A term popped into my head the other day: "Theoretical Genealogy".  By it I mean the mathematics of populations - genetic diffusion, the probability of surname survival, how population growth skews the pool of descendants, etc.  This post is about just one topic, suggested by some recent research: diffusion.

Diffusion

While using Family Tree Maker’s search capabilities, I found I could add quite a lot of ancestors; there is no sound way to be sure they’re correct, and it’s hard to get an intuition about the reliability of the data, but it is a relatively rapid process.  As I chased lines back into the Middle Ages the doubts increased – but if nothing else the information may be used in the future as a starting point for, say, using DNA to verify links.  That is, it’s better than nothing, though perhaps not as reliable as I would like.

I noticed one phenomenon early on – many of my lines run through England (1600’s, 1700’s), and occasionally one of these would lead to some minor nobleman.  That person would in turn lead back to more important nobility, and finally to some recognizable king (e.g., William the Conqueror).  After this sort of thing happened a few times I began to be concerned that this really represented wishful thinking of someone, or some genealogist, along the line.  Am I really descended from Billy (above), as well as Charlemagne (several ways), along with various Viking and early Irish kings?  I didn't think so  because it seemed so surprising, and began that slightly unnerving process of figuring out where in the line of descent fiction crept in.

Now I’m not so sure.  The records of the minor nobleman and his ancestors seem fairly sound, I expect because property, wealth, and some level of authority changed hands with each generation.  The main weak point was the link between my known ancestry and that nobleman – that is a big jump.  Often it seemed to be the third daughter or so of the nobleman marrying my ancestor, who might have been a well-off farmer.  That sort of thing doesn’t seem unreasonable.  In the cases when this happened in the 1600's-1700's, sometimes coincident with travel to America, it was documented.  It might not have been were it just one more element of small town life in England.

Moving backwards in time from the minor nobleman the links seem fairly solid, for the same reason as above, it mattered at the time in substantial ways.  I’m sure there is questionable data in there – perhaps the occasional infidelity not identified as such ("Yes, he's your son, ignore the red hair") – but otherwise the genealogical data seems as sound as one might expect.

However, looking at the totality of the lines I’ve traced, I find I’m related to all sorts of kings and notables, in Ireland, France, Scandanavia, etc.  Is this reasonable, or is it the cumulative effect of past genealogists fudging the data a bit to claim famous ancestors?

To address this I turned the problem around, and imagined one of these notables (king, count, whatever) – they often had some semblance of wealth and a number of children.  The oldest few, particularly the males, would likely have married into other noble families, and it is from those lines that the people holding the noble titles today are descended.  The other kids did as well as they could, but often married significantly lesser nobility.  When this process repeated itself it eventually would mean some descendants were marrying commoners - perhaps on the well-off side, but non-nobility nonetheless.  This is not at all unreasonable - and if you think about it, the descendants of the original king/count/whatever would end up spreading out throughout the population.  Working backwards, then, as genealogists do, it isn't implausible that one might be caught up in that spread and then subsequently be led to the original notable as an ancestor.

What this really is is just genetic diffusion in the population, and when looked at from that perspective it seems unsurprising.  There have been recent articles about Genghis Khan’s descendents – apparently about 10% of males in the area of his former empire are related to him (or his family; one might imagine a brother, for instance).  As future generations arise the mixing will of course go further, until nearly everyone will be able to claim him as an ancestor.  Of course the number of generations back to Genghis is so large that the percentage of genetic data from him is quite dilute, and will become more so, but this is just the other side of the genetic diffusion coin.

Of course just as many people might trace their lineage back to Charlemagne, or Genghis, there are also some likely unknowns who cast similar genetic shadows over the future - some unknown peasant father and/or mother, who had numerous children, healthy, good looking, both sons and daughters, whose descendants spread out just as widely.  We just don't know their names.  The nobility, even minor nobility, shows up in church and civil records; the farmer doesn't.  Perhaps DNA analysis might at some point in the future reveal his existence, even if tentatively. 

(It is one of the striking things about doing this kind of research - how many people left so little trace other than through their children.  Even their names are missing.  I wish I had a at least a page, or even a paragraph, of information about each - I'm sure their challenges weren't fundamentally so different from ours.)

So - is there any way to quantify any of this, even crudely?

My background is European; the population of Europe in 1700 was about 50 million.  That is about the number of your ancestors back 25 generations (assuming no repeating ancestors).  At 20 years per generation, that’s 500 years.  By 'repeating ancestors' I mean no ancestor appearing twice or more - saying it that way makes it seem easy.  Turning it around - it means that say, at the 15th generation, two people who marry must have absolutely no ancestry in common.  I think this would be rather hard in a society where long-distance travel was rare.  The 500 year figure might well be half of that - 250 years - which, while long, is perhaps close to accessible oral history, particularly in fairly stagnant populations.  In either case, 300+ years on, a crude analysis suggests that pretty much anyone in Europe then might well be one of my (or your) ancestors.

The process of genetic diffusion is an intriguing one.  One might imagine as a simplified ideal a uniform population in which any person is likely to marry any other person in the population with roughly equal probability (excluding close relatives).  In that case the mixing will be maximized, that is it will happen as rapidly as possible.  Of course such populations may not really exist – social stratification, for instance, will lead to several (possibly overlapping) subpopulations that intermix that way, but not so much with each other.  Or there may be geographical separations that cause small ‘pockets’ of population to intermix internally but not externally.  I would think population genetics might be able to detect traces of such historical isolation from the genes and histories of people today.  It would take the right sampling to be able to draw solid conclusions, but it might be done.  While it seems an abstract notion, I think it might be practical, at least for recent cases.

For example, a number of my ancestors were among the early Dutch settlers of what is now New York City.  When the city became British in 1665, the Brits considered the Dutch second-class citizens, and intermarrying with them was rare; consequently the Dutch who remained ny necessity intermarried among themselves.  The end result is that, very loosely speaking, if you have a Dutch ancestor in that group it’s not unlikely you’re related to many of the other Dutch families who were present.  This phenomenon should be detectable by examining the DNA of descendants of that time – there would be areas of commonality due to that (socially) isolated population mixing as it did.  It would be more interesting to deduce such isolated populations entirely from the DNA as a way to augment history.  Doing it in the more distant past might depend on tracking mutations, and these might not happen rapidly enough to spread through a location such as 17th century New York City.  It might be different for, say, 6th century Naples.

The resulting model might be one of relatively static pools of population, connected by some punctuated diffusion.  This might not match historical reality exactly (say, an individual might have married into an immigrant family in his town, then his descendants might have moved back to the source of the immigration), but it might be a useful model nevertheless.  It seems ripe for mathematical modeling.