Monday, April 23, 2018

Genomic Collapse is a Bitch

Sometimes distant cousins marry.

Sometimes not-so-distant cousins marry.

And then there's Jamie and Cersei Lannister, but that's another story.

In any case when this happens, the existence of shared ancestors begins to shrink down the number of people in the family tree, compared to what could possibly be there.

I'm defining "Genomic Collapse" as:

The ratio of unique people in a subset of the family tree to the number of "filled slots" in that subset.
 So in the extreme case of Joffrey Lanister (whose parents were brother and sister), that's 50% genome collapse at a minimum because the maternal and paternal blood lines are identical; and "at a minimum" because another consanguine relationships further up continue to contribute to the genome collapse.

So - what is it for my maternal family tree?

  • Out to 10 generations:  41.4% complete tree but with 30.2% collapse (296 people in 424 filled slots out of 2046 total slots);
  • Out to 15 generations: 5.9% complete but with 49.0% collapse (988 people in 1,937 filled slots out of 65,534 total slots);
  • Out to 20 generations: 0.2% complete but with 51.4% collapse (1,074 people in 2,208 filled slots out of 2,097,150 total slots).
I'm not sure if this is the right way to do this because one you hit a non-unique ancestor, that effect double with every generation back.

In any case, going from generation to generation it looks like this:

The blue line is the percent overlap at that generation.   The green line is the % overlap for that generation and all the ones preceding it.    The orange line is the highest possible percentage of overlap (i.e., all unknown ancestors for that generation are all repeats of known ancestors), the red line is the lowest possible percentage (all unknown ancestors are new people).

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