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From: "D. Spencer Hines" <>
Subject: Re: Genealogical Demographic Probability Model
Date: 17 Oct 1998 03:35:10 GMT


As Theodore Roosevelt [1858-1919] would have said, "Deeelightful!"

Thank you Ed Kane for a superb summary!

Now, can we critique this probabilistic mathematical model? Are there weak
points in the assumptions or the calculations that undo it?

Or is it robust enough to hold up to that type of close critique and
analytical pressure?

D. Spencer Hines

Lux et Veritas
--

D. Spencer Hines --- The Wall Street Journal reports that "Mike Tyson,
ear-chewing pugilist and bad date" has bared his soul with a remarkable
knack for psychobabble. Mr. Tyson indicates that, "I have no self-esteem,
but the biggest ego in the world." Further, the WSJ reports, "Depression's
dark cloud, he continued, kept him from seeing that ear-chewing is not a
valid form of self-expression." 14 October 1998, p. A22

Ed & Joan Kane wrote in message <>...
>D. Spencer Hines wrote:
>> . . . .
>> Might she be referring to?:
>> Kenneth W. Wachter, Ancestors at the Norman Conquest, Genealogical
>> demography, ed. by Bennett Dyke and Warren T. Morrill, Academic Press
>> [1980], 85-93 [Reportedly A Discussion of the Numbers of Ancestors in
>> Generations As One Moves From 1947 to 1247 in Time]
>> . . . .
>> If someone has read it, could they give a summary that might start an
>> interesting discussion?
>> . . . .
>
>The article "Ancestors at the Norman Conquest" by Kenneth W. Watchtel
>also appears as a chapter in his book _ Statistical Studies of
>Historic Social Structure _, Academic Press, 1980. It is an engaging
>essay. By the second paragraph the author, concluding that the marriage
>of distant cousins limits the number of unique ancestors in a pedigree,
>wonders what that limited number actually could be. Several very well
>written and entertaining pages review the contributions of others to
>this topic before he clarifies the problem with the construction of a
>mathematical model, establishing a probability distribution of the
>number of distinctly unique ancestors. He assumes 30 years per
>generation and a few other things, including a hypothetical individual
>whose ancestry is strictly English. The mean of that distribution is
>x-x(1-(1/x))^(m+f) and the proportion of actual ancestors out of the
>pool of total ancestor "slots" in a pedigree is
>m(g+1)/((x(g+1)) = 1 - exp [-2(m(g)/x(g)) * (x(g)/x(g+1))].
>
>A shortened summary of the tabulated results of the model:
> ancestral
>generation potential distinct population population
> # date ancestors ancestors of England proportion
> 1 1947 2 2 -
> 13 1587 8,192 7,938 3,500,000 .0022
> 15 1527 32,768 31,438 2,200,000 .0142
> 20 1377 1,048,576 628,576 2,250,000 .2793
> 25 1227 33,554,432 2,012,114 2,500,000 .8048
> 27 1167 134,217,728 1,478,584 1,700,000 .8697
> 30 1077 1,073,741,824 952,279 1,100,000 .8657
>
>Thus around the year 1500, an individual with strictly English ancestry
>would have (by the model) more than 60,000 distinct ancestors, and 95%
>of the slots in that pedigree would be filled by different people (about
>5% duplication rate). Around the year 1377 the number of distinct
>ancestors is greater than 600,000, but almost a third of the slots in
>the family tree for that generation are filled by *duplicate* people.
>Just before the Black Death (generation 21 in the model) nearly 30% of
>the population of England are ancestors of this one hypothetical
>individual. Around the year 1287 the number of ancestors in that
>generation reaches a high point of around 2 million. By this time each
>ancestor occupies an average of sixteen slots in the pedigree. About 80%
>of the population of England are ancestors of that individual.
>
>According to this model, the percentage of population who are ancestors
>of that hypothetical individual never reaches 100%; indeed it seems to
>hover around 85%. Since not everyone has descendants, it is possible
>that this portion of the population does not have any descent reaching
>to the present, whereas everyone with English ancestry alive today is
>descended from the other 85% of the population then living.
>
>The article is, in my view, quite amazing. Some might say it is
>speculative, a not uncommon gripe about statistics, but statistics and
>mathematical models are useful where deliberate knowledge is scarce. It
>is amazing to be able to tentatively count ancestors about whom we (most
>of us) otherwise can know little or nothing.
>
>--
>Ed Kane mailto:
>40*01'20"N 76*07'53"W Gordonville, Lancaster County, PA 17529, USA
>

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