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On Exponential Growth and Fag Ends

I have often been confused when people talking about family history—often people with good genealogical knowledge—talk about their family “coming from” a particular location in the distant past. Don’t they know anything about exponential growth? When you talk about your family living in some small region of north Norfolk 400 years ago, what does that mean? That’s (inbreeding aside) over 32,000 people! Surely they didn’t all live in a few local villages.

Now, I appreciate that this is a bit of an exaggeration. Over a few hundred years there will be some (hopefully fairly distant) inbreeding and so each person won’t have tens of thousands of distinct relatives. I appreciate, too, that people travelled less in the past, and that even if you are genuinely descended from thousands of distinct people, those people will have been more concentrated in the past. But, still, the intuition that “your family” (by which they are imagining, I think, a few dozen people at a time) “comes from somewhere” still seems a little off.

The naïve explanation is that they just don’t realise the scale of this growth. I would imagine that most people, asked for an intuitive stab at how many great-great-···-grandparents they had 400 years ago, would guess at a few dozen, not a number in the tens of thousands. Perhaps they have some cultural bias that a particular part of the family tree is the “main line”, perhaps that matrilineal or patrilineal lines are the important ones, and that other parts of the family are just other families merging in. Or, perhaps they recognise that in practice main lines emerge in families when there are particular fecund sub-families, and other branches fade out.

Overall, these “fag ends” are not very well acknowledged. Most people depicted in fiction, e.g. in the complex family interconnections of soap operas, have a rich, involved family. There isn’t much depiction of the sort of family that I come from, which is at the ragged, grinding to a halt twig of a family tree.

Let’s think about my family as an example. Both of my parents were somewhat isolated within their families. My mother had three siblings, two of whom died in infancy. The other, my uncle, went on to have three children, two of whom in turn have had children and and grandchildren, and the one who didn’t married into a vast family (his wife has something like ten siblings). By contrast, my mother had only me, who hasn’t had any children, and didn’t get on particularly well with her brother, so we were fairly isolated from her side of the family after by grandmother died. So, from the point of view of my grandmother’s position in the family tree, it is clear that my uncle’s line is the “main line” of the family.

Similarly, on my father’s side, he was similarly at a ragged end. He had three sisters. One died fairly young (having had Down’s syndrome). The one he was closest to went to Australia and had a large family—four children, lots of grandchildren, etc; but, they were rather geographically isolated. The one that lived a few miles from us he wasn’t particularly close to, and only had one child, who remained child-free. He had one child from his first marriage (who had children and grandchildren and great-grandchildren, which bizarrely meant that by the age of 42 I was a great-great uncle), and had only me from his marriage to my mother. Again, there are big branches and fag ends: the branches of the family tree that dominate hugely are the Australian one, and the one starting from my half-brother, whereas mine (no children), and my aunt (who had only one child) are minor twigs.

So, perhaps there is some truth in the genealogist’s intuition after all. A small number of branches in the tree become the “main lines”, and others become “fag ends”, and there isn’t much in between. It would be interesting to formalise this using network science ideas, and test whether the anecdotal example that I have in my own family is typical when we look at lots of family trees.

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