Yesterday, I was visiting my three children in Long Island City, Queens and, while my kids were asleep, I decided to kill some time by running a little test of my theory that after a certain number of generations, all but one type of mitochondrial DNA or whatever would die out.
I used a deck of cards to produce a random element, faster than flipping a coin, so if a red card was drawn the child was a girl and if a black card was drawn the child was a boy.
Starting by analogy with four males named Al, Bill, Charles and Dave, in my experiment all the names but Bill died out after four generations.
This result was what I predicted, but the way it was reached was not.
After the first generation, because five red and three black cards were drawn, there were only three boys left.
In the second generation, two black cards and four red cards were drawn, so only two boys were left.
This meant that the entire human race was on the verge of extinction.
Fortunately, humanity recovered and after two more generations there were three boys, and all of them were named Bill.
However, in real populations, this would not happen. If there were two boys and six girls left, making a total of eight, the two boys would get all six girls pregnant and, on average, twelve children would be produced, not four.
Next, I ran the experiment with eight males, Al, Bill, Charles, Dave, Ed, Frank, George and Henry.
This time, it took 11 generations before only George was left. Everybody else died out.
My original prediction was it would take 7 or 8 generations, but in no case more than 10.
The reason it took more than expected was again due to the luck of the draw. After one generation, there were nine boys and after two generations there were 12 boys. By then, only two boys names had died out, Al and Ed.
For the next three generations, nobody died out and then a bunch of red cards came up and in generation 6 there were seven boys left. Fred had died out. It took five more generations and another run of red cards and then only 5 boys were left. All of them were named George.
Once again, in real human populations, if there were 12 boys, there would only be four girls. All 12 boys would try to get the four girls pregnant. Some of the boys would fail. (They would probably kill each other off.) In order for the next generation to have 24 children, each girl would have to have 6 babies who survived, which would be unlikely among those stone age people.
Although mine were very unscientific tests, I think they show something. Girls will probably tend to produce the same number of children from one generation to the next, regardless of how many available fathers there are, whereas if there is an overpopulation of boys, the boys will produce less children each, and if there is a shortage of boys each boy will have more kids.
However, each of these factors will tend to lead to the same things. It will tend to keep the numbers of boys and girls about the same. It will also tend to keep the overall population about the same, even if a disproportionate number of boys or girls appear by random luck in a generation.
More importantly, these fluctuations from one generation to the next will shorten the length time when all of the boys except for one type will die out.
Now, I want to make a computer program to try to do this with bigger and more realistic numbers. I used to be a good programmer, but that was years ago. The last time I wrote a computer program was in 1986.
Also, I need to come up with more realistic numbers. Obviously if every parent had two children, the human race would die out quickly. For survival, a few women have ten children, a few more have 9, and more have 8, but still throughout human history the overall population remained about the same.
An additional factor is my system does not take into account that even if one generation by luck failed to produce any boys at all, that would not end the human race, because men from the second and third generation could make children with girls from the fourth generation, for example. This is why men have longer reproductive lives while women more consistently produce about the same number of children.
(I recently got back in touch with my old Icelandic girlfriends from 1972 and all of them now have four children.)
I have been thinking about this and it seems to be a harder programming problem than might first be apparent.
The current issue of Science Magazine, available at http://www.sciencemag.org/cgi/content/summary/286/5438/229a (but you have to register) puts our common ancestor as living 145,000 years ago. I believe this result might be somewhat more recent and, more importantly, I believe this result will be reached by pure mathematics, without any need for testing DNA samples.
Sam Sloan
If you make certain initial assumptions, then that theory would certainly hold, and there is a formula for calculating the expected number of generations this would take, depending on the initial population size.
However.....
The initial assumptions you have to make include no mutations to the mDNA, a closed population, long-term stable population size, random mating, no selection, equal probability of reproduction for all those with different mDNA.
Those assumptions simply do not hold in any real-world scenario.
Random mutations will increase the mDNA variability in the population over time, and the same happens if the population is not closed, for example if there is any immigration. On the other hand, a sudden drop in the population size - like what happened during the Black Death - might result in the total elimination of some of the mDNA types. Also, random mutation is simply not the rule - if it was, then you would have virtually no "full" siblings, only half-siblings.
All those factors can be simulated with a program, but in most cases one has to estimate the size of each factor....some of which can be estimated with a reasonable level of accuracy (like the mutation rate), while others are pure speculation.
-frisk
Fridrik Skulason Frisk Software International phone: +354-5-617273
Author of F-PROT E-mail: frisk@complex.is fax: +354-5-617274