Pedigree Collapse

The last time I loaded the list of my ancestors, it had the oddity that some people appeared twice. The Family Historian software that I use has been updated to stop double appearances – but now I see another oddity, because at least one person is on the same generation as her parents. This isn’t Family Historian behaving oddly – this is something called Pedigree Collapse and it’s life that’s behaving oddly!

I’ve found it happening with Ann Healow, daughter of William Healow and Mary Farrington, and it may happen with others. Ann is on the eighth generation, so you’d expect her parents to be on the ninth. Actually, they’re on the same generation as her. That’s because I’m descended from William Healow and Mary Farrington twice over – once through their daughter Mary, and a second time through their daughter Ann. William Healow and Mary Farrington appear on the eighth because their daughter Mary is on the seventh. Their other daughter, Ann, is also on the eighth, but she doesn’t trigger her parents to appear on the ninth because they’re already in the report (on the eighth) and no couple should appear twice.

In fact, William and Mary are both my 5-greats grandparents and my 6-greats grandparents. The problem starts with my great-great grandparents, William Cooper and Hannah Newton, who were second cousins once-removed. In this case, it was William’s father, John Cooper, and Hannah who were second cousins.

If I forget about the “second cousins once-removed” bit and trace the Cooper and Newton lines back, then along the Coopers I get to another William Cooper, who is my 5-greats grandfather, while along the Newton (and Windsor) line, I get to George Windsor, who is my 4-greats grandfather. That’s fine. Their wives are respectively Ann Healow (my 5-greats grandmother) and Mary Healow (my 4-greats grandmother). And guess what – both Healow women are daughters of William Healow and Mary Farrington. So that couple are my 6-greats grandparents via their daughter Ann, and my 5-greats grandparents via their daughter Mary. And of course, their parents in turn are both my 7-greats grandparents and my 6-greats grandparents, and so on…

You may say, “Thank goodness I’ve got nothing like that”. Oh, but you will have, it’s just that you haven’t found it yet. Hold on and we’ll do some sums. After one generation back, you have two ancestors. After two generations back, you have four ancestors. After 10 generations back, doubling each time, you’ll have (trust me) 1,024 ancestors. Unless, that is, some of your umpteen great-grandparents are, like William and Hannah, related, in which case it won’t quite double. And it’s a mathematical certainty that this will occur in your tree as well. Think about it – if you’ve got a potential 1,024 ancestors after 10 generations, then you’ll have 1,024 x 1,024 ancestors after 20 generations. Call it one million. And after another 10 generations again, you’ll have a potential 1,000 million ancestors (in round numbers). But 30 generations is only about 900 years ago, and there just weren’t that many people around then. According to Wikipedia, between 1250 and 1350, the population of Europe is believed to have reached a peak of 70 to 100 million. Nothing like enough to give you 1,000 million separate ancestors in 1100 AD. What stops the relentless multiplication by two, is that on each generation, some of your ancestors will be umpteenth cousins so-many times removed (Pedigree Collapse).

So you see, you will have the complication of people being both your x-greats grandparents and your y-greats grandparents – you just might never find it.

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About brucefuimus

Retired IT professional; family historian and mathematician by training.
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