Counting your ancestors

Posted: November 30, 2013 in Family History, Genealogy, History

This is the text of an article publish in Family Tree magazine in March 2013. A more extended version can be found here.

Tackling a numerical problem – just how many ancestors have we got and how on earth could we count them? Here Stephen Lewis explains how to make sense of a seeming paradox…

Almost everyone with an interest in family history and genealogy will at one time or another ask themselves how many ancestors they have. As we research our roots further and further back, the numbers seem to explode, and it starts to become incredibly difficult to keep track. What determines the number of your ancestors? What factors are at play?

An explosion of ancestors

On the surface the question of how many ancestors you have might seem simple to answer. After all you have two parents, four grandparents, eight great-grandparents and 16 great-great-grandparents do you not? Don’t you just need to do a simple mathematical calculation to work out the number of your direct ancestors who were living and breeding so many generations ago? The numbers surely just double in each generation: 2, 4, 8, 16, 32, 64 and so on, forming a pyramid.

Using 1947 as a reasonable starting date and 30 years as the average inter-generational length, ten generations ago – which takes us back to the time of the English Civil War and to the early days of British settlement in North America – it seems we should all have had 1,024 eighth great-grandparents. You might also be interested in working out how many direct ancestors you might have had in total between a certain date in the past and now. You can just add up the numbers for each generation. Going back 10 generations (starting from your parents) the total is 2,046 direct ancestors.

But, as many will have noticed, there is a problem with this. If we calculate the numbers 30 generations ago, at about the time of the Norman Conquest in 1066, we would seem to have needed about 1.1 billion direct and distinct ancestors alive at that time, and in only one generation. Obviously this is impossible, as the total world population in the 11th century is estimated to have only been about 250 to 300 million.

So the number of our ancestors can’t keep on doubling as we go further and further back. Sooner or later the number of your ancestors must have stopped exploding and must have started to shrink, and shrink fast. What causes this so-called ‘Pedigree Collapse’ and what determines when it happens? Both questions are answered by understanding the nature and extent of cousin marriage, or inbreeding if you like; levels of migration and outbreeding influence this.

Cousin marriage

In some societies cousin marriage is either illegal or socially taboo. In England, even though Henry VIII abolished  restrictions on marrying ‘cousins’ so he could marry Catherine Howard (Anne Boleyn’s cousin), for centuries there have been both ecclesiastical and  other controls on marriage between family members. Today in the West, close cousin marriage is rare, although recently an Australian research scientist, Dr Alan Bittles, concluded that ‘slightly more than 10per cent of marriages worldwide are between people who are second cousins or closer’. In the past, not only was some degree of cousin marriage likely, it must have been extremely common. Without it we couldn’t even attempt to make sense of the development of human numbers over the centuries and millennia.

The first effect of cousin marriage is to reduce the rate of growth of the actual number of your ancestors, as compared to the theoretical maximum. If your parents were first cousins this means they shared one set of ‘duplicate’ grandparents and thus rather than them having the maximum of eight grandparents between them, they would have had only six. This is a 25per cent reduction in their grandparental ancestry, a reduction that goes back forever. Similarly, a marriage of second cousins would reduce numbers by one-eighth, or 12.5per cent, in each generation.

The problem is that no matter how high the historic level of individual first and second cousin marriage – and it wasn’t very high – although it will reduce the rate at which the number of your ancestors increases, it will never put the process into reverse. For example, using the completely unrealistic assumption that every single one of your ancestors married a second cousin, which would reduce the supposed number of your ancestors at the time of the Norman Conquest by a staggering 96per cent from the theoretical maximum of about 1.1 billion, it would still mean that your distinct direct ancestors (in one generation) alive at the time numbered about 4.4 million, still more than the estimated total British population. And this is without taking account of the fraction of the population accounted for by one generation and the percentage of people alive at the time who had no descendants or whose descendant line died out.

Multiple relationships

It’s relatively easy to show that as the practice of individual cousin marriage increases your ancestor pyramid will narrow. Yet the total number will still keep on growing. It will never go into reverse. However such a reversal must have happened – both in total and for every single one of us. Simply put, the reason for the reversal is that when your ancestors married or bred with a cousin (of whatever degree) they very often also had more than one family relationship with their mate – sometimes many more.

Let’s use a very simple hypothetical example to elucidate this. Imagine again that your parents were first cousins, so they shared a common pair of grandparents. But they could also be second cousins as well, in which case they would also share a common pair of great-grandparents. The first cousin relationship would reduce the number of your ancestors in, for example, the fourth generation from 16 to 12. The addition of the second cousin relationship between them would reduce this number still further – from 12 to 10. As we go back in time, such multiple relationships between spouses proliferate. They might be second cousins twice over and third cousins or fourth cousins many times over. Such multiple relationships have an additive effect on the reduction in the number of your ancestors. The further you go back into your history the more likely you will find that this has been the case – in fact it is absolutely inevitable.

This is all mathematically, biologically and historically certain. With enough multiple relationships, with enough breeding between males and females who are related in multiple ways, the cumulative effect of removing duplicate ancestors will at some point eventually outweigh the doubling effect and the number of your discrete ancestors will start to shrink.

Try a thought experiment. Imagine a Mr and Mrs Crusoe washed up on a desert island. Any children they have will need to breed with each other – heaven forbid with their parents! Their children will all be first cousins. As the generations go by, all the couple’s descendants will become related to each other in multiple ways. If you are a descendant of the Crusoe family today and calculate the number of your ancestors, it will first quickly grow but eventually it will shrink back to just two – Mr and Mrs Crusoe.

Such an expansion and contraction in ancestor numbers is a phenomenon well known to breeders of pedigree dogs and horses. The shorter life span of these animals, plus the fact that breeders must keep detailed records, often enables them to clearly plot such pedigree collapses. Indeed these collapses often happen more than once. The main problem with applying this analogy to humans is that animal breeders are consciously trying to breed ‘pedigree’ animals; they are artificially and deliberately restricting the opportunities for dogs or horses to breed outside a very restricted group. Just as, in a similar way, the inhabitants of our hypothetical Crusoe Island have also been restricted in their breeding – by geographic separation.

Migration and outbreeding

So it is because humans historically have bred with people with whom they have multiple relationships that pedigree collapse happens. For any person or any country, when exactly the reversal in numbers happened is thus in the first instance determined by the level of inbreeding – how quickly the number of duplicate ancestors outweighs generational doubling. In England this reversal happened in the High Middle Ages, probably in the 1200s; for individuals or in other countries the timing can be different. But humans generally try to avoid incest or inbreeding. The extent that they can do so will mostly be determined by another factor: the available breeding pool. The people with whom our ancestors could breed was not limited to all those living in their village or even in their country. People moved; they migrated. Every time one of your ancestors moved into or out of one of their ‘ancestral’ areas, whether a few miles or hundreds or thousands of miles, they brought or took with them an untold number of ancestors of their own. These ancestors have become your own. If people hadn’t moved at all we would all be able to trace our lineage to one ‘Adam and Eve’ founder couple in the not too distant past, just like in the Robinson Crusoe example. The more your ancestors moved the further back in time your own pedigree collapse will be pushed.

What’s the answer?

So how many direct ancestors do you have? The answer, I’m afraid, is that you will never be able to calculate precise numbers. Reliable records just don’t go far back enough. The number might be more than you imagined, as the seemingly relentless doubling goes on. Yet we know that sooner or later their number will start to decline. It might be, though it is extremely unlikely in the time frames we have been considering, that your ancestry goes back to only one locale at a certain point in history or even to one ‘founder’ couple. But remember this: it has been shown that the human race went through at least one population bottleneck during its history. At certain times it appears that humankind almost went extinct. Scientists have suggested that around 70,000 years ago the total world population dwindled to only a few thousand Africans – the so-called Toba catastrophe. They are the ancestors of all of us.

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