The rate of molecular evolution considered from the standpoint of population genetics

The rate of amino acid substitutions in the evolution of homologous proteins is remarkably constant. Furthermore, estimated rates of amino acid substitutions based on comparisons of the alpha hemoglobin chains of various mammals with that of the carp are about the same as those based on comparisons of the carp alpha and mammalian beta or the alpha and beta chains in mammals. These uniformities are regarded as evidence for the hypothesis that a majority of amino acid substitutions that occurred in these proteins are the result of random fixation of selectively neutral or nearly neutral mutations. TWO IMPLICATIONS OF THIS POSSIBILITY ARE DISCUSSED: (a) Random gene frequency drift is playing an important role in determining the genetic structure of biological populations and (b) genes in "living fossils" may be expected to have undergone as many DNA base (and therefore amino acid) substitutions as corresponding genes (proteins) in more rapidly evolving species.

Natural selection and gene substitution

Using models which describe the change, by natural selection, of the actual numbers of genes rather than their relative frequencies, it is demonstrated that the equation familiar to geneticists, i.e.dp/dt=sp(1 −p), is appropriate under a wide range of circumstances. It was pointed out that, for realistic treatment of the evolutionary process through which gene substitutions are repeated, the models must have the property such that the total population number remains constant or nearly constant throughout the process, and is not appreciably influenced by the genes being substituted.

The load or cost for a gene substitution was studied assuming a haploid population and the effects on the load of such factors as epistatic gene interaction in fitness, finite population number and slow change of environment were investigated. The load may become very large under a strong ‘reinforcing’ type epistasis between advantageous genes. In a finite population, the load for one gene substitution may be inflated by about unity if the product of the effective population number (Ne) and the selection coefficient (s) is large butNesp0is much smaller than unity, wherep0is the initial gene frequency. On the other hand, slow change of environment may decrease the load somewhat. It was concluded that despite these and other complicating factors, Haldane's original formula, –logep0, for a haploid population (−2 logep0for the case of a diploid without dominance) is still useful for assessing the approximate amount of selective elimination that accompanies the process of gene substitution in evolution.

Genetic variability maintained in a finite population due to mutational production of neutral and nearly neutral isoalleles

1. The average and the effective numbers of alleles maintained in a finite population due to mutational production of neutral isoalleles were studied by mathematical analysis and computer simulation.

2. The exact formula was derived for the effective number (ne) of alleles maintained in a population of effective sizeNe, assuming that there areKpossible allelic states and mutation occurs with equal frequency in all directions. If the number of allelic states is so large that every mutation is to a new, not pre-existing, allele, we havene= 4Neu+1 − 2Neu2, whereuis the mutation rate. Thus, the approximation formula,ne= 4Neu+1, given by Kimura & Crow (1964) is valid as long as 2Neu2≪ 1.

3. The formula for the average number of alleles (na) maintained in a population of actual sizeNand effective sizeNewas derived by using the method of diffusion approximation. If every mutation is to a new, not pre-existing, allele, we obtain

whereM= 4Neu. The average number of alleles as a function ofMandNis listed in Table 1.

4. In order to check the validity of the diffusion approximations, Monte Carlo experiments were carried out using the computer IBM 7090. The experiments showed that the approximations are satisfactory for practical purposes.

5. It is estimated that among the mutations produced by DNA base substitutions, synonymous mutations, that is, those which cause no alterations of amino acids, amount roughly to 0·2–0·3 in vertebrates.Incompletely synonymous mutations, that is, those which lead to substitution of chemically similar amino acids at a different position of the polypeptide chain from the active site and therefore produce almost no phenotypic effects, must be very common. Together with synonymous mutations, they might constitute at least some 40% of all mutations. These considerations suggest that neutral and nearly neutral mutations must be more common than previously considered.