Terran ATA Gene Math

I'm often plagued by random thoughts, very few of which have any useful purpose, even whatever story I happen to be working on:

Today's random thought is if Ianus is the forefather of all Terrans with ATA genes, then how many people with ATA genes are on Earth?

This is quite a complicated question, which causes me to have to assume quite a lot of factors. For instance, The Exodus was, in this 'verse, in the year 139 AL, which is 8199 BC, or 10,203 years before the Expedition arrived in Atlantis.

So that's 10,203 years of population growth to account for. (Actually, I've Ianus' half-Terran son Davidus Constantín, as being born in 143 AL, so that's 10,199 years of population growth.)

Then, of course, is the problem of figuring out how long the average generation might be. Historically, this is sixteen years, ie, the average age of a woman at the birth of her first child. This was the case until c. 1800 AD, when it started creeping upwards as a result of urbanization. But we're also talking about people who are part-Alteran and who, especially in the first few generations, would experiencing a longer-than-human-average lifespan and the somewhat slower aging rate that would result. But, despite this, I've chosen somewhat arbitrarily to assume the average generational length for those first 8,400 years is, in fact, 16 years. For the 200 years that follow, I also assume it to be the 25 years it is for the rest of the world.

So, for those of you following along, that is:
(8400 / 16) + (200 / 25) = # of generations
(525) + (8) = # of generations
533 generations

So 533 generations have passed since Janus arrived on Earth.

But how many people were born to each generation? Today's Total Fertility Rate (# of children born to a single woman) is 2.36 in the US. But in 1950 it was 4.95 and, historically, has been much higher. Since intensive internet seraching hasn't provided me with the guesstimated TFR of 8000 BC, I've decided to with a standard doubling (ie, each kid in each generation will have two kids of his/her own which will surive to adulthood), so:
2 ^ (n-1) = Size of N

wherein n equals the number of generations removed from Janus. So
2 ^ (533 - 1) = Size of N in 2004
2 ^ (532) = Size of N in 2004
1.41 e+160 = Size of N in 2004

Now, as this number is quite a bit larger than the current population of the planet, it is probably safe to assume that everyone on Earth is descended from Janus - and, therefore, Ancient!John, to some degree or another.

So that's that. Iohannes has 6.8 billion neices and nephews. Not all of them, obviously, have the ATA gene though, and only 47% of all people given Carson's gene therapy have the gene activated. Assuming that this number is higher than average amongst Expedition members than it would be in the general population - as factors like higher intelligence (which would be useful in getting a position in the Expedtion) could be a side effect of even having the dormant gene - I'm going to assume that the real number is about half that. Which would make it about 25% effective on the general public.

So we've learned that the ATA gene is recessive, and about 1.7 billion people could be expected to be able to operate it, if they have gene therapy.

But that number is still grossly higher than the percentage of people who have the gene without the therapy. Given that the Expedition, before leaving Earth, had only a handful of people identified as having the gene, this number has to be very low. After all, even a top secret organization like the SGC would have a lot of personel, and all wold have DNA on file.

Fort Bragg has a population of 39,000. In 2004, the size of all parts of Homeworld Security, to include the SGC, Prometheus, Antartic Outpost, and those on the international community who'd need to be aware of it... This is probably about the size of the pool they had to search. Since a handful is generally five, that's about 0.0128% of the general population.At most.

So, assuming this, about 87,179,487 people with the active ATA gene on Earth without the gene therapy. Which, ironically, is almost exactly the size of the population of California.

There's really no point to this, except that I kinda wanted to figure it out.

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This took me three (very dull) SG1 episodes to work out. I was going to assume different TFRs throughout the various millenia, but it proved pointless, as standard doubling proved my point.

Glad you liked though.
It may have come on randomly, but a lot of interesting discussions (or even fics in some people's case) come out of random thoughts.

For example, I got an idea for an original character / small-time known character fic snippet from this :) But I'm not a writer by any means, so if you or anyone else seeing this wants to write it up - go ahead! Though, I didn't come up with this interesting bit of trivia so I probably shouldn't be the one giving the go ahead.

It went like this:
Two people - whether little-known show characters or original characters - are sitting somewhere, bored together. They could have a slow day of work or be stuck in an elevator, whatever. One of them gets the random thought in their head, similarly to you, of "I wonder how many gene carriers are there on Earth. As in, the whole planet." So they start with listing up facts they know about the gene and continue with the math. Then, once they reach the number for all possible gene carries, they're on a roll and decide to go ahead with calculating the number of natural carriers. Obviously, they'll need a calculator unless one of them is a maths genius :P

As a standalone, the ficlet wouldn't have much point to it other than training both the authors writing muscles and calculating muscles, but IMHO it would be just as interesting as this post was. Which is very :)
Eh, maybe one day. Right now I'm just trying to finish up "Legati," which is killing me, though I've no honest idea why.

Thanks for the idea though. :)