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From: "John B. Robb" <>
Subject: Re: [DNA] How Clades Begin
Date: Sun, 04 Dec 2011 22:55:16 -0500
References: <F71A8D189D6C4FA9BC63C2DD2E305AAE@kenPC><00d001ccb2b3$9b284720$2f01a8c0@blue><60F978524EB0424EB7106AE34DB6D50D@kenPC><010901ccb2bf$50e3b620$2f01a8c0@blue><19253046984C4B4882D173B6ED6ED559@kenPC>


OK, Ken, I acknowledge that pedigree collapse doesn't contribute to the rate of extinction (or proliferation) of male lines, so I seek other explanations compatible with the actual family size data I, or any highly experienced American genealogist has encountered.

First, here are the numbers you suggest I work out:

expected #sons
#sons probability per generation
0 .15
1 .10 .10
2 .20 .40
3 .25 .75
4 .15 .60
5 .10 .50
6+ .05 .30
----
2.65

and allowing for an equal number of daughters, this yields an overall population increase of (5.3 - 2) / 2 = 165% in a generation
of 34 years, while your distribution yields

expected #sons
#sons probability per generation
0 .30
1 .30 .30
2 .40 .80
----
1.10

or 2.2 children per generation (counting daughters) and an overall population increase per generation of just 20%, with a population doubling every 6 generations (200 years) or so. This is clearly way wide of the mark for both America and England, just as your average family size of 2.2 children bears no relationship to the actual American and British families for the period of genealogical time (back to the advent of hereditary surnames in the 12th and 13th centuries, except for the last 2-3 generations.

To be sure, the British population has been releatively stagnant for long periods of its history, but this is largely due, not to radically smaller family sizes, but to the classical stressors of famine, pestilence, and war. The most catastrophic of these factors, the Black Death of the mid-14th century. reset the English population by 30-50%, and disrupted the family lives of another 20% or more, but in addition to countless lesser events, there have been the running sores of poverty and malnutrition dragging the natural population growth rates down,

Any experienced American genealogist can tell you that American family sizes were several times larger than 2.2, and this carries back in
New England right to the founding generation of the 1630s, whose familes averaged 8 in size (with 4 sons); this is documented in Victoria
DeJohn Anderson, New England's Generation: The Great Migration and the Formation of Society and Culture in the Seventeenth Century
(Cambridge University Press, 1991).

Average family sizes for England covering much of genealogical time are documented in Wrigley & Schofield, The Population History of England, 1541-1871: A Reconstruction (London, 1981), and Household and Family in Past Time, Laslett & Wall eds. (1972), and these and other works explicitly rule out fluctuations in family size as a significant factor in population growth (or decline). Rather, the wild card turns out to be the number of males who survived to marriageable age, and then were able to afford to marry and found a family.

To back up these claims for the American data, we have wills, family bible records, and for New England lines, complete family vital records (marriages and births) that go back to the very beginning. We also have the USCensus.

I have sampled family sizes in the censuses from 1820-1850 for a number of US counties in different areas chosen for their population stability (little in- and out-migration), and found average family sizes of 5.5 including the parents. However, this includes the households of the unmarried, of "empty nesters", and of young men not yet married, and this was a decidedly young and burgeoning population. The average size of these families when completed was probably about 9, including the parents, and so about 7 without them. Yes, a few households harbored the odd aged parent, uncle, or aunt, but this had little effect on the overall statistics.

To validate my estimates of family size, and to ascertain a natural rate of population increase under the most stable conditions for a successful, unstressed, agricultural society, I selected the period of 1820-1850. Americans were still on the move during this period, from the more settled regions to the less, but it was a time of peace and social stability, and immigration was at a minimum (about 1-2% of the population as a whole, not counting Ireland, and to a lesser extent, Germany), and to minimize the effect of immigration I chose as exemplar a decidedly British (primarily English) surname that is one of the most common in the U.S., but is greatly under-represented in Ireland: LEWIS. The following table shows the population figures for LEWIS households in the US from 1820-1854, or 34 years, the average length of a generation:

Households headed
by Surname LEWIS
in the USCensus cumulative increase
over the 1820 base in
households %ages
1820 3328
1830 5082 1754 52%
1840 6793 3465 104%
1850 8687(est 5359 161% (47781 / 5.5 = 8687
1854 9271 5942 178%

Since the 1850 census was an every-name census, I somewhat arbitrarily divided the number of individual LEWISes by 5.5 to arrive at an estimate of the number of households. In justification of this 5.5 average members of a household (derived by sampling the census of 1820-1840) I note that the actual increase in LEWIS households from 1820-1840 was about 49%, while the increase from 1830-1850 (for which latter I use the synthetic figure 8687) was 58%, and note that this was a period of growing agricultural exploitation, so expect that family size grew apace.

The total population growth from 1820 to 1850 was thus 5359 on a base of 3328, but this 30 year period represents only 90% of a generation. Adjusting for this, and factoring out immigration of 1% yields (5359 x 1.12) x .99 = 5942 estimated new LEWIS households over a generation, or an increase in the number of LEWIS sons of 178% in a single generation.

This number probably represents an extreme for the American population, since all factors were working in favor of large family sizes: peace, a healthy rural farm life (free from city-bred disease), with plenty to eat for all, and an economic incentive to produce lots children to exploit the abundant land. Most of these factors were muted or variable for England during much of its history, so England had a much slower population growth, absent catastrophe, more or less in line with your estimates, but as I have noted, the principal variable that kept population growth restrained was not small family sizes but a much larger percentage of men who did not marry and found families, and probably somewhat higher average ages at marriage.

More specifically, the English population grew at a rate of 55% from 1821-1855 with the burgeoning of the Industrial Revolution, compared with the 178% growth for those American LEWIS families during a comparable period, and with the 20% growth that your family structure is predicated on. For earlier times of relative peace in England, but with the other favorable factors in America, the numbers do average about 20% per generation,

Given that for American genealogists who trace back to the early immigrant founders about half of genealogical time (on average) has occurred in America under these more favorable conditions for growth, while the other, much less fruitful half has occurred in Britain under much less favorable conditions, I've created a revised table to reflect an average of the two periods. I've shaved the estimates for the larger families, but mostly I've bumped up the percentage of men who produced no children:

The # of sons per family for the period 1250-1950
in England and America (weighted equally and averaged):

0 .35
1 .15 .15
2 .18 .36
3 .16 .48
4 .10 .40
5 .05 .25
6+ .01 .06
----
1.7

This produces an average population growth rate of about 70% per generation for both the two areas averaged together, compared with

The # of sons per family for the period 1630-1950
in America
expected #sons
#sons probability per generation
0 .15
1 .10 .10
2 .20 .40
3 .25 .75
4 .15 .60
5 .10 .50
6+ .05 .30
----
2.65

or a 165% growth rate per generation.

I would be very interested to see the extinction rates for both these of these more empirical family structures over the period of genealogical time.

John Robb


----- Original Message -----
From: Kenneth Nordtvedt
To:
Sent: Sunday, December 04, 2011 3:12 PM
Subject: Re: [DNA] How Clades Begin




-----Original Message-----
From: John B. Robb

But you have apparently failed to consider the phenomena of interbreeding
and collapsing pedigrees, whereby most living descendants of ancient British
ancestors are cousins of each other many times over.

[[ We are talking about the converging male lines as we go back in time ---
not counting the increased number of ancestors an individual has. You have
wandered off into a different subject.

Run your alleged probabilities of 0,1,2,3,4... sons for each male through
just half a dozen generations and see how the population literally
explodes. ]]



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