Abstract
I have already mentioned that there are two major features of molecular evolution, namely “rate constancy” per year and “conservatism” of the modes of change; how can these features be explained by the neutral theory?
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Notes
- 1.
The “infinite allele model” is a model often used to deal with the amount of variation from the standpoint of population genetics, on the assumption that intraspecific variation at the molecular level is neutral with regard to natural selection. It assumes that an infinite number of multiple alleles may exist at one genetic locus, and that whenever a mutation occurs a new allele arises that has never existed before. The motivation for such a model is that, molecularly speaking, a gene comprises many (for example 1000) nucleotide sites, and that, whenever a base changes by mutation, there is a high probability of the change occurring at a different site than before, and that as a result a new allele always arises. Supposing that a gene comprises 1000 nucleotide sites, each of which may be occupied by one of the four kinds of bases, the possible number of alleles is 41000, i.e., about 10602 (in effect an infinite number). Hence, this model applies approximately (this author and J. F. Crow proposed this model in 1964 to deal with variation at the molecular level).
Let us now consider a random mating population, and let its effective number be Ne, and the rate at which neutral mutations arise at a genetic locus per generation be v0. If we assume in this model that the alleles arising by mutation are all either neutral or deleterious, and that the deleterious ones are removed from the population and do not contribute to variation, it can be proved that the average heterozygote frequency per genetic locus at equilibrium is
$$ {\overline{H}}_e=4{N}_e{v}_0/\left(4{N}_e{v}_0+1\right). $$When this formula is compared to k = v0, which gives the evolutionary rate, it can be seen that, under the neutral theory, the evolutionary rate and the heterozygote frequency are almost proportional.
Comparing homologous DNA base sequences at a particular genetic locus obtained from several individuals in a population and treating intra-population variation statistically will in future increase in importance. For this purpose a new mathematical theory called the “genealogical process” of a gene is useful. For readers wishing to know details of this, I recommend the review article by Dr. Naoyuki Takahata that is cited at the end of this book.
References
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Takahata N (1986) Coalescent processes and diffusion processes in population genetics. Math Sci 272:34
Yamao F, Muto A, Kawauchi Y, Iwami M, Iwagami S, Azumi Y, Osawa S (1985) UGA is read as tryptophan in Mycoplasma capricolum. PNAS 82:2306
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Kimura, M. (2020). The Neutral Theory and Molecular Evolution. In: My Thoughts on Biological Evolution. Evolutionary Studies. Springer, Singapore. https://doi.org/10.1007/978-981-15-6165-8_8
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