There are a number of very serious problems with mutation rates that call the theory of evolution into question. It has taken me a long time to appreciate the magnitude of these problems. These problems with mutation rates do not seem to be appreciated by most biologists, and even the creationist sources I have read do not seem to comprehend the seriousness of the problems posed for the theory of evolution by the rates of mutation observed and assumed for evolution. I would encourage those among you who are taking biology courses to present this material to your instructors and see if they can give you an adequate answer to it. If there are any mistakes in this article, please inform me of them (email@example.com).
The general situation is that rates of mutation high enough to account for the ape-human split would lead to the rapid death of the species. Even rates of mutation often quoted by biologists would do the same. A lower rate of mutation would make the assumed evolution of apes and humans from a common ancestor impossible. If the rate of mutation really is high, then the human race must be very young and on the way to extinction. Whether one believes in evolution or not, the issue of how high the mutation rate is should be of interest to anyone concerned for the future of humanity.
First, I present some very general and simple results from
population genetics. For a justification of these results, see the
article Population Genetics Made Simple at
this web site, or any text on population genetics. A more
detailed and technical discussion of the assumptions behind these
calculations can be found in the article Effects of Redundancy on Mutation Rates.
Equilibrium is defined as the state at which the fraction of the population having harmful mutations is constant. This state should eventually be reached if conditions are more or less unchanging. The first result we need to know is simple and very surprising -- when a population is at equilibrium, then the chance that a gamete (egg or sperm) will have a new, harmful mutation not possessed by the parents as gametes is smaller than the chance that a zygote (fertilized egg) will die without offspring. It doesn't matter whether the mutation is dominant or recessive or how harmful the mutation is, since less harmful mutations will spread to more of the population. It's not necessarily the zygotes that have the harmful mutations that are unable to reproduce, but the rate of harmful mutation still influences the chances of not reproducing as stated above. Put another way, the chance that a zygote can survive and have offspring is less than the chance that a gamete has no new harmful mutations, when the population is at equilibrium.
In fact, one should really consider the mutations in the zygote, rather than the egg or sperm, according to (Proc. Natl. Acad. Sci. USA Vol. 94, pp. 8380-8386, August 1997), which states that the great majority of mutations are partially dominant and that this has a larger effect on zygote survival than the recessive part. This roughly doubles the number of mutations and means that all the figures below should be squared. So if a survival rate of (1/e)2 is given below, it should really be (1/e)4, making the difficulty much more extreme.
The next point is that equilibrium should nearly be reached in a few hundred generations. If the human population is not at equilibrium, then it must be very young (less than a few hundred generations) and created perfect or nearly perfect, without harmful mutations. The calculation of the time to equilibrium is sketched in the article on population genetics at this web site.
Later we will argue that most harmful single-gene mutations will at least come to the birth. In any species, individuals that are not able to reproduce will still require pregnancy and nurture, will consume food and occupy territory, and possibly compete for mates. In addition to not being able to reproduce, these individuals will make it more difficult for the remaining population to survive. Their genetic defects will be of many different kinds and will appear at many different stages of life. If a species has a considerable fraction (say, half) of individuals with such defects, it would appear that the species could hardly survive due to the added burden.
It is reasonable to assume that individuals with such defects not only cannot survive themselves, but also result in other individuals not being able to reproduce. So we can assume (say) that for every ten such individuals, one other individual becomes unable to reproduce. This means that if 10/11 of the population is defective in this way, then the population will die out no matter how many offspring each parent has.
Now, suppose there is one new harmful mutation per gamete, on the average. Then it follows that the chance of a gamete being free from a new, harmful mutation is 1/(2.718), or about 37 percent. This means that at equilibrium, only 1/(2.718) of the zygotes can become reproducing adults. Of the remaining 63 percent of the individuals, more than half will probably come to birth (as we argue below), meaning that there will likely be more defective births than defect-free births. Even this seems like an unbearable rate of mutation, especially for higher organisms such as mammals which must care for their young and have a limited number of pregnancies. And there are other causes of mortality in addition to single-gene genetic defects.
If there are three non-neutral mutations per zygote for humans (a rate quoted on talk.origins), they are all most probably harmful, leading to only 1/(2.718)1.5 of the zygotes that can reproduce. This is only about 22 percent. This would imply that only about a fourth of all babies would be able to survive to reproduce, since single-gene mutations are likely to come to birth.
Now, about 10 percent of DNA is typically assumed to code for genes, and the rest is mostly non-functional. A mutation to the functional DNA will change the amino acid more than 2/3 of the time, and if it does, the mutation will be harmful about 9/10 of the time or more (according to estimates by biologists). The fact that silent sites vary between organisms about 5 times as much as replacement sites implies by simple population genetics that at least 4/5 of the substitutions at replacement sites must be harmful. Furthermore, some proteins (fibrinogen peptide) vary about twice as much as silent sites, implying that about half of the substitutions at silent sites are harmful, by evolutionary assumptions. This in turn implies that 9/10 of the substitutions at replacement sites are harmful. So we see that there is not much room for altering this 9/10 figure. Thus we can assume that 2/3 of the point mutations to functional DNA are harmful. The non-functional DNA changes at the same rate as that at which mutations occur.
From standard reference materials, such as the on-line
Encyclopedia Britannica at
http://www.eb.com:180/, observed mutation rates in humans appear
to be between .5 and 4 per 100,000 gametes (sperm or eggs). However,
there is a lot of variation from gene to gene, and males seem to
mutate a lot faster than females. The average is about one per
100,000 gametes among living organisms, but may be considerably
higher. For humans, the average is about four per 100,000 gametes,
according to one source. This would lead to eight mutations per
zygote (fertilized egg) on the average, at 100,000 genes in the human.
This would mean that at equilibrium, only about
1/(2.718)8/3 or about 7 percent of the zygotes could
develop into reproducing individuals. This would imply that probably
about a tenth of the babies at most could grow up and reproduce, at
This can only be reconciled with reality by assuming that the human race is only a few hundred generations old at most, initially defect-free, or that the harmful mutations are clustered in a few individuals who are very unlikely to have surviving offspring. In the latter case, the number of effective mutations available for evolution would be much smaller.
The talk.origins site mentions a rate of evolution for silent
sites at 4.61 per billion years. (See also Mol Biol Evol 1985
March; 2(2):150-174.) It is reasonable to assume that this is due to
point mutations at this rate, since silent sites are essentially
neutral (not changing the amino acid coded). However, sometimes
silent sites are conserved for other reasons, implying that the rate
of mutation could be higher. Mammals typically have genomes of at
least 1.5 billion base pairs, and assuming 10 percent of this is
functional, there would be 150 million base pairs of functional DNA.
Assuming a mutation per base pair every 200 million years (4.61 per
billion years), this means 150 million point mutations in the
functional DNA and at least 100 million harmful mutations every 200
million years, since 2/3 of the mutations are harmful. This is a
harmful mutation every other year on the average. Fibrinogen peptide
mutates about once every 100 million years, meaning a harmful mutation
every year on the average. Thus each gamete would have one harmful
mutation per year of generation time. With a one year generation
time, this would be an intolerable rate of mutation, as mentioned
above (only 37 percent of the zygotes could have offspring). This is
even worse for organisms that have longer generation times. If one
assumes that the rate of mutation slowed down for these latter
organisms, then it had to be even higher for the earlier ones.
A rate of 10-9 substitutions per base pair year for humans and apes is assumed in (Evolution of the primate lineage leading to modern humans: Phylogenetic and demographic inferences from DNA sequences, PNAS 1997 94: pp. 4811-4815 by Naoyuki Takahata and Yoko Satta). This amounts to 2 * 10 -8 substitutions per base pair per generation, assuming a 20 year generation time. The same mutation rate is given in (Science, 6 Jan. 1995 pp. 35-36). Based on this rate, they concluded that ``the human ancestral lineage became distinct from the NWM 57.5 million years (Myr) ago, the OWM 31 Myr ago, the gorilla 8.0 Myr ago, and the chimpanzee 4.5 Myr ago." If the true rate of substitution were 10 times smaller, then these age estimates would be 10 times larger, with the divergence from NWM (new world monkeys) at 575 million years ago. So there is not much room for change in the substitution rate, by evolutionary assumptions. However, the true rate would have to be about twice as large, on evolutionary assumptions, since silent sites also appear to be about half conserved. This implies 4 * 10 -8 substitutions per base pair per generation, and an extremely high death rate. A mutation rate of 2 * 10 -8 per generation was inferred by Kondrashov, A. S., 1988, "Deleterious mutations and the evolution of sexual reproduction," Nature, Vol. 336, December 1, pp. 435-440, supported by some direct observational evidence. This is the rate of change per generation, so the copying errors could be even more frequent.
The following facts are obtainable from standard reference
materials, such as the on-line Encyclopedia Britannica:
15 - 20 percent of diagnosed pregnancies miscarry. Up to 60 percent are due to faulty chromosomes. This includes all miscarriages after the first two weeks of pregnancy. Before that, one can only speculate. It is thought that more than 60 percent of conceptions are spontaneously aborted, including spontaneous abortions during the first two weeks. 40 to 50 percent of spontaneous abortions have chromosomal abnormalities. 3 to 4 percent of newborns have birth defects. At least half have a genetic contribution. About 7 percent of all births show some mental or physical defect. Genetic defects (often minor) are present in 10 percent of adults.
The fertilized egg implants in the uterus on about the seventh day. It then causes hCG to be produced, which prevents menstruation. Cells in the fetus begin to differentiate after about the first week. After four weeks, only very primitive arms, eyes, legs, lungs, brain, and heart (mostly just stubs) appear. After about two months the fetus' organs begin to function, but not fully till after birth.
Now, we attempt to analyze the above data. Only a small percentage of genes are expressed in eggs and sperm and during the first two weeks of pregnancy. So the percentage of single-gene genetic defects causing abortions then should be very small. Later, about 15 to 20 percent of pregnancies miscarry, and this can be caused by chromosomal abnormalities and other causes. Counting birth defects and adults with defects, some of which are minor and do not prevent reproduction, there should be about 5 percent of adults that cannot reproduce due to single-gene genetic defects.
Since the womb is such a sheltered environment, and the fetus will likely survive if it develops a heart and circulatory system, one would expect most individuals with single gene defects to at least be born. For example, frog embryos have recently been produced lacking heads, and this is also claimed to be possible for humans. (See Science, vol. 278, 31 October 1997, page 798.) This means that at most 5 percent of zygotes will be aborted due to harmful single-gene mutations. So it is reasonable to estimate the total percentage of zygotes that cannot reproduce due to point mutations at about 10 percent and possibly much less. It would seem difficult to stretch the figures to make this more than about 30 percent in any event.
Therefore, based on genetic defects, the rate of harmful single-gene mutations in humans can be at most about 10 percent per gamete per generation, possibly 20 or 30 percent per gamete at the most. This conflicts sharply with the rate of 3 or 4 mutations per generation that is often quoted. It conflicts even more with 4.61 mutations per billion years, which would imply 15 per gamete per generation, with only an astronomically small portion surviving to reproduce. This seems to imply that the human race is young and not yet at equilibrium.
It is important to remember that females produce about one egg per month for about 30 years, about 360 in all. During their most fertile periods, they can often become pregnant a few months after a previous pregnancy ends. This implies that the percentage of zygotes that can, if fertilized, survive until birth is at least 10 percent and probably much higher, including the effects of all kinds of genetic defects, even those that affect many genes.
Now, apes and humans are thought to have split about 5 million
years ago, according to a number of sources, and have about a 2
percent difference in DNA. The human genome has about 3 billion base
pairs and about 300 million base pairs of functional DNA (assuming 10
percent of 3 billion base pairs are functional). Assuming that most
of this 2 percent change is non-functional DNA, this implies a rate of
evolution of two percent in 10 million years, which implies 6 million
point mutations in 10 million years in the functional DNA. Two-thirds
of these would be harmful, or, 4 million in 10 million years. This is
about two point mutations in the functional DNA every five years, or
about 12 every generation. Counting both parents, this gives 24
mutations per zygote, with a chance of only 1/(2.718 12 )
(less than 1 in 100,000) that a zygote will survive and be able to
have offspring at equilibrium. Of course, this is ridiculous.
How much must we reduce the functional DNA to make this acceptable? It would have to be at least a factor of 12, to about 25 million base pairs (less than one percent of the DNA). This would imply one harmful mutation per zygote, and would contradict estimates that 10 percent of the DNA is functional. Typical genes have 1000 base pairs, so this would be 25,000 genes. Even this rate of mutation is much too high, so there would probably have to be only about 15,000 genes. A typical cell has over 10,000 proteins, so this is about the number of genes needed for a single cell. So this is too few to specify a complete human being. It also conflicts with estimates that humans have 100,000 genes.
How long ago would apes and humans have to split to allow evolution to have occurred? It would have to be 12 times 5 million years, or 60 million years. Even this is too high a mutation rate, as mentioned earlier. And at the rate of about 5 percent of gametes having a harmful mutation, it would have to be about one billion years. If the mutation rate was faster in the past, one wonders why it slowed down.
We might assume the ape-human split occurred 10 million years ago, that the functional DNA is only about 100 million base pairs, and that the ape (chimpanzeee) human difference is only one percent. This would reduce the mutation rate by a factor of 12, to one harmful mutation per generation. Even this is fairly high, implying only 1/e of the zygotes can survive due to mortality caused by single gene defects, and contradicts a number of sources.
It is interesting that a recent study has shown that mitochondrial DNA in humans mutates 20 times faster than previously thought, which would give rise to the current 3 percent difference in mitochondrial DNA among humans in about 6000 years. See Parsons, Thomas J., et al., A high observed substitution rate in the human mitochondrial DNA control region, Nature Genetics vol. 15, April 1997, pp. 363-367. The article is summarized in the article about mitochondrial DNA mutation rates at this web site. Chimpanzees and humans differ by 27 percent in their silent sites in mitochondrial DNA, nine times as much as humans differ from each other. (See also Proc. Natl. Acad. Sci. USA 1995 Jan 17;92(2):532-536 which has a higher estimate.) At the current mutation rate of mitochondrial DNA, this would imply that the ape-human split occurred about 9*6000 or 54,000 years ago. This is about 90 times shorter than the 5 million year figure, leading to a rate of harmful mutations 90 times faster, and zygote survival rates of at most 1/(2.718 12*90 ) or less than 1/(2.718 1000 ) assuming a 2 percent difference between humans and apes, and 1/(2.718 12*90*5 ) or 1/(2.718 5400 ) assuming a 10 percent difference.
Another possibility is that the rate of mutation really is very low, and that the divergence in DNA is due to a few mutations that change many base pairs (such as inversions or copyings). This seems unlikely, but we will soon know from DNA sequencing. Methods of measuring DNA similarity, based on chopping up the DNA into small pieces, would be likely not to detect inversions and copyings, in any event, so this 2 percent difference is most likely due to point mutations or small insertions and deletions. Furthermore, inversions and recombination errors are not likely to occur in non-functional DNA, since they require the repetition of a sequence, which is unlikely in non-functional DNA, randomized by mutations. This poses a severe problem for the theory of evolution. Also, if the divergence in silent sites in nuclear DNA between apes and humans is at least about 2 percent, which seems likely, this also implies that such a rate of mutation as computed above did take place, and would seem to be an additional refutation of evolution. And indeed, based on some selected genes, the difference in silent sites between humans and chimpanzees is about 1.6 percent, and for gorillas it is about 1.8 percent. (See Table 3 of ``Evolution of the primate lineage leading to modern humans: Phylogenetic and demographic inferences from DNA sequences,'' PNAS 1997 94 pp. 4811-4815.) If silent sites are conserved about half of the time, this would imply a total difference of at least about 3 percent between humans and chimpanzees. It is interesting that the difference in silent sites in the mitochondrial DNA between humans and apes is 27 percent, a significant fraction. Mitochondrial DNA is thought to mutate about 6 to 17 times faster than nuclear DNA, implying a 2 or 3 percent difference in the silent sites. Some sources say 3 to 5 times as fast, implying about a 6 percent difference in the silent sites.
Actually, there is good reason to believe that the difference between chimpanzees and human DNA is about 4 percent rather than 2 percent. (See http://www.geocities.com/Heartland/7547/quikfact.html.) About half of the DNA is in the form of repetitive sequences (see Science, vol. 278, 24 Oct. 1997, p. 613) , which must have some function or else they would long ago have been destroyed by random mutations. Since this part of the DNA probably would evolve much more slowly than the non-functional DNA, we would expect about an 8 percent difference in the non-functional DNA between humans and chimpanzees in order to make the total come out to 4 percent. One source even says that typical genes between humans and apes differ by 10 percent. An 8 percent difference would make the rates of survival per zygote about 1/(2.718 48 ) or worse. This is less than 10 -20.
We are not even counting point mutations and small insertions and
deletions to the repetitive DNA. Recombination errors to the
repetitive DNA are common, but these only change the number of units
of repetition. Since this DNA seems to resist point mutations, it
must be that point mutations to it are harmful, and are therefore
eliminated from the population. Such point mutations may affect the
ability of the cell to divide, or the ability of the DNA to wind
around nucleosomes, or something similar, and so will not necessarily
come to birth. Such mutations would probably be dominant, also. The
repetitive DNA is about half of the DNA (see Science, vol. 278, 24
Oct. 1997, p. 613), which would increase the rate of harmful mutation
by a factor of 5 (going from 10 percent to 50 percent functional DNA)
and by a factor of 3/2 (since there do not appear to be any ``silent
sites'' in the repetitive DNA, as variations from one repetition to
the next are typically extremely rare). Based on the ape-human split,
this would imply a zygote survival rate of at most about 1/(2.718
48 * 5 * (3/2) ), or 1/(2.718 360 ). This
assumes an 8 percent difference in the DNA; for a 2 percent
difference, the rate of zygote survival would be at most 1/(2.718
90 ). There are also grounds for thinking that mutations
to this part of the DNA would be dominant, which would reduce the
survival rates to 1/(2.718 720 ) or, for a 2 percent
difference, 1/(2.718 180 ). Even if these mutations were
expressed and eliminated in the germ line, as discussed below, the
rates would be too high at equilibrium.
The rate of mutation has been directly observed for one gene (for hemophilia B), and it is about 3 * 10-9 per base pair per gamete, but I don't know if this is for males or females. (See Am J Hum Genet 1990 Aug;47(2):202-217) Apart from any considerations of the ape-human split, this rate would, based on the repetitive DNA, lead to 4.5 harmful mutations per gamete, and a zygote survival rate of at most 1/(2.718 4.5 ), or about one percent. If the mutations to repetitive DNA are dominant, which seems likely, it would be at most 1/(2.718 9 ), or about one in 10,000. These rates would quickly cause the death of the human race, since a female only produces about 400 eggs. This also seems to imply that the human race is young and not yet at equilibrium, and that these mutations to the repetitive DNA have a small selective disadvantage, which causes them to take longer to come to equilibrium. It is also possible that mutations to the repetitive DNA cause the death of cells in the germ line right away, and are eliminated in this manner. If this is true, then such mutations also probably affect cells in the developing embryo as well. With about 50 cell divisions per generation, this would be about one mutation every 10 cell divisions, or about a 10 percent rate of cell death during the embryonic and fetal phase. To have 10 percent of the cells in an embryo or fetus non-functional seems like an unbearable burden. This could be another evidence that we are not at equilibrium, or else we can assume that these mutations only influence the ability of the zygote to survive. Or it could be that these mutations are occuring mostly in the male line, with as many as 400 cell divisions per generation. This would reduce the cell death rate to about two percent at equilibrium, which seems more reasonable. The female line typically has about 25 cell divisions per generation. However, the problems mentioned above with single-gene mutations remain, since these are not likely to be expressed along the germ line.
I'm not interested in furthering anyone's agenda, but people
do deserve to know the problems with the theory of evolution. I also
don't favor the teaching of religion in public schools. However, the
fact that evolution is taught in tax-supported schools and claimed to
be scientifically supported gives it a greater burden of proof. Some
general references related to the above discussion are (Dev Genet
1994;15(3):205-213; Science, vol. 278 3 Oct 1997 p. 34;
Proc. Natl. Acad. Sci. USA Vol. 94, pp. 3823-3827, April 1997; J Theor
Biol 1995 Aug 21;175(4):583-594; Proc. Natl. Acad. Sci. USA Vol. 94,
pp. 8380-8386, August 1997; Genetics 1996 Jul;143(3):1467-1483;
Kondrashev, A.S., 1988, "Deleterious mutations and the origin of
sexual reproduction," Nature vol. 336 Dec. 1 pp. 435-440).
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