Ancestors are daggy

I learned that excellent adjective quite recently, from a young cousin in Australia. Something is said to be daggy when it exhibits an indigestible mixture of several negative or frankly nasty features. It's generally scruffy, dirty, broken, something that would best be discarded as rubbish. Although I like the fresh Down Under twang of this word (like bogan, an equally pejorative epithet), it goes without saying that the title of this blog post is not intended to cast aspersions of any kind upon the fine folk who were my forebears. No, I've decided to invent (facetiously) a totally new meaning of the adjective "daggy"...

Let me explain. The only serious way of understanding the phenomenon of ancestors is to represent them by means of illustrations of the kind that mathematicians refer to as DAGs: directed acyclic graphs. Unless you do this, you're liable to remain forever confused by the sheer quantitative proportions of the vast hordes of procreators who have been responsible, ever since life has existed on the planet Earth, for copulating, conscientiously and copiously, in ways that have led to your present existence.

Genealogists have often used tree diagrams to represent ancestors, and half the community feel that the roots should be down at the bottom and the leaves at the top, whereas the other half find that it would be preferable if such diagrams could reveal their content in a chronological top-to-bottom direction. Obviously, the best way of ending this dispute is to lay your family-history charts out in a horizontal fashion, because nobody would ever dream of putting old folk to the right and living individuals to the left.

In fact, the ancestral scene has always been a jungle, rather than a tidy forest. And the only aspect of the situation of which we can be relatively certain is that there are far more human beings on the planet today than when all the diligent copulating got off to a start, long ago.

Some folk have the pleasure of emerging from ancestral contexts in which so much irregular screwing of all kinds was taking place constantly that it can become quite a difficult task to distinguish between the various roots and leaves, and to determine where certain rooting leaves off, while elsewhere certain leaves take root… if you see what I mean. [If I weren't sure that you've heard it already, I would throw in here the joke about the rare Tasmanian marsupial that eats, roots, shoots and leaves.] I warned you that the situation is daggy.

Here's a typical example of a graph of the directed acyclic kind:

Clearly, it's a graph, since the diagram is composed of labeled vertices (nodes) linked by lines. It's a directed graph because all the lines carry arrow heads to indicate their respective directions. And it's acyclic, above all, in the sense that, no matter where you start, you'll never find yourself going around in circles. To put it bluntly, there's no way in the world that a young lady might give birth to a child who turns out to be the girl's father. Not even in the Holy Bible, where supernatural birth is a common phenomenon, would you find such a far-fetched tale as that (unless it has escaped me). Now, this kind of DAG provides an elegant way of indicating how humans might procreate. Admittedly, at times, the relationships are not particularly Christian. But who cares?

— Fred and Kate gave birth to a son, John.

— Kate appealed to a different father, Ken, to produce a daughter, Alice.

— These naughty kids, John and Alice, promptly got together to give birth to Bill… who probably ran into various terrible health problems later on.

— Meanwhile, Alice was seduced by John's dad, Fred, who bore her a son, Tom.

— Alice, a spirited young woman, also had a daughter, Mary, whose father is unknown.

As I said, the overall situation is mathematically "daggy" in the sense that no unthinkable acts have ever taken place. There are no vicious circles. No closed loops. No offspring has ever ended up becoming the genitor of his or her own father or mother. So, the overall situation is perfectly human, all too human.

Many observers who see how genealogical researchers behave are inclined to cry out in disbelief that their activities are crazy. For example, I'm proud of the fact that I can document—more or less clearly and plausibly—the 29 generations that take me back to William the Conqueror. [My "pride", of course, is perfectly irrational and superficial, on a par with saying that I'm proud to be Australian, say, simply because my ancestors happened to be led to that land, for various random reasons.] Certain observers are shocked by my evocation of the Conqueror, and they hit out with bad arithmetic: "William, your alleged royal ancestor is merely one of N individuals who played a role in your procreation, and the value of N is approximately 2 to the power 29, that's to say 536 870 912." The problem, here, is that this number no doubt exceeds the total number of inhabitants who were looking around for a bit of procreative Franco-British rock 'n' roll back at the time of the Conqueror. So, there's something basically wrong with the use of binary trees when calculating the volume of your ancestors. What's wrong, as I've been saying, is that you have to use DAGs, not binary trees, to represent your ancestral jungle.

Other observers throw up their hands in despair and say: "It's impossible to explain the situation. Back at that time, clearly, everybody was related to everybody else." In France, for example, people like to claim that every living French citizen is a descendant of Charlemagne… which is ridiculous. For all we know (and we shall never know such things, of course), my global circle of forebears at the time of the Conqueror may have been limited to little more than a handful of rural villages in Normandy. I hasten to add that, in making such a suggestion, I'm forgetting, of course, that ancestors in all kinds of remote places no doubt got into the act of procreating me, further down the line. There were lots of Irish copulators, for example, and I have no reason to believe that they were necessarily hanging around in Normandy at the time of the Conqueror. But, if we were to know the numbers, the entire team, maybe scattered throughout several regions of the planet, might have been relatively modest. In any case, it's absurd to imagine that a host of medieval folk—more than the current population of the USA—were copulating furiously, day and night, in a sense that would ultimately lead to my peephole opening on a September day in 1940. My crowd of ancestors must not be likened to the armies of Joshua at Jericho, or the host of angels on Judgment Day.

Let me finish with an anecdote. I was pleased, a few weeks ago, to have made contact with a prominent American scientist named Skevington, and I immediately tried to persuade him to obtain his Y-chromosome data, to see whether we might be related. I was amused by his immediate reaction. He evoked the notorious but very real phenomenon of so-called non-paternity events: that's to say, cases where a child's genuine father is not the guy whose name appears in the records. Often, we hear amazing figures concerning the proportion of male babies who grow up (and maybe spend their lives) without ever becoming aware of the true identity of their biological father. Now, while it's probably high, the figure is not as high as it's often made out to be. For example, it's silly to suggest that 10% of English-speaking males have a mistaken idea of the identity of their fathers.

Click the banner to access a scientific article on this question entitled Founders, Drift and Infidelity: The Relationship between Y Chromosome Diversity and Patrilineal Surnames by Turi King and Mark Jobling.