A Yudkowsky post of November 4th, 2007 tried to argue mathematically that there could be at most 25MB of meaningful information (or thereabouts) in the human genome, but computer simulations failed to bear out the mathematical argument. It does seem probably that evolution has some kind of speed limit and complexity bound - eminent evolutionary biologists seem to believe it, and in fact the Genome Project discovered only 25,000 genes in the human genome - but this particular math may not be the correct argument.
The first lemma of Yudkowsky's argument was the idea that if, say, 2 parents have 16 children, and on average only 2 of those children survive, then 1 out of 8 children survive, which corresponds to 3 bits of information-theoretical information. This part of the argument is taken from R. P. Worden's paper A Speed Limit For Evolution1 but would not seem to agree with the computer simulation in question, so it is possible that Worden imposed additional conditions (or perhaps the paper itself is wrong). According to Worden's paper, this is an evolutionary limit on the whole species - if the average surviving child is part of a litter of 16, then the 3-bit bound on information accumulated is not per couple but for the species as a whole. In general Worden speaks of a species accumulating at most O(1) bits of information per generation.
The second lemma of Yudkowsky's argument is a well-known principle known as "one mutation, one death" which states that deleterious mutations (and the vast majority of mutations are deleterious) cause an equal number of deaths in the gene pool, whether the mutation is very harmful to an individual or only slightly harmful. At equilibrium, deleterious mutations must be eliminated from the gene pool at the same rate they are introduced: each event in which a copying error creates a mutation, must be eliminated by an extra death of an individual bearing that mutation. If a mutation is only very slightly deleterious - if it only kills one out of ten thousand bearers, say (or prevents one out of ten thousand children from being born) - then the mutation will spread farther before causing the deaths that prevent the mutation from spreading further. (This is a very disheartening Malthusian principle in general; if you invent glasses to make nearsightedness less dangerous, then more people will become nearsighted and the total danger will go back up.)
From the "one mutation, one death" lemma, Yudkowsky argued that each meaningful DNA base would require around the same amount of selection pressure to support its continued existence. Worden calculates a selection pressure of O(1) bits per generation in mammals, and the mutation rate in mammals is 10^-8 errors per base per generation. From this, Yudkowsky argued that at most 10^8 DNA bases = 25 megabytes of meaningful information, could be sustained by mammalian evolution against the degenerative pressure of mutation.
The idea of an upper bound on the sustainable information in a genome, and that mammals are already at this upper bound and have probably been there for tens of millions of years if not longer, is not original to Yudkowsky; it is found for example in George Williams's Adaptation and Natural Selection
Although the actual