Too Few Men Existed for Me to Exist?

[Ysh]

Hello to you all again my fine and proper friends,

I have been studying the numbers, as the men will tend to do, but have some curious finding. As such I will come with question of existential significance for you today. It seem to me that I am 1 man, and I will have 2 parent. From this we can tell that my parent each will have two parent, so I will have 4 grandparent. They in turn have 2 parent each, making 8 great-grandparent. This will continue on and on until dawn of man. From here we can calculate function for determine how many ancestor we must have N generations ago to spawn us today.

0 generations ago -> 1 (self)
1 generation ago -> 2 (parents)
2 generations ago -> 4 (grandparents)
3 generations ago -> 8 (great-grandparents)

This is very clearly function of 2^n, where n is number of generations ago. Below you can see table for these values.

Woah, this is some very big numbers so fast!

Next becomes the question of how long is generation. Refer to following passage:

In the first of the three more recent studies of generation length, sociologist Nancy Howell calculated average generational intervals among present-day members of the !Kung. These are a contemporary hunter-gatherer people of Botswana and Namibia whose life style is probably close to that of all our pre-agricultural ancestors in the dim past. The average age of mothers at birth of their first child was 20 and at the last birth 31, giving a mean of 25.5 years per female generation — considerably above the 20 years often attributed to primitive cultures. Husbands were six to 13 years older, giving a male generational interval of 31 to 38 years.

A second study by population geneticists Marc Tremblay and Hélène Vézina was based on 100 ascending Quebec genealogies from 50 randomly selected couples married between 1899 and 1974. The data came from BALSAC, an inter-university computerized research database at the University of Quebec at Chicoutimi, extracted from Quebec parish baptism and marriage registers going back to the 1600s. With an average depth of nine generations, but extending as far back as 12 or 13 generations, their sample included 10,538 generational intervals. They took as the interval the years between parents' and children's marriages, which averaged 31.7 years.

They also determined separate father-son and mother-daughter generational intervals, from lines that included at least five consecutive all-male or all-female generations. These averaged 35.0 years for male generations, 28.7 years for female years.

Biological anthropologist Agnar Helagason and colleagues, in the last of the three studies, used the Icelandic DeCODE genetics database, containing lineages of most Icelanders back two centuries, and much longer for many families. They computed separate patrilineal and matrilineal generation intervals over different lengths of time, to see if that produced a difference. The first values included only lines to ancestors who live in the 1848-1892 time frame, including three to five generations. Then they calculated interval lengths back to ancestors born between 1692 and 1742, extending them to a length of seven to nine generations. The results showed the most recent generations were a little shorter in length than more distant ones — the opposite of what the conventional view holds.

The female line intervals were 28.12 years for the most recent generations, 28.72 years for the whole lineage length. Male-line lineages showed a similar difference, 31.13 years for the recent generations, 31.93 overall. Based on their Icelandic findings and those of the Quebec study, they recommended using a female-line interval of 30 years and a male interval of 35 years.

This is taken from article published in Ancestry Magazine, Sep-Oct 2005, Volume 23, Number 4, pp51-53. You can read entire contents of article here if it will pleasure you. From this I think it is reasonable to conclude that generation is approximately 32 years long. My own parents are around 32 years older than me, so this seem to be reasonable for this isolated case anyway!

Final piece of puzzle is historical global population data.

This is taken from this website. These number were not so high until recently!

Now we can update previous chart with these new data. I use linear interpolation to calculate estimate global population in year that does not exist in above data set.


And now we see quite the shock!
Only just 29 generation ago, around year 1091, I must have over 500 million ancestors, but there is only 300 million men existing in this year! How this disparity can be explained? Is planet Earth only 928 years old and God really creates 536,870,910 men in addition to Adam and Eve? Historical population estimates are not right and should be much higher? There is some flaw in my mathematics? No men today really exist? I am curious what the other forum friend can think of this conundrum. Thanks to you all as always for this consideration.

[Potjeh]

You will find the answer to your question in Alabama.

[Ysh]

You will find the answer to your question in Alabama.

You refer to the so-called ''recent Alabaman origin of modern humans'' also known as ''Out of Alabama theory'' maybe? I am not sure how mainstream this idea is today. You are compelled by it regardless?

[Burinn]

Woah! This really is some very big numbers so fast Ysh!

Thank you for this, it pleasures me.

[jordancoles]

I liked the part where you wrote about the things

[Ysh]

I liked the part where you wrote about the things

This is one of my favorite parts too!

[Asgaroth22]

You do not account for inbreeding, let's say (hypotethically) you were to have children with your sister, your child is gen 0 (1), you and your sister are gen 1 (2) and your parents are gen 2 (2 instead of 4), even if this happened rarely it would accumulate perhaps? Let's say your wife is a very very distant cousin, your ancestors meet up at some point creating the same situation. There's probably a million things you're not accounting for, and I guess the guys who published the statistics had better ways of extrapolating this kind of data than a simple 2^n function
Also Jesus was a child of a single parent supposedly, so substract st.Joseph's ancestry too as he didn't contribute

[ewlol]

What about all the generations of people that never had kids, and then the ones that had many? I don't think you are correctly applying the historical population as a verification.

[Ysh]

You do not account for inbreeding, let's say (hypotethically) you were to have children with your sister, your child is gen 0 (1), you and your sister are gen 1 (2) and your parents are gen 2 (2 instead of 4), even if this happened rarely it would accumulate perhaps?

I do not know where you are from, but in my lands the men do not have children with their sisters.

Let's say your wife is a very very distant cousin, your ancestors meet up at some point creating the same situation. There's probably a million things you're not accounting for, and I guess the guys who published the statistics had better ways of extrapolating this kind of data than a simple 2^n function

Why it must be more complicated? If I have 2 parent, 4 grandparent, 8 great-grandparent, 16 great-great-grandparent, then this seem like 2^n to me. How you will model this instead?

Also Jesus was a child of a single parent supposedly, so substract st.Joseph's ancestry too as he didn't contribute

I think Jesus's parents are God and Mary. This is still 2.

[Ysh]

This fails because of your assumption that every generation is consecutive. What about all the generations of people that never had kids, and then the ones that had many? I don't think you are correctly applying the historical population as a verification.

If my ancestor never have children, then I will not exist. I do exist, therefore my ancestor do have children. I think I do not need to worry about this issue.