting.Judy

Carrie Ann Davis Todd Warren and judy as well try here http://en.wikipedia.org/wiki/Pedigree_collapse

Wow thats a really helpful link there Mike. :D Thanks!

my 17th cousin once removed don't remember his name but he shared that with me...

Ya someone keeps changing facts, so its getting smaller and smaller

isn't the truth,
that they kept a closer watch on the lineages of their cats, dogs, horses, and, their own royal family lines - than, they kept ancestral lineage tabs on the people, except, of course, when it came to taxing them ?

ancestral collapse ? never, heard that term before

i thought, it was called pedigree collapse

i guess it's just a fanicer name of saying the same thing..

I have several paths to several people.

This "measures" endogamy (incest) and is defined for the n-th generation of a ancestor tree T as:
In(T)=An−Bn
An

where An=2"
represents the theoretical number of persons in that generation (1son, 2parents, 4grand-parents, 8grand-grand-parents and so on), and Bn is the actual number of distinct persons in that generation.

I found this to be too imprecise a measure of endogamy (take the simple example where a grandmother has a child with her son, for this little incestuous tree we have In=0
for all three generations), for it does not take into account the interplay between generations. All we can say for sure is that In>0 for some n implies some arbitrary measure of incest is going on, and the inverse ain't true (cf. naughty grandma example full 3-generation tree below).

Full 3-generation ancestor tree of Jhonny. Does his mother sends him to his grandmother's house at summer vacations?

So, as a wannabe-mathemagician, I couldn't let this atrocity into our family book. Let Ω
Ω
be our probability space consisting of all possible ancestor trees of a common starting person p1. For T to be a ancestor tree with starting person p1 means that (T,≤) is a directed poset (where p≤q means that there is a direct line of ascendancy from p to q), and p1 is the unique minimal element on it. The condition of "directed" also means that every point in our tree is "connected to p1".

The question is, how to define a random variable E:Ω→ℝ that captures endogamy? I have one suggestion:

A closed path C in T is a bidirected (directed with respect to both ≤ and it's dual ≥) subset of T containing a minimal and a maximal element (think for instance a triangle or a diamond). All finite chains in T are trivially closed paths. An endogamic path is a closed path that is not a chain. Our example above has 3 endogamic paths (all closed paths containing Penny-Joe-Jhonny triangle) in a total of 24 closed paths (did I counted it right?). We cound then say that it's endogamy is:

E(T)=324=12.5% Is this a random variable E:Ω→ℝ? Does it have nice properties like normal approximations depending on the size of T that allows us to estimate the error of E(T)? What does this community thinks? (I apologize in advance if I said something grotesque, I'm very unacquainted with even the most elementary facts of probability theory but I think that this study could be a relevant contribution of mathematics to genealogy)

Ancestral collapse is a farce

Actually, ancestral collapse, which is also called pedigree or tree collapse, is very real. I have a set of 2nd great grandparents who are 1st cousins. Their fathers were brothers.