GENEALOGY-DNA-L Archives

Archiver > GENEALOGY-DNA > 2011-09 > 1316281485

From: "Kenneth Nordtvedt" <>
Subject: Re: [DNA] Wild Demographic Dice
Date: Sat, 17 Sep 2011 11:44:45 -0600
References: <5122B444EF8D435CAF45B594A4742035@kenPC><COL118-W14D7241784382069B0E939A0090@phx.gbl>

Having a program, I can of course alter those probabilities of having zero,
one, two, three ..... sons.
But I used p(0)=.3, p(2)=p(0)+r, and p(1)=1-p(0)-p(2) for my runs this
morning.
r is the population growth rate I want to look at. If I want to add p(3)
nonzero and higher the constraint for r is from:

1+r=p(1) + 2p(2) + 3p(3) + 4p(4) + ......
sets p(1) in terms of higher p(i) and r, and then p(0) is set by sum of
p(i)=1

I did not trace things in the program to answer your "more than one son"
question. But I suspect most of the 13 percent did have descendants through
more than one son.

-----Original Message-----
From: Gareth Henson
Sent: Saturday, September 17, 2011 11:28 AM
To:
Subject: Re: [DNA] Wild Demographic Dice

Ken

What were your assumptions as to the probability of each male having zero,
one, two etc sons (in order to get the 4% growth rate)?

Of the 13 percent of the original 1000 whose lines survived the 150
generations, how many have living descendants through more than one son?

Gareth

> From:
> To: ;
> Date: Sat, 17 Sep 2011 10:47:21 -0600
> Subject: [DNA] Wild Demographic Dice
>
> I am studying again the wild statistical flucuations of y line survival
> and prosperity due to PURELY the statistics of reproduction.
>
> Here is a run I did this morning to illustrate things. A population of
> 1000 males undergoes 4 percent per generation growth for past 150
> generations, resulting in 370,000 males today. With sufficient dna tags
> (STRs, SNPs, etc) one could imagine each of those 1000 original males
> representing a distinctive genetic y line.
>
> What do we see today among those 370,000 descendants in the way of
> distinct original lines? 87 percent of those 1000 lines went extinct;
> they are gone from today’s population. The most populous represented
> original line accounts for 4.4 percent of today’s population. The 10 most
> populous lines represented today account for 24.1 percent of the 370,000.
> And the 20 most populous lines represent 40.6 percent of the 370,000.
>
> The above results indicate the very strong creation of demographic
> “winners” and “losers” of y lines based solely on statistical
> flucuations --- before any other factors are brought into consideration.
> This source of demographic winners versus losers must be understood before
> speculations about connnections of populous y haplogroups today to
> advanced......... etc. tribes of the distant past can be even tried
> intelligently. There are some forums engaging almost exclusively in
> various speculations of this latter type, and I think this is all mostly
> fairy tales until we can better understand how much of the y haplogroup or
> clade clumping looking back several thousand years to its foundings is
> accounted for by the basic statistical flucuations of routine male
> reproductive results.
>
> So I’m urging some mathematically inclined folks to get into extinction
>
> Ken

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