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Can it be calculated how far back we need go before each of us, with high probability, is descended from everyone then living? Does the question even have an a

Can it be calculated how far back we need go before each of us, with high probability, is descended from everyone then living? Does the question even have an answer?

graham_coop 13y ago
Yes, people have developed simple models to give us some intuition about this question. The first thing to keep in mind is that not everyone at a particular time in the past will leave descendants to the present day. But quite a high proportion of the population will leave descendants to the present day. It's been estimated that around 80% of the population at a given time will. So we can ask how long far do we have to go into the past until we can expect everyone in the population (who left any descendants in the present) to be our genealogical ancestor. Your number of ancestors grows very quickly, k generations you have up to 2^k ancestors (2 parents, 4 grandparents etc). So if our population has N individuals in it, we need to go back log2(N) generations until our number of ancestors is on the order of the population size. So even if our population was made up of a billion people it takes only 30 generations (~1000 years) for us to reach the point where it is likely that you are descended from everyone in the population. What’s happening here is that if we go back far enough everyone in the population (who left descendants) is your ancestor many times over (via various routes back through your family tree). Now this is only an approximation, and this statement has been made more precise by Chang (1998) http://www.stat.yale.edu/~jtc5/papers/Ancestors.pdf http://www.stat.yale.edu/~jtc5/papers/Ancestors.pdf .
- graham_coop 13y ago
  However, in the calculation above we have ignored the fact that populations are structured, i.e. individuals any where in the world are not equally likely to be your parents. This means going back a few generations in the past individuals in your geographic area may be your ancestors, but individuals in geographically remote areas may likely not be. This means that while in a well mixed population (where individuals) move around a lot the above result will hold, in populations where migration is geographically limited it may take far longer for you to be descended from everyone (who left any descendants). However, some individuals within populations do migrate, and so some individuals in the population will have an ancestor in some distant geographic location in the previous generation. You only need to trace part of your family tree back to one of these migrant individuals in order for you to start having ancestors at geographically distant locations. Given the vast numbers of ancestors you have only a small number of generations back, it is quite likely that you trace your ancestry back to many different migrant ancestors. In turn these migrant ancestors quickly themselves have many ancestors further back in time, and so your ancestry quickly spreads around the world. Indeed Rhoades, Olsen, and Chang (2004) estimated under some fairly conservative assumptions about human migration that you might well trace your ancestry to everyone in the the entire world (who left descendants) may be just ~three thousand years ago. See http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureCommonAncestors-Article.pdf http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/Nature...
  - graham_coop 13y ago
    Carl Zimmer has a really nice writeup on this, http://phenomena.nationalgeographic.com/2013/05/07/charlemagnes-dna-and-our-universal-royalty/ http://phenomena.nationalgeographic.com/2013/05/07/charlemag... , where he discusses Chang's result and Peter Ralph and I's paper on this topic http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001555 http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjo...

Can it be calculated how far back we need go before each of us, with high probability, is descended from everyone then living? Does the question even have an answer?

graham_coop 13y ago

Yes, people have developed simple models to give us some intuition about this question. The first thing to keep in mind is that not everyone at a particular time in the past will leave descendants to the present day. But quite a high proportion of the population will leave descendants to the present day. It's been estimated that around 80% of the population at a given time will. So we can ask how long far do we have to go into the past until we can expect everyone in the population (who left any descendants in the present) to be our genealogical ancestor. Your number of ancestors grows very quickly, k generations you have up to 2^k ancestors (2 parents, 4 grandparents etc). So if our population has N individuals in it, we need to go back log2(N) generations until our number of ancestors is on the order of the population size. So even if our population was made up of a billion people it takes only 30 generations (~1000 years) for us to reach the point where it is likely that you are descended from everyone in the population. What’s happening here is that if we go back far enough everyone in the population (who left descendants) is your ancestor many times over (via various routes back through your family tree). Now this is only an approximation, and this statement has been made more precise by Chang (1998) http://www.stat.yale.edu/~jtc5/papers/Ancestors.pdf http://www.stat.yale.edu/~jtc5/papers/Ancestors.pdf .

graham_coop 13y ago
However, in the calculation above we have ignored the fact that populations are structured, i.e. individuals any where in the world are not equally likely to be your parents. This means going back a few generations in the past individuals in your geographic area may be your ancestors, but individuals in geographically remote areas may likely not be. This means that while in a well mixed population (where individuals) move around a lot the above result will hold, in populations where migration is geographically limited it may take far longer for you to be descended from everyone (who left any descendants). However, some individuals within populations do migrate, and so some individuals in the population will have an ancestor in some distant geographic location in the previous generation. You only need to trace part of your family tree back to one of these migrant individuals in order for you to start having ancestors at geographically distant locations. Given the vast numbers of ancestors you have only a small number of generations back, it is quite likely that you trace your ancestry back to many different migrant ancestors. In turn these migrant ancestors quickly themselves have many ancestors further back in time, and so your ancestry quickly spreads around the world. Indeed Rhoades, Olsen, and Chang (2004) estimated under some fairly conservative assumptions about human migration that you might well trace your ancestry to everyone in the the entire world (who left descendants) may be just ~three thousand years ago. See http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureCommonAncestors-Article.pdf http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/Nature...
- graham_coop 13y ago
  Carl Zimmer has a really nice writeup on this, http://phenomena.nationalgeographic.com/2013/05/07/charlemagnes-dna-and-our-universal-royalty/ http://phenomena.nationalgeographic.com/2013/05/07/charlemag... , where he discusses Chang's result and Peter Ralph and I's paper on this topic http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001555 http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjo...