Rate of Information Acquisition by a Species subjected to Natural Selection
David J C MacKay
At what rate, in bits per generation, can the blind watchmaker
cram information into a species by natural selection?
And what is the maximum mutation rate that a species can withstand?
We study
a simple
model of a reproducing population of N individuals with a genome of size
G bits; natural selection selects the
N fittest children at each generation, variation among the children
being produced by mutation or by recombination.
We find striking differences between these two cases:
if variation is produced by mutation, then the maximum rate of
information gain by an entire population is of order
1 bit per generation, whereas if variation is created by
recombination,
information can be gained at a rate proportional
to \sqrt{G}, the square root of the size of the genome.
Furthermore, the maximum mutation rate that can be tolerated
by a species that has recombination
is greater than the maximum mutation rate tolerated
by a non-sexual species by a factor
of order \sqrt{G}.
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