A possibly idle question about human population genetics

Larry Tapper said:

Let N(g) = the number of distinct ancestors a person has g
generations back.

Thus for most people, N(1) = 2, N(2) = 4, and then
patterns will vary according to local custom, degree of
gene pool isolation, etc. Possibly N(6), which can be 64
at most, would actually turn out to be 40 or 50 on the
average.

For any given member of [censored] sapiens, the values of g
range from 1 to something like 50,000 or whatever,
depending on how we date the origin of our species.
However the _maximum_ value of N(g) is very likely found
at some fairly low value of g, in fairly recent historical
times I would think.

A question for population geneticists: is anything known
about this function N(g)? If so, is it considered to have
any theoretical interest in some context?

I'm just wondering about this ---

I'll bet the function is changing as humans become more
mobile. But without a massive, world-wide effort in
geneology I doubt there is much known on this topic. We've
probably only very recently begun to keep the sort of
records that would even make this study feasible. Collecting
those records seems like a gargantuan task.

I read somewhere that George Bush and John Kerry are
sixteenth cousins but I'd bet that kind of data probably
hasn't been put together for, and probably isn't available
for, most people.

--Jeff

--
A man, a plan, a cat, a canal - Panama!

Ho, ho, ho, hee, hee, hee and a couple of ha, ha, has;
That's how we pass the day away, in the merry old land of
Oz.

Hi Larry,

in article [email hidden], Larry Tapper at
[email hidden] wrote on 3/11/04 8:30 AM:

Quoted message said:

Let N(g) = the number of distinct ancestors a person has g
generations back.

Thus for most people, N(1) = 2, N(2) = 4, and then
patterns will vary according to local custom, degree of
gene pool isolation, etc. Possibly N(6), which can be 64
at most, would actually turn out to be 40 or 50 on the
average.

For any given member of [censored] sapiens, the values of g
range from 1 to something like 50,000 or whatever,
depending on how we date the origin of our species.

Why would the origin of our species have anything to do with
it? Are you assuming special creation, in which case the
earliest members of our species would not have had
ancestors? The only upper limit I can imagine would be set
by the number of generations back to individuals without
ancestors.

Quoted message said:

However the _maximum_ value of N(g) is very likely found
at some fairly low value of g, in fairly recent historical
times I would think.

Why would it asymptote at all? I would expect a graph of
N(g) vs. time (looking backwards) to behave as follows. The
slope of the curve relating
N(g) with time would decrease during historical periods in
which the termini of cycles in family pedigrees
accumulate at relatively high rates. Periods in which
the rate of accumulating termini of pedigree cycles
decreases (looking backwards from the present) would be
reflected in an increasing slope. The total number of
ancestors identified (as opposed to the number present
in any particular generation) would increase
monotonically without any tendency to asymptote.

Quoted message said:

A question for population geneticists: is anything known
about this function N(g)? If so, is it considered to have
any theoretical interest in some context?

I personally have not seen this parameter considered, and it
looks very interesting to me.

Cheers,

Guy

[email hidden] (Larry Tapper) wrote in message news:<[email hidden]>...

Quoted message said:

Let N(g) = the number of distinct ancestors a person has g
generations back.

Thus for most people, N(1) = 2, N(2) = 4, and then
patterns will vary according to local custom, degree of
gene pool isolation, etc. Possibly N(6), which can be 64
at most, would actually turn out to be 40 or 50 on the
average.

For any given member of [censored] sapiens, the values of g
range from 1 to something like 50,000 or whatever,
depending on how we date the origin of our species.
However the _maximum_ value of N(g) is very likely found
at some fairly low value of g, in fairly recent historical
times I would think.

A question for population geneticists: is anything known
about this function N(g)? If so, is it considered to have
any theoretical interest in some context?

I'm just wondering about this ---

LT

I have no actual data for you, but I doubt that the
function, as you define it, is the right embodiment of the
concept you are trying for. Consider that the ancestors that
you are counting in N(10,000) lived roughly 250,000 years
ago, but the range in when they lived is something like
350,000 to 200,000 years ago. That is, you will be counting
the ancestors of your ancestors in many cases. There could
have been a bottleneck in the human population in that era
of 100 people, say, but N(10,000) coud be 20,000 people
spread over 50 generations.

I'd be curious to know what is the "right" way to define
the concept.

On Thu, 11 Mar 2004 16:30:57 +0000 (UTC), [email hidden]

(Larry Tapper) said:

Let N(g) = the number of distinct ancestors a person has g
generations back.

Thus for most people, N(1) = 2, N(2) = 4, and then patterns
will vary according to local custom, degree of gene pool
isolation, etc. Possibly N(6), which can be 64 at most,
would actually turn out to be 40 or 50 on the average.

For any given member of [censored] sapiens, the values of g
range from 1 to something like 50,000 or whatever,
depending on how we date the origin of our species.
However the _maximum_ value of N(g) is very likely found
at some fairly low value of g, in fairly recent historical
times I would think.

A question for population geneticists: is anything known
about this function N(g)? If so, is it considered to have
any theoretical interest in some context?

I'm just wondering about this ---

LT

Remember mitochrondrial Eve.

Dunk

[email hidden] (Larry Tapper) wrote in news:c2q481$lfb$1
@darwin.ediacara.org:

Quoted message said:

Let N(g) = the number of distinct ancestors a person has g
generations back.

Thus for most people, N(1) = 2, N(2) = 4, and then
patterns will vary according to local custom, degree of
gene pool isolation, etc. Possibly N(6), which can be 64
at most, would actually turn out to be 40 or 50 on the
average.

For any given member of [censored] sapiens, the values of g
range from 1 to something like 50,000 or whatever,
depending on how we date the origin of our species.
However the _maximum_ value of N(g) is very likely found
at some fairly low value of g, in fairly recent historical
times I would think.

A question for population geneticists: is anything known
about this function N(g)? If so, is it considered to have
any theoretical interest in some context?

I'm not a population geneticist, but the answer is yes.
According to Olson in Chapter 2 of _Mapping Human History_,
the maximum value of N(g) is found at a g value of about 40,
on average. Some of the researchers mentioned in the book,
in case you want to look into this further, include Susumu
Ohno, Lois Horowitz, Joseph Chang, and Kenneth Wachter.

Yours,

Bill Morse