Where Are the Mutations?

Where Are the Mutations?

Jan. 2, 2002


When writing an article on protein evolution, I suddenly realized that commonly occurring mutations cannot explain evolution. I had been conditioned into thinking that with enough time and large enough populations, evolution would become more likely. But even with large populations and millions of years, there are not enough mutations to drive evolution. Only rare and improbable mutations could possibly explain evolution, but this possibility rests on faith, because such mutations are so rarely seen. Furthermore, it is not valid to extrapolate from the small changes seen in organisms today, to the large changes required by the theory of evolution, because these large changes are fundamentally different in nature. The small changes seen today are either not due to mutations at all, but to selection among alleles, or else are caused by mutations that cannot explain evolution in the large.

This distinction is due to some simple mathematics. Consider a typical gene that has 1000 base pairs of coding DNA, or, about 333 amino acids. How many substitutions of one base pair for another are there that will cause a change in an amino acid? There are 3000 substitutions altogether (1000 bases and each one can be replaced by three others), but most of the ones in the third codon position will not have an effect; of the 333 third codon positions, about half do not permit a change in the amino acid, and half do, for about 167 total substititions that will change the amino acid. So the total number of substitutions that change the amino acid is about 2,167. Generally less than one mutation in a thousand is beneficial, so that about two of these substitutions will be beneficial, and probably less. It won't take a large population or a long time for these two substitution to occur, and when they occur enough times, they should spread through the population. Then evolution of this gene by substitutions will reach a dead end.

If one assumes that after each mutation occurs, the probabilities that the remaining substitutions are beneficial, are again randomly assigned (which is unlikely), then there will be about two beneficial substitutions after the first beneficial mutation. Even under this generous assumption, evolution will not get very far. The chance that there will not be any beneficial substitutions is about (999/1000)2167 or about 0.114. This means that the expected number of times this process can repeat before a dead end, is about 8 or 9. Then evolution of this gene will stop.

Deletions of DNA will almost certainly be harmful unless the number of bases deleted is a multiple of three. How many ways can three bases be deleted? There are less than 1000 ways, so this possibility should lead to at most one beneficial deletion, on the average, and probably much less, since deletions are likely to be harmful. The same is true of insertions, except that there are more of them. There are about 64,000 ways that three base pairs can be inserted adjacently into a gene of 1000 base pairs. If one counts insertions at a codon boundary, then there are about 333 such boundaries, and each insertion can lead to 20 amino acids, for about 6660 such insertions total. This would probably permit at most 6 or 7 beneficial insertions and probably not nearly this many. If one counts insertions within a codon, then two amino acids can be affected, and this can happen in at most 64 * 666 ways, for a total of under 43,000 additional mutations, of which probably many fewer than 43 will be beneficial, and then evolution will be blocked.

If one considers insertions and deletions of more than three base pairs, but still a multiple of three, then there are more possibilities to consider, and evolution might be able to progress farther. But since such mutations are so rare, and large insertions and deletions are so much less likely to be beneficial than small ones, such beneficial mutations are virtually never observed. Thus the assertion that such mutations explain evolution is a statement based on faith, not evidence. Also, this assertion is not an extrapolation from the kinds of beneficial or neutral mutations observed to cause minor changes in existing species. The same comments apply to larger scale mutations such as those caused by transposons or gene duplications or other large scale changes.

There may be more neutral mutations than beneficial ones, and these can cause a species to change with time by genetic drift, but this is not likely to have much of an effect on the species, because these mutations are neutral. Therefore this process cannot explain evolution, either.

If the environment changes, then some mutations may become beneficial that were not so previously, but even this is unlikely, because most of the function of a gene is determined by basic biology, and not directly by the environment.

So how is one to explain a large scale change, such as fish developing legs and crawling out of the water? With two beneficial substitutions per gene, after which evolution reaches a dead end, how are the complex interactions going to develop that will result in the development of legs and lungs? It is an apparent impossibility.

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