March 19, 1988
Dear Mr. Christophersen,
Thank you so much for your detailed response, dated February 2nd, to my letter of January 11th regarding your cover story about the "Eve hypothesis" in Newsweek Magazine of the same date.
If you assume that at some point in human history there were 256,000 women in the world (as convenient a number as any), and that each one of these women had different mitochondrial DNA (which is passed on only by female offspring), and that each woman produced exactly two surviving children, and that 50% of all surviving children were female and that this continued for at least several thousand years, we see the following:
After one generation, 25% (or 64,000) of the mitochondrial DNAs have become extinct because those mothers produced two sons; 25 % (or 64,000) have two surviving examples (two daughters) and 50% have one surviving example (one daughter and one son).
After the second generation, 25% of those 64,000 which had two examples also produced two daughters, so now there are 4,000 (25% times 25% times 64,000) types of mitochondrial DNA with four examples each. There are also 16,000 DNAs with three examples each, 24,000 plus 32,000 (56,000) with two examples each, 16,000 plus 64,000 (80,000) with one example each and 4,000 plus 32,000 (36,000) more which have become extinct.
I hope you are able to follow what I just said. It comes from high school algebra, where (x + y) squared = x squared + 2xy + y squared and (x + y ) 4th = x (4) + 4x(3)y + 6x(2)y(2) +4xy(3) + y(4) and so on.
Thus, it can be seen that after only two generations, 100,000 varieties of mitochondrial DNAs have already become extinct, 64,000 in the first generation and 36,000 in the second generation.
After the third generation, there will be only 15.625 types of DNA with eight examples each (25% times 25% times 25% times 25% times 4,000), 500 with seven examples each and so on, while 15.625 + 250 + 3,500 + 20,000 = 23,765.625 more types will have become extinct.
As noted above, after just three generations, nearly half of the different types of DNA have become extinct. Therefore, three generations might be thought of as a "half-life" of a variety of mitochondrial DNA. (I realize that this is not exactly right). Since 2 to the 18th power equals 262,144, it might take only 54 generations (18 times 3) for 252,144 types of DNA to be reduced to just one.
In real life, of course, every woman does not have exactly two children. In some underdeveloped countries where I have been, there is still no birth control and no doctors. In such places, 10% to 20% of all women die in childbirth even in this modern age (usually while giving birth to the first child), while a tiny percentage of women give birth to ten or more children. Applying such more realistic data and assuming a high percentage of women dying in childbirth in pre-historic times, while the overall population still remain stable, it will be seen that the rate of reduction of the number of different types of mitochondrial DNA is even more rapid.
Now, you say in the article that the existence of only one type of mitochondrial DNA shows that there was "little or no mixing". I, however, believe that this shows exactly the opposite. Consider the country of Iceland, which was settled starting in 874 AD and which, after the initial settlement period, has had virtually no immigration. If you ask around, you will find that any two given Icelandic persons will be able to find one common ancestor just a few generations back. One reason for this is that the Icelanders discovered free sex hundreds of years before it became popular in other countries. Traditionally, the vast majority of women in Iceland have their first child prior to getting married, and then get married to a man other than the father of their first child. As a result, because of this mixing, Iceland has perhaps the most homogeneous population of any country in the world.
If there were no mixing, there would still be isolated pockets in the world with different types of mitochondrial DNA. Only with free mixing would these pockets disappear.
Going back to the initial mathematics, I think that it would not be too difficult to write a computer program to show how long it would take for all but one type of mitochondrial DNA to become extinct. My rough guess, however, is that it would take just about exactly 200,000 years.. Therefore, I conclude that your expert's discovery that all mitochondrial DNA still in existence are derived from just one original example which existed 200,000 years ago, tells us exactly nothing about the origins and history of the human race, except that the human race must be at least 200,000 years old (which we know already).
Very Truly Yours,
M. Ismail Sloan