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Evolutionary Rate at the Molecular Level

b y M O T 0 0 KIMURA National Institute of Genetics,

Japan

Calculating the rate of evolution in terms of nucleotide substitutions seems t o give a value so high that many of the mutations involved must be neutral ones.

COMPARATIVE studies of haemoglobin molecules among change in for a chain consisting of some amino- different groups of animals suggest that, during the acids. For example, by comparing the and chains of evolutionary history of mammals, amino-acid substitution man with those of horse, pig, cattle and rabbit, the has taken place roughly at the rate of one amino-acid figure of one amino-acid change in x was obtained'.

This is roughly equivalent to the rate of one amino-acid substitution in for a chain consisting of amino-acids.

A comparable value has been derived from the study of the haemoglobin of primates. The rate of amino-acid substitution calculated by comparing mammalian and avian cytochrome c (consisting of about 100 amino-acids) turned out to be one replacement in 48 x 106 yr (ref. 3). Also by comparing the amino-acid composition of human triosephosphate dehydrogenase with that of rabbit and

figure of a t least one amino-acid substitution for every X yr can be obtained for the chain con- sisting of about amino-acids. This figure is roughly equivalent to the rate of one amino-acid substitution in

x yr for a chain consisting of amino-acids. Averaging those figures for haemoglobin, cytochrome c and triosephosphate’ dehydrogenase gives an evolutionary rate of approximately one substitution in 28 x 108 yr for a polypeptide chain consisting of 100 amino-acids.

I intend to show that this evolutionary rate, although appearing to be very low for each polypeptide chain of a size of cytochrome c, actually amounts t o a very high rate for the entire genome.

First, the DNA content in each nucleus is roughly the same among different species of mammals such as man, cattle and rat (see, for example, ref. 5 ) . Furthermore, we note that the G-C content of DNA is fairly uniform among mammals, lying roughly within the range of 40-44 per

These two facts suggest that nucleotide substitution played a principal part in mammalian evolution.

I n t h e following calculation, I shall assume that the haploid chromosome complement comprises about 4 x loo nucleotide pairs, which is the number estimated by Muller from the DNA content of human sperm. Each amino-acid is coded by a nucleotide triplet (codon), and so a polypeptide chain of 100 amino-acids corresponds to 300 nucleotide pairs in a genome. Also, amino-acid replacement is the result of nucleotide replacement within a codon. Because roughly 20 per cent of nucleotide replacement caused by mutation is estimated to be synonymous, Chat is, it codes for the same amino-acid, one amino-acid replacement may correspond to about 1.2 bme pair replacements in the genome. The average time taken for one bme pair replacement within a genome is therefore

4 x 10 28 x IO6 yr + (-2) + yr

This means that in t h e evolutionary history of mammals, nucleotide substitution has been so fast that, on average, one nucleotide pair has been substituted in the population roughly every

This figure is in sharp contrast to Haldane’s well known estimate that, in horotelic evolution (standard rate evolution), a, new allele may be substituted in a population roughly every 300 generations. He arrived at this figure by assuming that the cost of natural selection per genera- tion (the substitutional load in my terminology is roughly 0.1, while the total cost for one allelic substitu- tion is about 30. Actually, the calculation of the cost based on Haldane’s formula shows that if new alleles produced by nuoleotide replacement are substituted in R population at the rate of one substitution every 2 yr, then the substitutional load becomes so large that no mammalian species could tolerate it.

Thus the very high rate of nucleotide substitution which I have calculated can only be reconciled with the limit set by the substitutional load by assuming that most mutations produced by nucleotide replacement are almost neutral in natural selection. It can be shown that in a population of effective size if the selective advan- tage of the new allele over the preexisting alleles is then, assuming no dominance, the total load for one gene

substitution is

=

IS J

where and p is the frequency of the new allele at the start. The derivation of the foregoing formula will be published elsewhere. In the expression given here

is the probability of fixation given

= ( 1 e -

Now, in the special case of formulae and ( 2 ) reduce to

Formula (1’) shows that for a nearly neutral mutation the substitutional load can be very low and there will be no limit to the rate of gene substitution in evolution. Furthermore, for such mutant gene, the probability of fixation (that is, the probability by which it will be established in the population) is roughly equal to its initial frequency as shown by equation (2’). This means that new alleles may be produced at the same rate per individual as they are substituted in the population in evolution.

This brings the rather surprising conclusion that in mammals neutral (or nearly neutral) mutations are occurring at the rate of roughly per yr per gamete. Thus, if we take the average length of one generation in the history of mammalian evolution the mutation rate per generation for neutral mutations amounts t o roughly two per gamete and four per zygote x 10-10 per nucleotide site per generation).

Such a high rate of neutral mutations is perhaps not surprising, for M u k a i has demonstrated that in Droso- phila the total mutation rate for “viability polygenes” which on the average depress the fitness by about 2 per cent reaches at least some 35 per cent per gamete. This is a much higher rate than previously considered. The fact that neutral or nearly neutral mutations are occurring a t a rather high rate is compatible with the high frequency of heterozygous loci that has been observed recently by studying protein polymorphism in human and Drosophila populations18-16.

Lewontin and H u b b y estimated that in natural populations of Drosophila psseudoobscura a n average of about 12 per cent of loci in each individual is heterozygous. The corresponding heterozygosity with respect t o nucleo- tide sequence should be much higher. The chemical structure of enzymes used in this study does not seem to be known at present, but in the typical case of esterase-5 the molecular weight was estimated to be about by Narise and H u b b y . I n higher organisms, enzymes with molecular weight of this magnitude seem to be common and usually they are “multimers”17. So, if we assume that each of those enzymes comprises on the average some 1,000 amino-acids (corresponding t o molecular weight of some 120,000), the mutation rate for the corresponding genetic site (consisting of about 3,000 nucleotide pairs) is

U. = 3 X 103 X B X 1.0-10 = 1.5 X 10-6

per generation. The entire genome could produce more than a million of such enzymes.

I n applying this value of zd t o Drosophila i t must bc noted that the mutation rate per nucleotide pair pe: generation can differ in man and Drosophila. There i; some evidence that with respect to the definitely dele terious effects of gene mutation, the rate of mutation pe. nucleotide pair per generation is roughly ten times a; high in Drosophila as in manl8.10, This means that tha corresponding mutation rate for Drosophila should bl U = 1.6 X 1O-6 rather than zc= 1-6 x 10-6. Another con sideration allows us to suppose that u= 1.5 x 10-6 is prob ably appropriate for the neutral mutation rate of e cistron in Drosophila. If we assume that the frequency of occurrence of neutral mutations is about one pel genome per generation (that is, they are roughly two t c three times more frequent than the mutation of the viability polygenes), the mutation rate per nucleotide pair per generation is 1/(2 x loa), because the DNA con tent per genome in Drosophila is about one-twentieth o that of manzo. For a cistron consisting of 3,000 nucleotide pairs, this amounts to u= 1.5 x 10-5.

Kimura and C r o w have shown that .for neutra mutations the probability that an individual is homo. zygous is 1/(4Neu+ I ) , where N e is the effective population number, so that the probability that an individual is heterozygous is H e = 4Neu/(4iVeu+ 1). I n order to attain a t least H e = 0.12, it is necessary that at least N e = 2,300 For a higher heterozygosity such as H = 0.35, N e has t c be about 9,000. This might be a little too large for thc effective number in Drosophila, but with migration between subgroups, heterozygosity of 35 per cent may bc attained even if N e is much smaller for each subgroup.

We return to the problem of total mutation rate From a consideration of the average energy of hydrogen bonds and also from the information on mutation of r I I A gene in phage T,, Watson22 obtained IO-*- lo-9 as the average probability of error in the insertion of a new nucleotide during DNA replication. Because in man the number of cell divisions along the germ line from the fertilized egg t o a gamete is roughly 80, the rate of muta- tion resulting from base replacement according to these figures may be BO x 10-8- S O X 10-0 per nucleotide pair per generation. Thus, with 4 x IO9 nucleotide pairs, the total number of mutations resulting from base replace- ment may amount t o 200- 2,000. This is 100-1,000 times larger than the estimate of 2 per generation and suggests that the mutation rate per nucleotide pair is reduced during evolution by natural selectionl8~19.

Finally, if my chief conclusion is correct, and if the neutral or nearly neutral mutation is being produced in each generation at a much higher rate than has been con- sidered before, then we must recognize the great impor- tance of random genetic drift due t o finite population numberz3 in forming the genetic structure of biological populations. The significance of random genetic drift has been deprecated during the past decade. This attitude 1as been influenced by the opinion a t almost no muta- ions are neutral, and also that th number of individuals forming a species is usually so Iarg f that random sampling )f gametes should be negligdle in iletermining the course )f evolution, except possibly through the “founder prin- : i ~ l e ” ~ * . To emphasize the founder principle but deny h e importance of random genetic drift due to finite population number is, in my opinion, rather similar t o assuming a great flood to explain the formation of deep valleys but rejecting a gradual but long lasting process of erosion by water as insufficient to produce such a result. received December 18,1967. Zuckerkandl, E., and Pauling, L., in Evolvz g &ne8 and Proteins (edit. by

Bryson, V., and Vogel, H. J.), 97 (Acad dip IC Press, New York, 1965). Buettner-Janusch, J., and II111, R. L. in Evolving Genes and Proteins (edit.

Margoliash, E., and Smith, E. L., in Evolving Genes and Proteins (edit. by by Bryson, V., and Vogel, H. J.), Id7 (Academic Press, New York, 1965).

Kaplan, N . O . , in Evolving Genes and Proteins (edit. by Bryson, V., and Bryson, V., and Vogel, H. JJ, 221 (Academic Press, New York, 1905).

S:rgcr, R., and Ryan, F. J., Cell Herdily (John Wiley and Sons, New York, Vogel, H. J,), 243 (Academic Press, New York, 1966).

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% Sueoka, N . , J . M o t . Biol., 8, 31 (1961).

8 Eimura, M., &net. Res. (in the press). 7 Muller, R. J., BuU. Amsr. Math. SOC., 64,137 (1958).

s Haldane, J. B. S., J . Genet., 55,511 (1957). lo Eimura, M., J . Genet., 57,21(1960). 11 Kimura, M., Ann. Math. Stat., 28,882 (1967). 1* Mukai, T.. Genetics, 80, l(1964). I* Harris, X., Proc. Rou. Soc., B, 164, 298 (1900). l 4 Hubby, J. L., and Lewontin, R. C., Genetics, 54,577 (1960). Is Lewontin, R. O., and Hubby, J. L., Genetics, 54,596 (1960). 18 Narise, 8., and Hubby, J. L., Biochim. Biophus. Acta, 122, 281 (1066). l7 Fincham, J. R. S., Uenetic Complenurnlataon (Benjamin, New York, 1906). L B Muller, H. J., in Herfiage from Mendel (edit. by Brink, R. A:), 419 ( V n i -

9 0 Report .of the United Nations ScientiJk Commitlee o n the Eflecle of Atomic 1o Kimura, M., Uenet. Res., 9, 23 (1967).

Rdzation (New York, 1958). EL Kimura. M.. and Crow, J. F., Genetics, 49,725 (1004). pp Watson, J. D., Molecular Biologu ofthe Gene (Benjamitl, New Tork, 1965). pa Wrlght, S., Uenetics,16,97 (1931). alMayr, E., Animal Spec!es and Evolution (Harvard University Press,

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