Thursday, March 15, 2012

Not much king left

kw: genealogy, analysis

Caucasian Americans have a fascination with European royalty, and I am no exception. In my own genealogical studies I find it interesting that I am descended through at least three lines, and possibly four, from either Edward I or Henry III. The two of them, father and son, are descended from Charlemagne, sixteen generations back from Edward, who is twenty-two generations back from me via one of the lines.

I began to wonder, just how much of Edward or Charlemagne, or anyone else for that matter, remains in my genetics, this many generations removed? For I have half my father's genes, and half my mother's (plus or minus some statistical variation), one quarter of each grandparent, and so forth. How much of my genome is likely to be descended directly from an ancestor 22 or 38 generations removed?

Ignoring minor variations caused by descent via a male versus a female line, the process of assortment during meiosis, that produces eggs and sperm, is rather blocky and imprecise, and determines what gets included in a particular gamete. There are three figures of interest here:
  • The total human genome consists of 3.2 billion base pairs for a woman, 3.1 billion for a man (the Y chromosome is shorter than the X).
  • The coding portion of the genome is just under 1.5%, or about 48 million base pairs.
  • There are 25,000 or fewer protein-producing genes.
Now I can pick a few ancestors and see how much "influence" each one has on my genetics.
  • John Kirkman and his wife Mary Boyd were immigrants from Ireland. They are four generations removed from me. The factor I'll call Descendancy Fraction (DF) is 2-4, or 1/16, or 0.0625. Genes are usually not chopped during assortment, so 25,000/16, or about 1,560 genes, came to me direct from each of them. Of coding base pairs, I have 3 million from each, and of total base pairs, about 190 million.
  • In the twelfth generation I find Peregrine White, the child born aboard the Mayflower in Plymouth Harbor, and his wife Sarah Bassett. The DF here is 2-12 = 1/4096 = 0.000244… The amounts I have from either of them amounts to just six genes—or enough fragments to make up six—, 11,700 coding base pairs, and about 780,000 total base pairs.
  • Edward I and his wife Eleanor of Castile, 22 generations back: DF = 2-22 = 1/4,194,304 = 2.384x10-7. Here the number of genes is less than one: 25,000/4 million means there is 1 chance in 160 that any of Edward's genes has found its way to me. Coding base pairs? Eleven (plus or minus one or two). Total base pairs: about 760.
  • Now for the real fun: Charlemagne, 38 generations back. DF = 1/2.75x1011 = 3.64x10-12. Here we'll just check total base pairs, and it comes to one chance in 86 that even one base pair from any part of Charlemagne's genome has made its way into mine!
I find that amusing. When my mother was a member of a genealogy club, and our probable connection to Charlemagne was discovered, everyone was so thrilled. If genes have anything to do with who we are, however, there is little chance that such remote ancestors shape any part of what we are. It is still true: you are what you make of yourself.

Now, briefly, let's turn the calculation around. I have one child. A friend of mine is one of fourteen children (he has only one child). Each child bears half the genetic component of each parent. But the assortment process is quite random, so that if you have two children, there is a 75% chance of any particular gene, or any particular bit of your genome, being passed into the next generation. The more children you have, the higher the percentage goes.

For both my friend and myself, half our genes have been sent into our offspring. But for his parents, it is a different story. The DF works in this direction, to calculate the fraction not passed forward. His father's DF, for fourteen children, is 1/16,384 or 0.000061… That means that, at most, one or two of his 25,000 genes was not reproduced into his children. The same for his wife. You can say that everything they are has been sent forward a generation. My friend's portion of his parents' genetics is, however, only 50% passed forward, but of course nearly all his siblings have one child or more, so a large proportion of the legacy of their parents lives on. Having children is still the most reliable way to have an impact on the future.

1 comment:

Tom Noir said...

To take you a little further down the rabbit hole: a recent paper shows that if you go back far enough you can guarantee that if X historical figure had any descendants at all, you are one of them. Not sure if this applies to Charlemagne, but it apparently applies to Confucius!

In other words, there is a date in the past such that at that time and before, the human population can be divided into two groups: those who have no current descendants and those who have all currently-living people as descendants. For people living at or before that time, if they are the ancestor of any modern humans, then they are the ancestor of all of us.

....

Wikipedia tells us that Confucius lived between 551 and 479 B.C., and that his first child was born when he was 20, in 531. 2012+531 = 2543 years ago. And 2543/28 = 91 generations ago.

According to Chang's formula, 91 generations would guarantee full mixing in a population of 2^(91/1.77) = 2^54.4 = 1.93*10^16 = 19.3 quadrillion, which is many times the current population of the world, much less its population over the past 2500 years. Specifically, it's about 2.8 million times the current world population — this seems like plenty of headroom to allow for geographical and cultural barriers to mating.


More on the paper at Language Log: http://languagelog.ldc.upenn.edu/nll/?p=3755