There's a useage problem here.

When a person says he's "one-fractionth X," that statement refers to direct lineage. Thus, if a person's father is half-Irish, half-English and his mother is half-Japanese, a quarter Thai and a quarter Greek, that would make him "one-quarter Irish, one-quarter English, one-quarter Japanese, one-eighth Thai, and one-eighth Greek."

But notice the math here: Everything got divided by two. This is because a person has precisely two parents (let's not wander off the ranch into a donor egg with transferred nuclear DNA, fertilized by a sperm donor, gestated by a surrogate, and raised by adoptive parents.) Therefore, the only possible fractions allowed must be strict powers of 2 and only 2.

Six is not a power of 2. It's 2x3. "Three"? Where did that third come from? A person can't be "one-sixth" anything in this sense since it would require three direct sources of DNA for a single person at some point.

To say that "one-sixth of his ancestors must have come from Africa" assumes that these SNPs are somewhat evenly dispersed across the genetic inheritance, but that ignores biology. I am not genetically close to all of my ancestors equally. I am closer to some than others. I am especially close to my parents...half of my genes come from one parent and the other half from the other parent. The further back you go, the less related you become.

Thus, suppose I go back four generations. That's 16 great-great grandparents, 8 great-grandparents, 4 grandparents, and 2 parents. That's a total of 30 ancestors. Suppose one of the great-great grandparents is considered "African." That would make one of the great-grandparents, one of the grandparents, and one of the parents "African." Thus, we've got about one-sixth of all ancestors being "African" (four-thirtieths), but if the genetic traits have been conserved over those generations, I will appear to be much more "African" according to my genes, conceivably one-half.

And I would call myself "one-sixteenth" African (100% great-great grandparent, one-half great-grandparent, one-quarter grandparent, one-eighth parent, one-sixteenth me).

And note, genetic traits are not conserved well due to crossover. When a cell undergoes meiosis, the chromosomes mix themselves up. That is, I receive one copy of chromosome 1 from my mother and one copy of chromosome 1 from my father. I will donate one copy of chromosome 1 to my child, but it won't be a pure copy of the one from my mother or my father. Instead, due to crossover, it will be a mixture of genes from both my mother and my father. Thus, my father's father's SNPs might vanish being replaced by my father's mother's SNPs and suddenly I appear to be a genetic stranger to him even though I share a significant amount of genetic material with him. Thus, I would appear much less "African" than I actually am.

I'd want to know more about the mathematical model involved that allows them to say "one-nth X." It would seem that the best they can possibly say is, "You have SNPs that tend to show up in these certain categories." There'd be no way to assign a number to that which would mean anything beyond that surface statement.

"A person can't be "one-sixth" anything in this sense since it would require three direct sources of DNA for a single person at some point."

You are missing something in your analysis. You can be something other than a power of 2 divisor. For example, if one of your parents is 1/2 of some "ethnicity", and the other is 1/4, you will be 3/8 of that.

FirstInLastOut:

You are missing something in your analysis. You can be something other than a power of 2 divisor. For example, if one of your parents is 1/2 of some "ethnicity", and the other is 1/4, you will be 3/8 of that.

I apologize if I was unclear. I was referring to the denominator. Look at your example. It's a power of 2: Three-eighths.

Yes, you can have all sorts of funky weirdness going on in the numerator. If my mother is half and my father is a quarter, that'll make me three-eighths. And if I have a child with someone who is one-sixteenth, our children will be seven-thirty-secondths.

But, you can't have anything but a power of 2 in the denominator. Since a person has two and only two genetic contributors to your genome, the only possibly division is by halves across all previous generations. The denominator of the fraction must be a power of 2.

You can't be a "sixth" of anything because that would mean at some point, somebody somewhere had three genetic contributors.

Perhaps his grandfather and grandmother were siblings.

Note that the research on Watson's genome was done looking at his SNPs not his family tree. Thus genome anlaysis is based on statistical frequencies not on arithmetic ratios.

It's certainly true that, as measured by one's family tree, the denominator in any fraction must be a power of two. But a fraction could come very close to resembling one-sixth when going back many generations. If a person's 32 great-great-great grandparents consisted of 5 people of a given descent, he or she would be 15.625 percent of that ancestry.

Here, one-sixth is a stand-in for the 16 percent figure that Kari Stefansson reported. But no one is claiming that exactly one-sixth of Watson's ancestors are of African descent in the last hundred-some generations, since that's not possible.

Particularly given Stefansson's doubts about the quality of the Watson genome sequence, it's possible that this figure is too high. Perhaps (for example) the actual figure is closer to 12.5 percent, which would suggest one great-grandparent of African descent.

The folks at 454 technologies, which sequenced Watson's genome, are preparing a paper on their analysis. It will be interesting to see what they come up with.

janeslogin:

Perhaps his grandfather and grandmother were siblings.

Doesn't matter. The only way to get a three as a factor in the denominator is to have three contributors at some point.

DAMOCLES SWORD:

Note that the research on Watson's genome was done looking at his SNPs not his family tree. Thus genome anlaysis is based on statistical frequencies not on arithmetic ratios.

I know, but that doesn't mean he is "one-sixth African." It's that one-sixth of the SNPs that were examined are commonly associated with African groups. I realize that the distinction is subtle. But because genetic mutations are not unique to population groups but are only commonly associated, we cannot make any real claims regarding ancestry.

If certain genetic markers get preserved along a lineage, then a person might appear to be much more recently connected to the original source than he or she actually is.

The point is that I should hope nobody is going to try to be making political hay out of the finding. Watson made some, oh, shall we say, "interesting" comments about intelligence and race and this finding isn't really a rebuttal to that.

There's nothing to rebut about Watson's "interesting" comments because their cognitive content was just about zero.