[ExI] digital resurrection of a genome
Anders Sandberg
anders at aleph.se
Fri Jul 3 08:45:38 UTC 2015
I agree with the previous posters. 25 kids is more than enough to make most of the genome likely to be preserved in the next generation.
...but then there is the second generation. If every generation has 25 kids, fine. (The family reunion may require a major convention city, though).
We can work backward: between you and your ancestor there are N generations. Each generation implies 50% chance of a change in gene. So for a given gene there is just 2^-N chance that it is the same. If there are D descendants, the chance that at least one has the original gene is 1-(1-2^-N)^D. If there are K genes, then the chance that there is at least one copy of each gene among the descendants is (1-(1-2^-N)^D)^K (phew).
Now, that probability declines fast as K increases but is counteracted by D. If you plot the probability as a function of D you will see a sigmoid curve. If you have N=4 and just look for one gene, you need 11 decendants to have 50+% chance of getting it, and 72 to get 99% certainty. For 10 genes, you need 42 descendants for 50% chance and 107 for 99%. For 1000 genes you need 178 descendants for 99%. For 20,000 genes you need 224 descendants.
Wow, that was way smaller than I thought! (of course, I could have messed up the math)
However, as N increases the population needed grows fast (it is after all in the innermost parenthesis). For N=5 you need 457 descendants, N=6 920, N=7 1849, N=8 3705... the number of descendants you need doubles per generation back to the ancestor.
Anders Sandberg, Future of Humanity Institute Philosophy Faculty of Oxford University
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