Some thoughts on generations

[Borodog]

Consider that the average length between human generations is approximately 20 years, meaning on average that there are about 5 human generations per century. If you don't like that number, it's ok; the number is certainly more than 3 and less than 7. Choose one to your liking.

What does that mean? Well it means that for every century you look back in time, an individual will have 32 times as many ancestors (2^5). You have 2 parents, 4 grandparents, 8 great-grandparents, 16 great^2-grandparents, and 32 great^3-grandparents. 20, 40, 60, 80, 100 years. Going back another century still, each of them would have 32 great^3-grandparents, meaning you will have 1024 great^8-grandparents. Round it off and call it an even thousand.

So for every two centuries farther back in time, you gain approximately a thousand times as many ancestors. What are the implications of this?

Well, if you go back 4 centuries, you have a million ancestors.

And if you go back 6 centuries, you and every other individual on Earth have a billion great^8-grandparents.

Except that 6 centuries ago, there weren't a billion people in the whole world. In fact, nowhere near. The inescapable conclusion is that the human race, over a scale of a few dozen generations, must be massively and totally inbred. In fact, since until recently the world has been isolated into much smaller groups that did not interbreed at all or only rarely interbred, the effect is even more pronounced.

I thought of these implications while reading Richard Dawkins' The Ancestor's Tale, which contained these interesting bits of mathematical flotsom about populations:

In a population of stable size N (which the Earth's human population is emphatically not, but historically has been approximately true in some isolated places like islands), the number of generations back in time to the Most Recent Common Ancestor is log_2(N). This assumes random mating, which is a terrible assumption, but it provides a good order of magnitude estimate.

Slightly less than that many generations back again (0.77 in fact) from the MRCA is an astonishing point, where, prior to that point in time, every individual in the population either must be an ancestor of all members of the modern population, or of none! More interesting still is that at that point about 80% of the individuals will be ancestors of the entire modern population! [img]/images/graemlins/shocked.gif[/img]

Strangest of all might be that you can be an ancestor of an individual, yet that individual might not contain any of your genes; in fact you could be a direct ancestor of every member of the entire population and yet have none of them carrying any of your genes!

Hence, having children may not be the genetic immortality you thought it to be.

[BluffTHIS!]

Boro,

This is familiar to those of us with an interest in genealogy and especially in the scientific side of same. The phenomenon you refer to is known as pedigree collapse, i.e. where you go back in your family tree a sufficient distance and find the same individuals repeated.

As well, the limitations on the number of genes in a chromosone lead to the other phenomenon where a certain distance back you start to "drop ancestors" where although they are definitely your ancestor and you would not be here but for them, you nonetheless don't necessarily contain any of their DNA. While you get exactly 1/2 your DNA from each parent, the portion of a parent's DNA you get from each of their parents varies. Thus you might well have more DNA from one grandparent than the others, and so forth each generation back. Which is why traits can be passed on to you and you might be said "to favor" a certain ancestor in appearance.

The only thing about the MRCA stuff that appears somewhat iffy to me, is that it seems somewhat less likely to me that the same figures can be applied to native Americans, unless you assume both a continuous influx of immigrants from Asia after the land bridge in the Bering Sea disappeared, and also random mating. That isn't to say it isn't true, but I don't think it's a slam dunk unless you go much further back for them. And this can be true as well for isloated sub-populations like the Basque who possess not only some unique genetic properties, but also a language that might be pre-Indo-European.

There is also another aspect to the MCRA thing, which is that not only are you most likely descended from the entirety of the human population a certain distance back in modern history whose descendant lines never died out, but that there are studies showing that going back hundreds of thousands of years, all humans descend from a common female ancestor, which of course corresponds precisely to Eve.

[Shadowrun]

taht is pretty intresting about there nothing being a billion people.

However have you Borodog considered the fact that they may have been significantly more people if you count the deaths?

Basically im trying to say that while its true there might have been only 2000 people alive last year (for arguments sake) 500 people died and 500 more people were born so in reality it was 3000?

That is the thought that popped to my head while reading your post not sure if its accurate or not though?

[Borodog]

The point is that all of your 1 billion great^8-grandparents must come from (approximately) the same generation; i.e. they all had to have been alive at more or less the same time. That means if you go back far enough, the same individuals must be represented amongst you ancestry many, many, many times, as BluffThis pointed out.

[MidGe]

Richard Dawkins' The Ancestor's Tale is a great read. I could not put it down, and read it in three days and a bit. [img]/images/graemlins/smile.gif[/img]

I picked it up on a recommendation by chezlaw on this forum.

[hmkpoker]

What's the minimum familial distance one needs to have to avoid the obvious defects like down syndrome? Second cousins?

Also, are siblings capable of reproduction?

[KUJustin]

First cousins are actually relatively safe unless your gene pool is not particularly clean (read: you have close relatives with genetic defects).

In many cultures cousins are the preferred choice for spouses. I believe US is the only (or one of very few) countries where it's taboo.

[madnak]

Sibling pairings are relatively common, and studies have indicated that siblings actually have high inherent levels of attraction.

[Darryl_P]

Someone should tell that to the thousands of species in which the males engage in mortal competition to shag the female. If they only knew their maths they'd realize it's totally pointless. Silly animals.

[FortunaMaximus]

[ QUOTE ]
Also, are siblings capable of reproduction?

[/ QUOTE ]

Yeah. It tends to create dynastic families that want to kill each other though.

[ QUOTE ]
Someone should tell that to the thousands of species in which the males engage in mortal competition to shag the female. If they only knew their maths they'd realize it's totally pointless. Silly animals.

[/ QUOTE ]

Yeah. That doesn't mean we should all go celibate, because sex is pointless, I hope. Reproduction may be. That machine seems to be working quite well these days. There are slightly more than 3 fools born every minute. How are we to keep up with that?