Thursday, 16 July 2015

Ancestor Paradox

'Tree of Doom' Steady Flaxen, this supposed to be a sensible post- arse

Most folk are interested in their antecedents and many have undertaken genealogical research. Are you related to the 17th century Earl of Wessex, or a sheep rustler hanged by the neck until dead? The simple answer is both.

Superficially, at least, how many ancestors you have appears an easy question to answer. Mathematically it represents a simple exponential progression. Thus, you have 2 parents, 4 grandparents, 8 great grandparents and 16 great, great, grandparents and so on..... After 30 generations, which would take us back to the middle of the 11th century, you would have a staggering 1.1 billion distinct ancestors alive in that generation! Just going back one more generation would generate 2.2 billion relatives. The  problem is that the world population of the time is estimated to be in the region of 250 million. Go back 50 generations and you have 1,126,588,362,522,624 ancestors. In this instance, the living ancestors are in the quadrillion- if you don’t believe me do the basic maths yourself.  So something must be seriously awry. But what could that be?

Inbreeding and Circumstance
Inbreeding is generally not practised in polite society. I use inbreeding in the sense of cousins marrying cousins of various relatedness (1st and 2nd etc). However, it is to be acknowledged that certain less
well- developed societies practise 1st cousin marriage as an act of virtue. In today's indigenous English population, 1st cousin marriage is rare, but in the past it was a relatively common. We take our mobility for granted. One hundred and fifty years ago people were more constrained geographically. Most folk walked everywhere and this would limit the individuals they interacted with and eventually married. The majority would find partners within just a few miles from where they were born. Under such circumstance, the chance of meeting a relative of some degree would be relatively high. The presence of 1st cousin marriage in a genealogy reduces the number of ancestors in comparison to the mathematical exponential maximum. If some of your ancestors indulged in first cousin marriage they would share common grandparents. If you don't believe me try drawing out the pedigree plot. I've illustrated an example below. 

Therefore, some of your ancestors are 'duplicates'. I'll consider an exceptional theoretical example and assume that all your ancestors married a 2nd cousin. Instead of having an exponential increase we actually start to see a regression in ancestral numbers. With each generation, we would see a reduction in ancestors by 1/8th. This reduction would accumulate as we progress through the generations until we come to the 30th generation in the 11th century. Here, instead of 1.1 billion mooching relatives, you would have a meagre 4.4 million ancestors alive at that time. This is not a realistic scenario, but I hope it illustrates how we can downplay and deviate from the ridiculously high theoretical maximum. However, even in this extreme example we haven't reduced the number of ancestors enough- 4.4 million people is still far too many. Other models have been proposed which also explain why are ancestral numbers are not impossibly large. They are often based on mathematical manipulations, which for obvious reasons, I will not consider. Professor Robin Fox, in his seminal tome, ‘The Tribal Imagination: Civilisation and the Savage Mind’, contends that about 80% of all marriages, in history, have been between 2nd cousins or closer. What I take this to mean is that not 80% of all matings were between 2nd second cousins but for all practical purposes, the additive ‘cousin’ effect was equivalent. I’m sure you will be able to discern the subtle distinction.

Another point I would like to make concerns population bottle necks and population catastrophe. In the past, there have been population disasters. The 'Black Death' in the Middle Ages is a notable example. During a relatively short period about a third of the population of Europe carked it. Therefore, the pool for breeding would have been significantly diminished. There is even evidence for catastrophic declines in population in pre-history. About 70,000 BC, the explosion of a super-volcano in Sumatra nearly caused humankind to become extinct. The best guess is that, after the event, there were only a few thousand individuals left and subsequent population recovery was very slow. This and other unknown events have taken their toll on our ancestors. 

I hope I’ve convinced you with my rather simple exposition that relentless doubling of your ancestors cannot occur due to ‘inbreeding’ and population 'bottle necks'. There are other factors in the mix but I’m disinclined to elaborate as further discussion becomes technical and burdensome (can't be arsed).

As an aside, I would like to consider the skewing of the data by a very prolific breeder. This concept only applies to men. Women are exempt for sound biological reasons because they are unable to have large numbers of offspring. But for men, the potential is limitless given unlimited access to females. Throughout history, there have been a few powerful men who have exercised this prerogative without restraint and consequently have sired large broods. For instance, Genghis Khan’s Y chromosome can be found in 1 in 200 men alive today. Not only did he have a lot of kids but his sons followed their father's ruthless proclivities.

It is often claimed that many Western Europeans are descended from the great Frankish king of the 8th century, Charlemagne. But before being carried away with our new found regal status it is sobering to note that 99.99% (or greater) of our ancestors were undoubtedly of simple, poor, peasant stock. So if you are tempted to adopt airs and graces, you are well-advised to cast off pretensions and embrace a humble demeanour, as befits your lowly station.

1 comment:

  1. Quite so. I married my 15th cousin!
    See :
    and :