General Resources

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The pages below are a general collection of information we have found useful, informative, or just plain fun, while researching Our Family records. More will be added from time to time.

Our Ancestors - Conceptions, Misconceptions and a Paradox

We found this series of articles while browsing genealogy sites on the internet. They provide a fascinating insight into the complexities of our historical relationships - and raise some interesting questions. We are grateful to the author, Brian Pears, for the opportunity to reproduce his work here.

You will need to get yourself sitting comfortably though - its a long read!!

 

Our Ancestors, Conceptions, Misconceptions and a Paradox

by Brian Pears

This article was written primarily for UK readers in 1985. At that time the then Bishop of Durham , David Jenkins, was causing a great deal of controversy by questioning some basic Christian beliefs - hence the references to previous occupants of that position. Prince Andrew was also in the news because of his "friendship" with a young lady called Koo Stark - but nobody noticed that joke even then. BP


Do you ever wonder what part your distant ancestors played in the events we read about in history books? I do, frequently. In fact I find it almost impossible to read of past events without such speculation. Did any of my ancestors patrol Hadrian's Wall or gaze across the North Sea at the approaching Vikings or fight against the Normans or die of the plague?

Of course there is no chance whatsoever of even identifying such remote forebears never mind documenting particular episodes in their lives, but still it's fun to speculate.

There are those who do claim genealogies extending to the Norman Conquest or earlier, often on the flimsiest of evidence, but I am always very sceptical of such claims. The male line, which is almost always the one traced, is of necessity the least certain. Just one act of infidelity on the part of the wife of any member of this line and the line could be severed. There is always room for doubt about the identity of a father, never, or hardly ever, about the mother. The male line, which contains the most fathers, must therefore be the least certain. And more generally, in any line, the more males the less certainty. Even our own paltry efforts spanning only a handful of generations must be looked at with a certain caution. Just because a certain pink piece of paper purchased at considerable expense from St. Catherine's House states that great-great-grandfather was so-and-so does not guarantee that he was. Great-great-grandfather might be the proverbial milkman. Only great-great-grandmother would know - and she wouldn't be telling, would she? Such uncertainties and the chance of simple error, increase with every generation, so what price a claimed descent from that Norman knight or Saxon Earl? Stark truths perhaps, but we may be sure that even the well attested and much published Royal pedigrees contain an "error" or two here and there.

At this point I suspect that many readers will be looking rather closely at their father's photograph on the sideboard, so perhaps I'd better change the subject quickly. Suppose you could trace your ancestry to some specific person who lived say a thousand years ago (a nobleman of course, it always seems to be a nobleman, doesn't it?). So what? Well, you might say, that person has contributed a certain proportion of his "blood" to me, a part, albeit a small part, of my physical makeup perhaps even of my character must come from him. If you are mathematically inclined you might even feel you could calculate just what that proportion is. But you couldn't, you know! There is no way such a calculation could be done. His contribution to you could well be absolutely nothing at all.

"Nonsense", I hear you say, but it is true. Let us come much closer to home. What proportion of your makeup, your genes to be more scientific, came from say your paternal grandmother? That's easy, a quarter of course. Wrong! You don't know. All you can say for certain is that half of your genes came from each of your parents. Of course they each got half of their genes from their parents, but the point is that your parents effectively mix the genes that they inherited before passing them on to you. Suppose your father's parents had genes ABCD and EFGH and your mother's parents had genes IJKL and MNOP (we really have tens of thousands of genes, not just four). Your father might then have genes AFCH and your mother IJOP, and you could well inherit IJCH. Everyone has inherited half their parents' genes, but look where your genes have come from. One of your grandparents has contributed precisely nothing.

In practice it is extremely unlikely that an ancestor as close as a grandparent would have contributed none of his tens of thousands of genes to you, but you certainly cannot say that each grandparent provided a quarter. There is just no way of knowing what their contribution was. So if you ever hear anyone say, "I'm a quarter Tahitian and three-quarters Eskimo", you can reply, "Says who?". With every generation the uncertainty grows as does the probability that any given ancestor's contribution was precisely zero. In another sense however there is something we owe to each and every one of our ancestors in equal measure - our very existence. For without all of them we would not be here.

Thinking of our ancestors in the dim and distant past raises the question of numbers. Let us go back about 900 years to the time when a certain Bishop of Durham upset his flock and was brutally cut to pieces by the inhabitants of Gateshead . How many of our forefathers were around then? It's a simple calculation! We all have two parents, four grandparents, eight great-grandparents and so on. The number just doubles at every step. But how many generations will fit into 900 years? How long is one generation for that matter? I can only take an average value, of course, and in the absence of more general figures I will use data on 60 or so of my own ancestors. My "average ancestor" was born to parents aged 30.4 years, let us say 30 years. With such a generation length we can conclude that around 30 generations have elapsed since the demise of poor Bishop Walcher. So how many ancestors? You won't believe this but, if you start with 1 and double it 30 times, you get the startling figure of 1,073,741,824 ancestors!

One thousand million! I said you wouldn't believe it, and I must admit that there is a certain problem with this figure. Although the population of our island at that time is not known very accurately it has been estimated as being between 1.5 and 2.5 million, and that of our entire planet as being rather less than 100 million. So where were our missing ancestors? Perhaps I'm being too ambitious. Let us move forward to 1385, 600 years or 20 generations ago, when, coincidentally, the then Bishop of Durham was having problems in Gateshead too. This time however it was only a legal battle with Newcastle Corporation over ownership of the Tyne Bridge and shipping rights on the river.

Does this calculation give more credible figures? It does, but only just. It seems that 20 generations ago we would expect some 1,048,576 ancestors. At this time the population is estimated to have been about four million. Enough people, but can I really believe that while Bishop Fordham fought to regain his third of the bridge, one quarter of the entire population of the country were my ancestors? Of course not. If I believed that I would have to believe that everyone was my ancestor less than two generations earlier!

I would imagine that many of you will already believe you have hit upon the solution to this paradox? You will probably be saying to yourself something like "People marry relatives from time to time and the progeny of these unions will have fewer ancestors than the simple doubling procedure would suggest. Everyone has some such marriages in their ancestry and their cumulative effect is to reduce the expected number of ancestors considerably". Indeed this is the explanation usually given, but does it really resolve the problem? It would if we followed the practice of the Pharaohs who usually married their sisters (this was to resolve the problem referred to earlier; even if their wives were unfaithful the "Royal blood" was still passed on). If everyone married a brother or sister then the number of ancestors in every generation would be exactly two. The problem would also be resolved if everyone married a first cousin, for then the number of ancestors would only increase by two with every generation instead of doubling (60 ancestors 30 generations ago). But if we are talking about anything less than first-cousin marriages all round then the paradox is far from resolved.

I'm certain that incredulity will be the order of the day once again. Surely the effect of second-cousin marriages can't be that much less than that of first-cousin marriages. It can. If every single marriage was between second cousins then 30 generations ago we would all have needed exactly 4,356,616 ancestors. Incredible isn't it? Even if all marriage partners in every generation were second cousins there would not be enough people around to be our ancestors just 30 generations ago. Marriages between third, fourth and more distant cousins have progressively less effect on the number of ancestors. In fact this effect is so small by the time we reach fifth-cousin marriages that we might as well regard the partners as unrelated.

Returning to reality. In this country about six in every thousand marriages are between first cousins and about one in every thousand are between second cousins. The effect of these proportions of such marriages on the number of ancestors is absolutely negligible (1,031,082 ancestors 20 generations ago instead of the 1,048,576 obtained by the doubling procedure). Perhaps cousin marriages were more common in the past. Once more I'll look at an extreme case. If out of every ten marriages, one was between first cousins and the remaining nine were between second cousins, we would run out of ancestors within 30 generations (30 generation figure: 2,910,160). No one would believe anything like such high proportions of first and second-cousin marriages of course. So do marriages between relatives resolve the paradox? Decidedly not.

What is the alternative? Well I'm afraid that we are forced to a seemingly absurd conclusion, one that I touched upon earlier and rejected. With any credible proportions of marriages between relatives of various degrees, the number of ancestors in any generation will be little different from that obtained by our simple doubling scheme. So each of us must indeed descend, from virtually the whole population of the country in the not too distant past. I would estimate that it could be as recent as 1300, just 23 generations ago. I'd better repeat that, if only to convince myself. We, each and every one of us, must descend from almost everyone who was alive on this island in 1300. (But probably not from the then Bishop of Durham who, predictably, was having a spot of bother, this time with his "convent"). In earlier generations almost everyone would be our ancestor too, but most would head not one, but many lines of descent to each of us.

Surely this is all a little fanciful, there must be a flaw in the argument somewhere. Well if there is I haven't found it. One suggested formula is perhaps worth mentioning. Could it be that most marriage partners are distantly related many times over, and these multiple relationships together reduce the required number of ancestors significantly. A nice idea, but it doesn't work, as I will illustrate by mentioning the remarkable pedigree of my great-grandmother Margaret Pears nee Philipson. What was remarkable was that both of her parents, and three of her grandparents were also born with the surname Philipson. Her paternal grandparents were first cousins and her parents were both third cousins and second cousins once removed. There can't be many folks whose ancestors were more interrelated than Margaret's, yet the net effect of her much convoluted pedigree is virtually identical to the case of a single second-cousin marriage. ("virtually" because the concept of generation breaks down when there are cross-generation marriages). Even if everyone had a pedigree like Margaret's, my proposition would still be valid, but it would apply to circa 1100 instead of 1300.

By way of a final corroboration, let us look at the problem from the opposite end as it were. Instead of asking how many ancestors we should have, let us ask how many descendants a typical citizen of 1300 might have today. For family size I'll use the present average of 2.2, although this is certainly an underestimate for all but the last 60 years or so. How many descendants would he have today if his children, grandchildren and so on for 23 generations all had 2.2 children? The answer: 75,114,133 people in generation 23, plus of course the survivors of generations 21 and 22. In other words, all of us - with a few left over for the colonies. What applies to my "typical citizen", would equally well apply to virtually anyone alive in 1300. Perhaps we should all put a few British history books beside our family history papers, since everything and everyone in them, up to the reign of the first Edward at least, will be as much a part of our family history as great-grandfather's last will and testament. The implications are quite staggering. I said earlier that we owe our very existence to all our ancestors. Just think what could have happened if just one more soldier had died in some ancient battle or if some Viking had done just a little more looting instead of ravishing, or even if someone somewhere had decided to have just one more headache!

© Brian Pears 1985, 1997, 1998, 2006

I would like to thank my former colleagues, Mr Len Hudson and Mr John Proud, for respectively checking the sums and drawing the cartoon. Also my first cousin twice removed, the late Mr William Nicholas Philipson, who did much of the work on the Philipson pedigree, and my third cousin, Miss Ann Lee, for the use of her computer - it was much better than mine! BP

The Ancestor Paradox Revisited

by Brian Pears

The previous article dealt primarily with what might be called "the paradox of the missing ancestors":- We have two parents, four grandparents, eight great-grandparents and so on; the number simply doubles with every generation. The trouble is that this doubling procedure soon gives improbable results. Just 22 generations ago we would all have had just over 4 million ancestors. Now that would be around 1300 (allowing 30 years per generation) when the population was also about 4 million. Can we possibly believe that virtually everyone alive at that time was an ancestor of each and every one of us and, furthermore, that most members of earlier generations must head not one, but several, lines of descent to each of us?

Eventually and reluctantly I concluded that we must indeed accept this somewhat astounding assertion but only after I had thoroughly tested and rejected the usual explanation of the phenomenon - that occasional marriages between relatives reduce the required number of ancestors to more acceptable levels. They do not! As I stated in the original article, even if every marriage in every generation was between second cousins, a quite unbelievable situation, we would still run out of people to be our ancestors within 29 generations, say 1100.

To be honest I did not really believe it myself, although I could find no flaws in the arguments, and I expected to be inundated with correspondence from demographers and mathematicians among the readership pointing out my errors. My expectation was not fulfilled; I received only one letter and that related to the earlier part of the article concerning the uncertainties inherent in tracing the male line. Did everyone accept that we do indeed descend from the whole population around 1300? Did nobody find this as incredible as I did? Or had I expressed myself so badly that nobody had understood what I was trying to say.

Since the article appeared I have discussed it in detail with many friends and colleagues in an attempt to understand the problem more fully. As a result a few new ideas emerged. The first - mobility, or rather the lack of it before, say, the industrial revolution of the late eighteenth century - seemed to be a major threat to the origin conclusion. Basically the idea is that until fairly recent times people did not move around the country to any great extent. We might well find that our immediate ancestors came from quite widely scattered locations. but we will then find that earlier generations will almost all originate from the vicinities of those same few locations. If this is true then perhaps all we can say is that we descend from the entire populations of a few distinct areas.

So, to use my own family as an illustration, I have great-great- grandparents who were born in St Petersburg, Norwich, Plymouth and Callington (Cornwall) and twelve who were born "locally" - within 50 Km of Newcastle. My information on previous generations is far from complete but I know of only one born outside these areas and he came from Scotland . So I cannot refute the objection, perhaps it is true that most of my ancestors came from these places.

Looking at early parish registers seems to confirm the view that people did not move very far. Marriage partners were usually "both of this parish" and most of the remainder would involve one partner from a neighbouring parish. Very few involved partners from more remote areas and they were nearly always from the wealthier sections of the community.

Assuming that this was generally true, how would it affect the geographical distribution of our ancestors? Would it really mean that all our forebears were born in a few parts of the country? There is no way to be sure but there is a way to form an impression - mathematical modelling. This is a very useful and widely used technique which can test out the likely consequences of hypotheses affecting the real world when the general rules can, at least, be estimated. Normally the technique is used to predict the future - perhaps global weather pattern changes - but in this case it is used to guess at a possible distribution of ancestors around the year 1300 which could have resulted in the known distribution of certain of their descendants. All such models need two basic ingredients; the initial conditions - or, in this case, the final conditions - and a rule which will enable the next - or, rather the previous - set of conditions to be determined. Here the "initial" conditions are the birthplaces of my great-great-grandparents (excluding the Russian), and the "rule" is a guess at the spread of distances between the birthplaces of one generation and the previous one.

Birth of g-g-Grandparents

Blanchland Rookhope Allenheads
Sparty Lea Wolsingham Satley
Kenton Ninebanks Birtley
Lambton Lanchester Windy Nook
Plymouth Callington Norwich

Distance-Proportion

0 Km 5 percent
3 Km (2 miles) 30 percent
9 Km (6 miles) 30 percent
15 Km (9 miles) 20 percent
30 Km (19 miles) 10 percent
60 Km (37 miles) 5 percent

The distance/proportion table is necessarily somewhat arbitrary but it is based loosely on an analysis of a small sample (530) of eighteenth century baptismal records which fortuitously gave the parents' birthplaces. The very occasional larger distances - as much as 235 Km in one case - were ignored, so the table is certainly on the conservative side.

Having fixed these parameters we can calculate a possible birthplace for a parent of any particular ancestor by randomly choosing one of the distances from the table (in such a way that there is a 5 percent chance of it being O Km, a 30 percent chance of it being 3 Km and so on) and a random bearing (direction) between 0 and 359 , then plotting the position at the chosen distance and bearing from the ancestor's birthplace. If this is done twice for each of the 15 great- grandparents we will have 30 possible birthplaces for the members of the previous generation. We can repeat the whole process for any required number of generations; at each stage we start with the birthplaces of one generation and end up with the birthplaces of the previous one.

In theory this could be done by hand but it would be a tedious and time consuming exercise; with a small computer it is easy and quick. Locations can be stored as grid references, random choices can be made without resort to picking from a hat and trigonometric calculations take only a few microseconds. To avoid complications minor geographic details such as mountains and other barriers to habitation and movement are ignored; only the Coastline is considered and, if a chosen distance and bearing happen to give a birthplace in the sea, a further random choice is made. The computer programme was designed to automatically work through 17 generations, that is 21 generations back from me, and in doing so it multiplies the original 15 locations to nearly 2 million. After the calculations a map is printed out showing the coastline and the distribution of ancestors in that earliest generation. A dot on this map represents a 3 Km square containing at least one ancestor.

What was the outcome? It was quite surprising. The programme was run several times and, although each run differed in detail as we might expect, every single one showed fairly complete coverage of England and Wales and much of Scotland. Judge for yourself, the example reproduced here is typical.

Of course this in only an idealised model and it cannot be taken too seriously. All it shows, and shows quite conclusively, is that the cumulative effect of several quite small movements - perhaps a girl marrying into the next parish or a family moving into a town from the country - is quite sufficient to ensure that our ancestors 21 generations ago could well have been spread over much of the country.

The next two ideas actually reduce the number of generations needed to reach the point where almost everyone would have to be our ancestor. In previous calculations I have compared the number of ancestors at a given time with the total population, but the population comprises members of perhaps three or four generations. What proportion of the population makes up one generation? A generation is really a rather hazy concept but a little thought will show that what we really need is the number of children born in a thirty year period who will survive to marry and have children themselves.

Although this might seem difficult to quantify, all we have to do is to move forward sixteen years and consider that those aged 16 to 45 constitute a generation. This is fairly easy to estimate. Today rather less than 40 percent of the population are in this age group, in earlier times there was a greater proportion below 16 than there is today - because a quarter or more never reached 16 - but this was more than offset by the much smaller numbers of older people - the average life expectancy for men was only 41 years as recently as 1871. The result was a proportion of about 45 percent in the range 16 to 45 years and this figure was probably valid for many centuries. So perhaps we should compare the number of ancestors with 45 percent of the population rather than all of it. This would bring forward the date when our ancestors comprised most of the population to about 21 generations ago, and I do mean most of the population because if we were descended from this 45 percent we would also be descended from most of the rest because they would also form the previous and next generations.

No, its not as simple as that; there is another complication - some lines will have disappeared. Some people had no children, others had children but no grandchildren and so on. The proportion with no children was reasonably constant until recent years - about 10 percent never married and a further 8 percent married but had no children - 18 percent of a generation whose lines died out immediately. How many more will have died out after one, two or more generations? It can be worked out using elementary probability theory but we need to know the proportions of various family sizes because these clearly affect the chances of anyone leaving descendants. I used figures from the period 1870 and 1879 - before family planning became a factor - and assumed that they applied to previous centuries too. It might be of interest to note that more than half of all families at that time were of 5 or more, and 11 percent were of 11 or more!

The results were surprising. Only 1 percent would have children but no grandchildren and only 0.1 percent (1 in a 1000) would have grandchildren but no great-grandchildren. From the way these proportions are decreasing it will come as no surprise that the chances that anyone had great- grandchildren but no great-great-grandchildren are infinitesimal. Indeed we can conclude that if anyone had children and grandchildren (81 percent of the population) it is virtually certain (99.9 percent chance) that they would have great-grandchildren too and descendants in all later generations. This is no longer true because of much smaller family sizes, in fact more than half of today's population will have no descendants within three generations.

So we no longer have the whole population to compare with the number of ancestors or even 45 percent of it, all we have is 81 percent of 45 percent or 36 percent of the population. On this basis the numbers match about 20 generations ago and a large part of this and earlier generations would have to be our ancestors. Quite amazing isn't it?

© Brian Pears 1991, 1998, 2006

The Ancestor Paradox Yet Again

by Brian Pears

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 Generation

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 percent 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