The Ancestor Paradox Yet Again

Following the publication of my previous articles touching on the “ancestor paradox” I have received letters from Mr Peter Hendra of Margate, Mr Andy Robson of Jarrow, Mr David Squire of Ealing and Mr J. Blenkin of Sutton Coldfield. These letters were all most interesting and enlightening; I am most grateful to all these gentlemen for taking the time and trouble to write to me. In addition to his letter, Mr Blenkin also published an article in The Journal of the Northumberland and Durham FHS Volume 13, No 1.

The following article deals with the various points raised by these gentlemen. Unfortunately copyright considerations prevent my reproducing Mr Blenkin’s article and the letters, but I hope that the substance of these will be obvious from my response.

First Mr Blenkin’s point that if we have no faith in the probity of our forebears we might as well discard our hobby. I have absolute faith in the probity of my parents and grandparents, but I did not know the others. Many were apparently fine upstanding citizens, others were cheats, liars, drunkards and womanisers; there were numerous illegitimate births and allegations of paternity; there was a bigamist and a forger who may even have been a murderer. Should I have faith in these people? Do not give up, Mr Blenkin, but it is no good wearing rose-coloured spectacles. An essential qualification for the genealogist and all historical researchers is a degree of scepticism!

Mr Blenkin also doubts that we have no way of knowing what proportion of our genetic makeup comes from any given ancestor (except our parents). I suggest asking an expert, but I doubt you will find a biologist who will challenge the premise. There is an exception. Men have some genes (those on part of the Y chromosome) which can only have come from their fathers. A man will therefore have some genes in common with all the members of his all-male line. (Apart from very occasional spontaneous changes called mutations).

The all-female line has something special too, but it has nothing to do with chromosomal genes in the cell nucleus. Our cells contain features called mitochondria which have their own set of genes, and our mitochondria always come from our mothers. Mitochondria vary from person to person but a given person’s mitochondria are always identical to those of his or her mother. So everyone, male and female, will have identical mitochondria to those of all members of their all-female line. (Again there could be very occasional mutations).

Now to the numbers of ancestors. The formula Mr Blenkin quotes is basically correct but it is not very useful in practice as it does not indicate when the reduction in numbers first occurs. And there is no need to use percentages or powers of two, multiplication and subtraction will suffice.

If you marry, say, your third cousin, your children will still have 2 parents, 4 grandparents, 8 g-grandparents and 16 2g-grandparents. But the number of 3g-grandparents will be reduced by 2 to 30 and of course, earlier generations would be reduced too; the sequence would be 1,2,4,8,16,30,60,120…… Notice that a 3rd cousin marriage only affects the 3g-generation and earlier. This is generally true and is a far more useful rule. Another example: if you marry a 5th cousin, then the number of 5g-grandparents that your children will have will be reduced by 2. The sequence will be 1,2,4,8,16,32,64,126,252….

To illustrate how easy this rule is to use, consider the case of a couple who are 1st cousins, 3rd cousins twice over and fifth-cousins six times over. To find the number of ancestors this couple’s children will have, proceed as follows:

Number in
Child 1
Parents   2 X 1 = 2 2
Grandparents   2 X 2 = 4 4
1g grandparents   2 X 4 = 8   Deduct 2 for 1st cousin 6
2g grandparents   2 X 6 = 12 12
3g grandparents   2 X 12 = 24   Deduct 4 for 2 of 3rd cousin 20
4g grandparents   2 X 20 = 40 40
5g grandparents   2 X 40 = 80   Deduct 12 for 6 of 5th cousin 68
6g grandparents   2 X 68 = 136 136
7g grandparents   2 X 136 = 272 272
8g grandparents   2 X 272 = 544 544

These calculations can be done by hand but the numbers soon become quite large. For those with the necessary skills, a very simple computer program can be written to carry out such procedures.

Cross-generation marriages cause some ambiguity because we could place the common ancestors in either of two generations. But if we always place them in the later generation the numerical effect is very simple and is perhaps best illustrated by example. A marriage between 2nd cousins once removed has exactly the same effect as a third cousin marriage (2 + 1= 3). A marriage between 3rd cousins twice removed has the same effect as a 5th cousin marriage (3 + 2 = 5). (A 3rd cousin twice removed is either the grandchild of a 3rd cousin or the 3rd cousin of a grandparent.)

Half-cousins of various degrees are easily dealt with too. (Half 1st cousins share 1 grandparent). Instead of reducing the appropriate generation by 2, we reduce it by 1. So, if you marry your half 3rd cousin, your children will have 31 instead of 32 3g-grandparents.

Before proceeding further let me first reply to the correspondent who asked if I could not produce “popular versions” of the articles for the less numerically minded. Those were the popular versions. I omitted the calculations and gave only results because I did not want to assume any mathematical skills on the part of the reader, but the results were numerical and as such were best expressed numerically. I hoped that the basic ideas would be quite easy to understand especially for genealogists – anyone capable of conducting genealogical research is certainly of well above average intelligence. In this article I have included the above calculations in the hope that this will demystify the numerical aspects of the topic; the calculations really are simple.

Many points were raised in these letters and there was quite a lot of duplication so, rather than deal with the letters individually, I will attempt to present the ideas in some sort of logical order. What follows therefore is due principally to the four gentlemen mentioned above with some input from myself.

One can easily summarise my conclusions in the two articles – Those of us with mostly British ancestors are descended from most of the population of our island as recently as 20 to 25 generations ago, say 1250 to 1400 A.D. The objections fall into two categories; i) because of inbreeding – marriage between persons related possibly many times over – the number of ancestors of each of us is not as large as I postulate ii) the geographical distribution is more restricted than I postulate. The two objections are, of course, related. If our ancestors occupied only a few areas, their numbers would be much smaller and the degree of inbreeding much higher.

Ultimately we, that is the whole human race, are related. According to the latest theories we all descend from a small group of people, most certainly black, who lived in Africa rather more than 100,000 years ago. But that is perhaps 4000 generations ago and has little to do with the present argument. Basically I am saying that most of the population of this island around, say, 1300, whatever its origin, will be a direct ancestor of most of us.

The only alternative to this hypothesis would be that we descend from the entire populations of isolated units of the population, be they hamlets, villages, parishes or whatever, which had been isolated for centuries. Mr Blenkin, whose terminology I have adopted here, thinks it is quite possible that he and I are the descendants of quite separate sets of isolated units, and would therefore be “unrelated”.

If such isolated units remained isolated until the beginning of the industrial revolution when we might have had only around 64 ancestors, and if each isolated unit had consisted of, say, 100 people for many generations. Then we might well have had no more than 6400 ancestors a few generations earlier, and the only 6400 ancestors for centuries before that.

The truth will clearly lie somewhere between the two extreme positions but I feel that it will be very much closer to my postulate. I say this because the idea of completely isolated units is difficult, if not impossible, to justify. Isolated units do occur; take the Amish people of Pennsylvania who number several hundred families and whose entire ancestry can be traced to a few dozen 17th century immigrants. But such units must be extremely rare in the western world and be confined to very strict religious sects. Where on our island could such a unit be found? Even in the 14th century was there ever a hamlet that had no contact with its neighbours? As I tried to show in the second article, if we allow for only a small proportion of children born more than a few kilometres from one or both parents we will inevitably find that over 20 generations or so the ancestors are scattered over much of the country.

The isolated unit theory is contrary to human nature. Very few people are attracted to members of the opposite sex they have known well since early childhood; perhaps it is a sort of extended incest taboo. Girls seem to find the “stranger in town” somehow more exciting than the boring home-grown male. I suspect that young people will always tend to seek a mate from outside their own “unit”. Perhaps someone in a neighbouring village, perhaps someone who has moved into the same village from elsewhere. Every time someone marries a person from outside their own “unit” their children’s pool of ancestors is increased.

Would someone living in a small hamlet in the 14th century ever have the opportunity to meet anyone from outside their community? Of course they would -people often travelled many miles to attend church or the nearest market, to give only the most obvious examples. Furthermore the idea that the population as a whole was static at any period of our history is very far from the truth. Take, for instance, the massive rural depopulation after the sheep-farming boom of the 15th and 16th centuries. Let me quote Dr Alan Rogers, a lecturer in mediaeval and local history: “Throughout the whole of English history, the population of the country has been on the move, drifting over the countryside like slowly moving clouds.” (p12 This Was Their World. BBC Publications. 1972.)

Certainly we will find branches of our families which seem to have remained more or less static for several generations. Mr Robson has attempted to trace all the ancestors of a 3g-grandfather throughout the 18th century and says he has yet to find one born more than a few miles from Haltwhistle. The obvious rejoinder would be that the ones he has yet to find are quite likely to have been born more than a few miles from Haltwhistle otherwise he would probably have found them. After all, knowing where to look is 90% of the task.

Sorry if that sounds facetious, but it is a valid point. Early in my own researches I looked for the ancestors of my g-grandmother, Margaret Philipson, who was born in Allendale Parish in 1870. At first it seemed as if her ancestors had always lived in the area because I found all of her male Philipson ancestors and most of the others, right back to c.1700, in the parish registers. Of the rest, those born in neighbouring parishes took longer to find, and those born elsewhere are yet to be located – how, for instance, do I proceed from “Ann daughter of William MacMillan of Scotland”? Furthermore, the originator of the male Philipson line in Allendale, Francis (c1700-1786), was apparently born in Stanhope and it looks as though his line may have had its origins in Cumberland. In fact, judging by the occurrence of surnames, very few of the “Allendale” families, which joined with the Philipsons and with each other to produce my g-grandmother, were present in Allendale before 1700.

The idea of Allendale as an isolated unit is a fallacy. It was simply a good place to live while the lead mines provided ample work and excellent social amenities. Many came into the area; few had reason to leave. But the lead mining boom barely lasted 200 years – just seven generations. Admittedly, during this period the degree of inbreeding was quite high, but it certainly was not an isolated unit; there was a lot of outside influence too.

One of the few groups of people who come anywhere near being an isolated unit are the aristocracy who rarely marry outside their “class”. But we are not only talking about marriage. Am I wrong in supposing that many masters sought to extend the duties of their female domestic staff. And then there is the “Lady Chatterley syndrome”. No doubt many a “noble” line has greatly benefited from the inclusion of some less than noble blood.

And while on the subject of illegitimacy; I believe it may be another mechanism for widening the distribution of our ancestors. Who was father to the child of “Mary Smith Singlewoman”? Was he a local lad? Most likely, yes. But, as I suggested above, the “stranger in town” can be quite appealing and, if he is just passing through, he is unlikely to worry about the consequences; he won’t be around when they arise. Even when a local lad is “blamed”, he may not be the true father. Blood-group studies in New York State and Sweden have shown that more than half of alleged fathers could not be the true fathers. Perhaps the girls were selecting the wealthiest or the most attractive gentleman from the list of their more intimate male acquaintances. Certainly they would choose someone who was still around. What girl would be keen to admit to a brief affair with a man she hardly knew and who was not available to marry or to support the child?

Look what happened in World War 2. How many girls had children to our G.I. allies? And it was not just the Americans; men from all parts of the country and many parts of Europe were stationed in large numbers all over the country. They were usually miles from home and the normal social restraints – parents, local gossip etc – were missing or, indeed, reversed. The result was inevitable. It wasn’t even restricted to our allies. There was a P.O.W. camp in the small mining village where I spent my early years and three local girls somehow contrived to give their eldest children German fathers! Conversely, we may speculate as to the possibility of our having half-brothers or sisters, for instance, in any of the places where our fathers were stationed!

Few periods of our history have been free of war – two World Wars, the Jacobite troubles, the Civil War and the Scottish Wars. How often did we find armies, friendly or otherwise, encamped in or passing through the North East? In 1314 King Edward II’s army of 92,000 men assembled in and around Newcastle prior to Bannockburn. In 1297 the Scots destroyed Corbridge, Ryton and Hexham; I need not detail the fate of many women in the area – even the nuns of Lambley did not escape the invaders’ attentions. What affect did such events have on the distribution of our ancestors?

Sometimes the Scottish forces included French and this brings us to a point raised by Mr Squire. He believes that I should not have restricted my arguments to this island because of the large numbers of immigrants over the centuries -merchants, fishermen, skilled workers (Flemish weavers, German miners, Irish navvies) adventurers, economic refugees and the persecuted (Jews, Huguenots).

He points out that if the numbers were small they may well have merged into the population leaving little cultural mark. Larger numbers might have tended to form mutually supportive communities which retained their culture (c.f. Chinese and other Asians today), but even these would inevitably have merged over the centuries. I completely agree with Mr Squire, but it would be very difficult to quantify the consequences.

Finally, let me return to the effect of multiple distant relationships between couples. Mr Robson and Mr Squire think that I oversimplified the problem by considering the effects of say “all marriages between second cousins” when, in the real world, we are more likely to find marriages between couples who are more distantly related many times over. I did simplify the problem, there is no other way of dealing with such complex issues. I quoted the effects of “all second-cousin” marriages as an extreme example which would reduce the numbers of ancestors to a much greater extent than any real situation. It would, for example, reduce the numbers of 6g-grandparents from 256 to 108; my information on that generation is far from complete but my 6g- grandparents number between 222 and 246, probably much closer to the higher figure.

I accept that every couple will be related distantly many times over but not to anything like the extent necessary to limit the number or distribution of our ancestors significantly – it would only affect the timing. As we go back through the generations the number and distribution of ancestors will always increase until they cannot increase further. That limitation occurs when the ancestry encompasses the whole population. In earlier generations we would expect the number of ancestors to follow the population size. On a small island in the middle of the Pacific or in an exclusive religious community the limit would be reached quite quickly and the degree of inbreeding would be high. In this country the limit would be reached about 20 to 25 generations ago. Or should we go further afield still and consider early immigrants too?. I wonder when our ancestry comprised most of the population of Europe.

© Brian Pears 1991, 1998, 2006