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Topic: How big is a family tree? (Read 464 times)
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kob3203
RootsChat Extra
Posts: 94
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I was looking through my notes from a few years ago and found this. I thought it might be worth sharing (apologies if there's already a posting somewhere along these lines - I couldn't find one!)...
Every person has two, exactly two, parents.
So each ancestral generation has twice as many lineal ancestors as the previous generation.
Therefore every person on earth has 2 parents, 4 grandparents, 8 great-grandparents, 16 great-great-grandparents, etc.
Hmmm... this sounds very much like the "grains of rice on a chessboard" problem...
To make the maths easy think very simplistically and assume that each generation lasts exactly 30 years (i.e. both parents are 30 years old when their child is born).
So a child born in 2000 has 2 parents born in 1970 (back one generation), 4 grandparents all born in 1940 (back two generations), 8 great-grandparents all born in 1910 (back three generations), etc...
By 10 generations, 1700CE, you have over a thousand (1,024) great-great-great-great-great-great-great-great-grandparents (great*8-grandparents)
By 14 generations, 1580CE, you have over 10 thousand (16,384) great*12-grandparents
By 17 generations, 1490CE, you have over 100 thousand (131,072) great*15-grandparents
By 20 generations, 1400CE, you have over a million (1,048,576) great*18-grandparents
By 24 generations, 1280CE, you have over 10 million (16,777,216) great*22-grandparents
By 27 generations, 1190CE, you have over 100 million (134,217,728) great*25-grandparents
By 30 generations, 1100CE, you have over a billion (1,073,741,824) great*28-grandparents
This prompts a couple of observations:
Firstly, when somebody claims that they've traced their ancestry back to 1700, then which of the 1,024 great*8-grandparents are they referring to?
Secondly, according to the US Census Bureau (http://www.census.gov/ipc/www/worldhis.html) the world population had been rising gradually from something between 170 million and 400 million at 1AD, and first reached a billion (1,000,000,000) some time between 1750 and 1850.
By my reckoning, this means that the number of individuals in the 28th or 29th generation back exceeded the entire population of planet earth!
This is impossible! But the answer is obvious after a little thought. We're assuming that each ancestor in a particular generation is a discrete, distinct, unique individual. This is not necessarily true. While it might be unusual to see marriages between first cousins, it becomes less unlikely with further degrees of separation.
Pete
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Researching Welsh and Irish family history from SE Asia...
Browne: Mallow, Co. Cork (1895-1935) + Cahir, Co. Tipperary (1860-1895) Purtell: Cahir (1860-1895) Fanning: Cashel (to1886)
Corbett: Mitchelstown, Co. Cork (1860-1935) Sweeney: Mitchelstown (1860-1935)
Griffiths: Llanelly, Carmarthenshire (1837-1934) Reynolds: Llanelly (1837-1901)
Williams: Llanelly (1837-1934) Lewis: Ton Pentre, Glamorganshire (1837-1901)
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Guy Etchells
RootsChat Aristocrat
Posts: 1103
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Yes, it is the age old topic that has been aired many times before.
Normally called pedigree collapse.
Which is why geneticists claim that everyone one earth is no more than 50th cousin apart from everyone else.
However the theory is simply a mathematical theory and has never been proved in the real world.
Cheers
Guy
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Nick29
RootsChat Aristocrat
Posts: 2886
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Well, just a couple of comments......
1. A new generation every 30 years is a possibility, not a certainty. I can go back to the 1700's in just 5 generations (but I am over 60 myself !).
2. The maths falls apart because it doesn't take inter-breeding between families into account. Heck, if you weren't allowed to marry cousins, the royal families of Europe would have died out centuries ago ! 
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Best Wishes, Nick. Research interests: Field - Luton & Islington Hole - Somerset, Suffolk & Surrey Farnish, Parker, Cattermole, Last, Wasp, Church - Suffolk Lewin/Lowin/Lowen - Hertfordhire Martin - Eltham & Greenwich, Kent (London) Stead - Greenwich, London (Kent) & Maidstone Wood - Hertfordshire Census information Crown Copyright, from www.nationalarchives.gov.uk |
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kob3203
RootsChat Extra
Posts: 94
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Thanks, that's the phrase I needed - "pedigree collapse". Obvious once you know it, and difficult to forget, but almost impossible to guess if you don't! Googled it and found http://en.wikipedia.org/wiki/Pedigree_collapse, among others.
Pete
Nick - your comment prompts another thought. If different branches of a tree had widely differing generation gaps but came from the same area, it's possible that members of different generations could intermarry, yes?
Not so much a family tree as a family bowl of spaghetti, eh!
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Researching Welsh and Irish family history from SE Asia...
Browne: Mallow, Co. Cork (1895-1935) + Cahir, Co. Tipperary (1860-1895) Purtell: Cahir (1860-1895) Fanning: Cashel (to1886)
Corbett: Mitchelstown, Co. Cork (1860-1935) Sweeney: Mitchelstown (1860-1935)
Griffiths: Llanelly, Carmarthenshire (1837-1934) Reynolds: Llanelly (1837-1901)
Williams: Llanelly (1837-1934) Lewis: Ton Pentre, Glamorganshire (1837-1901)
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dave448
RootsChat Extra
Posts: 89
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The 30 years is a bit arbitrary, as my grandfather was born in 1867 and his father in 1827, and that's just 4 generations.
I try to complete as much of my pedigree as possible, but some lines are easier to find than others.
I, too, have found plenty of cousins marrying, and second cousins, etc
regards
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maidmarion
RootsChat Senior
Posts: 420
Census information Crown Copyright, from www.nationalarchives.gov.uk
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Hi
I too come from a line of late breeders
4X Gt Grandfather being born 1765 and I'm a snip of a girl being only 40+ 
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aghadowey
Global Moderator
RootsChat Marquessate
Posts: 13610
Census information Crown Copyright, from www.nationalarchives.gov.uk
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It certainly isn't just a matter of so many individual ancestors in each generation and 30 years between each one.
One of my ancestors had a large family and I'm descended from three of his children (and a cousin in that family married a 1st cousin once removed which confuses the generations). Another ancestor married twice and I'm descended from a child from each marriage.
There's 89 years between my husband's birth and his grandfather's birth (and he's the eldest of the grandchildren). Also Eighty-four years between my youngest child and her grandmother. And on it goes...
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LizzieW
RootsChat Marquessate
Posts: 3278
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I've traced many of my ancestors back to mid 1500s, but the furthest back I've got is my paternal g.grandmother's line which has been traced back to my 13th g.g.grandfather who was born abt.1430. I know his parent's names but not when they were born. That is with paperwork etc to prove this.
Sadly, however, on my paternal g.grandfather's line I can get no further back than my paternal g.grandfather and I can't even find his birth in the mid to late 1850s. 
Lizzie
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BENSON- Dalton in Furness (Ulverston) and Hull
BETTISON - Derbys
BOULTON - Dalton-in-Furness and surrounding areas
BRAND - Lincs
COCKETT - Lincs, Yorks, Lancs
DA COSTA (or variants) - Spain or Portugal, London (Middx), ?Hull
GILCHRIST - Scotland, Lincs
HINGLEY - Derbys/Yorks
MANN - Sussex, Kent, Herts
MUMBY - Lincolnshire and Hull
PEMBERTON - Ches, Lancashire
STANTON - Lincs
ROBINSON - Lincs
WHITTAKER/WHITAKER - Ches/Lancs
WRIGHT- Bethnal Green
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aghadowey
Global Moderator
RootsChat Marquessate
Posts: 13610
Census information Crown Copyright, from www.nationalarchives.gov.uk
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I think most of us have that same problem, Lizzie. I can trace parts of my family back to before 1000 AD (although some Royal lineages need to be taken with a grain of salt) but my grandfather's grandfather seems to have appeared from nowhere ands I'll probably never find out more on him.
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