Chang was able to demonstrate that once two parents were considered, even using simplifications that make complex tangled families** impossible, the inclusion of the second parent meant that common ancestors cropped up far more recently than was suggested by the female-only line. As Chang puts it ‘mixing occurs extremely rapidly in the two-parent model, so that [common ancestors] may be found within a number of generations that depends logarithmically on the population size.’
Let’s unpack that word ‘logarithmically’. This means that the population size would be around 2N where N is the number of generations to the most recent common ancestor. For example, in a population of 1 million, the number of generations required to reach a most recent common ancestor is just 20, as 220 = 1,048,576. For the same size population, mitochondrial Eve with her single-parent lineage would require thousands of generations.
This is striking enough, but there is a more remarkable result still from taking this approach. This calculation might give an approximate value for the number of generations to a most recent common ancestor. But this certainly isn’t the only common ancestor. There may be more than one in that same generation. And for certain there had to be at least two in the previous generation, four in the generation before that and so on – because each of the most recent common ancestors’ parents, grandparents etc. would also be our common ancestors.
This back-in-time spread of common ancestors increases exponentially as we get earlier in time. Eventually there must come a point where everyone in a generation whose line didn’t die out – everyone who has descendants living now – is a common ancestor of today’s entire population. At this point anyone in the population we’re looking at can say that everyone in that ancient generation who has living descendants is their ancestor. Surprisingly it doesn’t take long to get back to a generation where this is the case – only around 1.77 times the number of generations required to reach the most recent common ancestor.
Of course, in the real world we have a population of a lot more than a million – at the time of writing about 7.7 billion. If we just plug the current population into the simple formula, that’s around 33 generations or 1,000 years to get a common ancestor of all of humanity. But here one of the principle assumptions of the model breaks down – even now, we are significantly more likely to have children with someone born in the same country than from another country, and going back in time this was far more likely still. But the model works on the assumption that anyone in the world can be your parent.
Given those provisos, Chang proved mathematically that his estimates for the number of generations to the most recent common ancestor, and for all the population with surviving descendants to be common ancestors, were realistic. This, however, was only the start. By 2004 he was able to publish in Nature a paper with Douglas Rohde and Steve Olson that took in the isolation of populations and the tendency to mate within social groups, providing a much more realistic model of our true ancestry.
The models showed that even in populations with significant internal structures, a most recent common ancestor would still be reached relatively quickly (far quicker than working back to mitochondrial Eve). With this more sophisticated model and conservative assumptions about migrations of individuals, Chang and colleagues came up with a worldwide most recent common ancestor date of 1,415 BC and a date when everyone with surviving descendants was your ancestor of 5,353 BC. With a rather more generous rate of migration and mixing, this can be made as recent as around 2,158 BC.
BRINGING IN THE GENES
Since Chang’s paper was published, there has been considerably more work done by other researchers, adding genetic information to the statistical data from the model, reinforcing Chang’s conclusions that, for example, within Europe you only have to go back 600 years to hit a most recent common ancestor and 1,000 years for everyone in Europe who has living descendants to have been one of your ancestors.
Of course, we have no idea who the most recent common ancestors of Europeans were – and the mathematics allows for many more than one common ancestor in a generation. But when we go back far enough for everyone who has living descendants now to be an ancestor, we hit royal pay dirt. A handful of people can trace back their ancestry to royalty from 1,000 or more years ago. And given that these people are still alive, that means everyone of European extraction is descended from those same royal individuals.
The specific example that tends to be picked out is Charlemagne, who was king of the Franks and Holy Roman Emperor, living from 742 to 814. There is good evidence that he has living descendants – so this means that if you are of European extraction you can claim Emperor Charlemagne for your family tree just as much as Danny Dyer has his royal background. Similarly, the current British royal family are thought to be descended from William the Conqueror, who is sufficiently far back in history that should you have European descent, he is almost certainly your ancestor too.
If you don’t think you have European ancestors, find yourself a suitable ruler far enough back in your own history and you will have a certain hit. And without doubt we are all descended, every one of us, from royalty in prehistoric dynasties who may not feature on the historical record, but existed nonetheless. The earliest known Chinese dynasties are said to stretch back to around 2,000 BC, encompassing the lower figure for ancestors of everyone in the world. Egyptian dynasties are said to go back to around 3,000 BC. Sumer was settled around 5,000 BC – so, the chances are that wherever you are from, you can claim a link to the Sumerian royal family.
There’s always the proviso of these common ancestors needing to have descendants still alive. Some won’t – but a percentage will. In the end, the individual doesn’t matter. The point is that in terms of what you think you are, there is no doubt that you and I share common ancestors, and we are both descended from royalty. Don’t get too full of yourself, though. You are also descended from murderers, vagabonds and thieves. (Actually, come to think of it, all of the above could apply in the case of the royalty too, and almost certainly did. You didn’t get to be royal in the early days without a spot of Machiavellian machination.) Your ancestors were also merchants and beggars, philosophers and artists, saints and sinners. Our true family trees are not the spindly little cherry-picked things we usually see – they are vast, intertwining forests that give each and every human being a rich and wonderful heritage.
Before we move on to take a plunge back into your very oldest origins, we should take a moment to dismiss a genealogical myth that should be obvious from what we’ve just read about worldwide common ancestors. Biologically speaking, there’s no such thing as race.
THE RACE CARD INDEX
We love to split things up – including people – into groups and categories. It’s how we understand the world, and often it is very useful. But with people, all too often the categories reflect those who belong and those who don’t. We’ve got plenty of ways of categorising humans that have some validity and usefulness. Although there is no biological basis for nationality, for example, it has legal standing and as such is part of what makes you what you are. Likewise, socioeconomic groupings and culture are not biologically based,†† but they certainly exist and are sometimes used to discriminate against individuals and groups. Then there are biological differences, whether at the gross level of gender, or the more sophisticated, but still biological, aspects of being, say, straight or LGBTQ+. We need to recognise all these groupings, both because they are part of our identity and because many of them can be used as a division for discrimination, which a civilised society needs to avoid.