Friday, 27 April 2012

Why Being Related to Diana, Princess of Wales Puts Me No Closer to a Place in Line for the British Throne

Yes, it is true. Diana is my ninth cousin once removed (which is really to say she and my father are ninth cousins).  That makes me 10th cousins with her son Prince William, who is second in line for the Throne after his father Prince Charles. While this sounds impressive to some, it shouldn’t. I’ll show you why.

The Basics: “Nth" Cousins, “X” Times Removed

Let’s start with a few simple definitions and observations that will help keep things straight.

Your 1st cousin is one with whom you share a pair of Grandparents (you have two pair). That is, one of their parents is a sibling of one of your parents.  The pair of common ancestors is two generations back from you.

Your 2nd cousin shares with you one pair out of your four pairs of Great Grandparents. Here, the common ancestors are three generations back.

Your 3rd cousin shares one of your 8 pairs of Great Great Grandparents (or “2nd Great Grandparents”), who are four generations back.

So now you can see the basic rule emerge:
Your “nth” cousin shares with you a pair of common ancestors, Grandparents with “n-1Greats in front of the Grand, who are “n+1” generations back from you.

My 10th cousin Prince William shares with me a pair of 9th Great Grandparents who lived 11 generations ago.  That pair was Jedediah Strong (1637-1733) and his wife Freedom Woodward (1642-1681).

“X times removed” just means you are that many generations down the line from the stated cousin relationship.  If Diana is my father’s 9th cousin, she is my 9th cousin once removed and my daughter Nicky’s 9th cousin 2x removed. Being one generation removed from Diana’s 9th cousin relationship with my father, I am 10th cousins with someone one generation down from her, i.e. Prince William.  And Nicky will be 11th cousins with any children born to Prince William and Kate Middleton, Duchess of Cambridge.

Now that that’s clear, let’s move on….

How Many Great Great etc. Grandparents Does One Have That Far Back?

Simple answer: potentially 1024 pairs (or potentially 2048 individuals). When we talk about first cousins, each has two pairs of grandparents, one pair of which is common to each individual in the cousin group. Second cousins each have 2 x 2 pairs at the level of the common pair.  Third cousins 2 x 2 x 2 = 8 pairs, etc.  For nth cousins, each has 2n pairs of ancestors at the level of the common pair.

So Prince William and I (whom we have already said share one pair of 9th Great Grandparents who lived 11 generations ago) each have 210=1024 pairs of 9th Great Grandparents, and one of my 1024 pairs is the same as one of his 1024.  Unfortunately for my royal aspirations, eligibility for the Throne is contingent upon descent from a different one of his 1024 9th Great Grandparent pairs, one that I do not share (that I know of, yet). That would be Electress Sophia of Hanover (1630-1714) and her husband Ernest Augustus, Elector of Brunswick-L√ľneburg, parents of George I of Great Britain.

Now for a minor adjustment that explains why I said “potentially” 1024. It is likely some of the pairs, in fact many of the pairs, in each group will be duplicates. My Great Grandfather Burpee Tupper married his first cousin Linda Azuba Tupper, which means their common grandparents show up twice in the 16-pair-long list of my 3rd Great Grandparents.  By the time this duplication ripples through my pedigree to the level of 9th Great Grandparents, it is responsible for 64 pairs of my 1024 pairs being duplicates of others in the group. This is the result of just one known overlap. There are undoubtedly many others and they become more likely to occur the further back the tree is constructed.

To calculate the potential size of groups in this exercise, one must assume no inter-marrying between related individuals.

How Many Other 10th Cousins Do Prince William and I Have In Common?

To answer this question one must make an assumption about how many children on average in each family group in each generation go on to have children of their own.  This number varies depending on culture, economic circumstances, child mortality rates and many other things. For the sake of this demonstration I am going to assume that each couple has three children that in turn reproduce.  This number may seem high by modern standards, but one doesn’t have to look back many generations to see families with double digit numbers of children were the norm.

If the original ancestral pair had three children and they each had three, then two generations down the line we have a total pool of 3 x 3 = 9 first cousins. (From the perspective of an individual member of the group that would be one “self” + two siblings + six 1st cousins). In the following generation there are 3 x 3 x 3 = 27 cousins (from the perspective of an individual member: one self, two siblings, six 1st cousins, and the balance of eighteen 2nd cousins). For simplicity’s sake let us just observe that the total number of cousins at a level that includes up to and including “nth” cousins is represented by 3n+1. If we had assumed four children per family we would use 4n+1, etc.

As we have assumed 3 children per family, Prince William and I as 10th cousins could be expected to belong to a group of 10th cousins numbering 310 = 177,147 (but again, from an individual’s perspective a couple of these are siblings, six are 1st cousins, 18 are second cousins, etc.).  To give you a sense of the power of our family size assumption, changing the assumed number of children per family from 3 to 4 pushes the 10th cousin pool size from 144,147 to over 4.1 million. Assuming 5 children per family makes it 48.8 million.  Suddenly being Prince William’s 10th cousin doesn’t seem quite so special.  It is even less special when one remembers that this is not even the “throne-eligible” cousin pool.  Prince William belongs to the Royal group, equally as large, that has descended from Sophia of Hanover.  And he also belongs to possibly over a thousand other equally large groups, each equally as un-royal as the one I share with him.

How Many Total 10th Cousins Might I Have?

The numbers we calculated above represent only the potential 10th cousin pool descending from Jedediah Stong and Freedom Woodward, the one ancestral pair that was common to me and Prince William. But each of us has potentially 1024 such pairs of 9th Great Grandparents.  Therefore with an average of 3 children per family one would have 1024 x 144,147 = 181.4 million cousins just extending out to the 10th cousins (adding more generations, e.g. 11th cousins, 12th cousins, etc. would grow this number exponentially). With a 4 child per family assumption the 10th cousin pool for each of us becomes 4.3 billion, while a 5 child assumption grows it to over 50 billion cousins each. And this is just at our own generation level.  What about when we add in the great many of our parents’ cousins (our cousins once removed) that would still be alive as well as the offspring of our many cousins who might have children of their own already? Now we’re easily into the realm of over 100 billion living cousins each! The entire population of the planet is estimated to be just over 7 billion. What is going on here?

The Grand False Assumption

The reason our calculation unrealistically brings us to many multiples of the total population of the Earth is that we made a whopper of a false assumption right at the start. We assumed “no inter-marrying between related individuals”. In fact for all practical purposes, virtually all marriages are between related individuals! By the time one looks back just ten or eleven generations the overlapping of tree branches is overwhelming and comprehensive.  If one has thorough information available one can find a connection to just about anyone.  Certainly 10 or eleven generations is enough to connect virtually any two persons of European descent, i.e. most of the population of Europe, North American, Australia and large parts of South America.  Just the living descendants of your many pairs of 9th Great Grandparents may number in the hundreds of millions.

Yes, I am related to Diana, Princess of Wales. But so are you. The difference is I have found enough information to connect a line of dots between her and me. There are likely many more possible connecting-dot-routes from me to the Princess.  And likely many routes connecting you to her, and you to me, and you to any one of my neighbours and quite possibly to everyone I’ve ever met.

So unless some cataclysm renders me the last person on Earth, I think I am unlikely to ever lay claim to the British throne.  But just in case, I plan to start working on establishing a legitimate line of descent from Electress Sophia.

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