In my research of August's heritage I've looked at 333 different individuals so far. Seven of those had at least one set of common ancestors (2nd cousins married married, 9 generations back from August - in the mid-late 1700's).
I'm not sure I'm mathematician enough to figure out just what this ratio means, given the composition of the tree I have. 7/333 is more than 2%, but I only have a very small number of the full mathematical complement of August's ancestors from 9 generations back. Look how quickly the proportion of known ancestors tails off after the great-grandparent level:
Of the 512 individual in a tree at the 9th generation level, we've identified only 27 for August. That's about 5%. So if 1 out of those 27 is the product 2nd cousins, does that mean that we can expect the same for 20 out of the full 512?
Any self respecting statistician would tell you that one data point in one non-random sample is indicative of nothing. But it would be surprising to me if the true number, for most people, were actually that low, especially if you get back into the 16th and 17th centuries. Most of the people we've found are farmers, from tiny little towns. Farming communities in Virginia in colonial times, rural England in the 16th century, farming communities in the mid-west in the 1800's. At least once in August's line we found a man marrying a woman who had the same surname as his grandmother. And if you're talking about Augusta County, Virginia around the year 1800, it doesn't take a mathematician to figure out what's going on!
And consider this: though we knew 27 of the 512 people at the 9th generation level, we didn't necessarily know if each of them were the product of 2nd cousins because to know that we'd need to know all of their ancestors, going back 4 generations. You can see that we don't have 27 * 2^4 = 432 great great grandparents for each of the 27 9th-great ancestors that we do have.
More analysis required.
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