I think MacKay’s “If variation is created by recombination, the population can gain O(G^0.5) bits per generation.” is correct. Here’s my way of thinking about it. Suppose we take two random bit strings of length G, each with G/2-G^0.5 zeros and G/2+G^0.5 ones, randomly mix them twice, then throw away the result has fewer ones. What is the expected number of ones in the surviving mixed string? It’s G/2+G^0.5+O(G^0.5).
Or here’s another way to think about it. Parent A has 100 good (i.e., above average fitness) genes and 100 bad genes. Same with parent B. They reproduce sexually and have 4 children, two with 110 good genes and 90 bad genes, the other two (who do not survive to further reproduce) with 90 good genes and 110 bad genes. Now in one generation they’ve managed to eliminate 10 bad genes instead of just 1.
This seems to imply that the human genome may have much more than 25 MB of information.
I think MacKay’s “If variation is created by recombination, the population can gain O(G^0.5) bits per generation.” is correct. Here’s my way of thinking about it. Suppose we take two random bit strings of length G, each with G/2-G^0.5 zeros and G/2+G^0.5 ones, randomly mix them twice, then throw away the result has fewer ones. What is the expected number of ones in the surviving mixed string? It’s G/2+G^0.5+O(G^0.5).
Or here’s another way to think about it. Parent A has 100 good (i.e., above average fitness) genes and 100 bad genes. Same with parent B. They reproduce sexually and have 4 children, two with 110 good genes and 90 bad genes, the other two (who do not survive to further reproduce) with 90 good genes and 110 bad genes. Now in one generation they’ve managed to eliminate 10 bad genes instead of just 1.
This seems to imply that the human genome may have much more than 25 MB of information.