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In principle, the function of major histocompatibility complex (MHC) molecules is simple: to bind a peptide and engage a T cell. In practice, placing this function within the context of the immune response begs questions of population biology; How does the immune response emerge from the interactions among populations of peptides, T cells and MHC molecules? Within a population of vertebrates, how does MHC polymorphism stamp individuality on the response? Does polymorphism confer differential advantages in responding to parasites? How are the pressures on the MHC reflected in turnover of alleles? The role of mutation, recombination, selection, and drift in the generation and maintenance of MHC class 1 polymorphism are considered.

A new model of invitational production of alleles was proposed which may be appropriate to estimate the number of electrophoretically detectable alleles maintained in a finite population. The model assumes that the entire allelic states are expressed by integers (...,A_ 1 ,A 0 ,A 1 , ...) and that if an allele changes state by mutation the change occurs in such a way that it moves either one step in the positive direction or one step in the negative direction (see also Fig. 1). It was shown that for this model the ' effective' number of selectively neutral alleles maintained in a population of the effective size N e under mutation rate v per generation is given by When 4:N e v is small, this differs little from the conventional formula by Kimura & Crow, i.e. n e = l+4ZV e «, but it gives a much smaller estimate than this when 4:N e v is large.

A mathematical theory is developed that enables us to derive a formula for the equilibrium distribution of allelic frequencies in a finite population when selectively neutral alleles are produced in stepwise fashion (stepwise mutation model). It is shown that the stepwise mutation model has a remarkable property that distinguishes it from the conventional infinite-allele model (Kimura-Crow model): as the population size increases indefinitely while the product of the effective population size and the mutation rate is kept at a fixed value, the mean number of different alleles contained in the population rapidly reaches a plateau which is not much larger than the effective number of alleles (reciprocal of homozygosity). Since we proposed (1, 2) the stepwise mutation model in population genetics, a number of papers have been published treating the model in various biological and mathematical contexts (see ref. 3 for a list of such papers). In its original form, the model assumes that the entire sequence of allelic states can be expressed by integers (. . . , A-,1, A, A1, .. .), and that, if an allele changes state by mutation, it moves either one step in the positive direction or one step in the negative direction in the allele space. Let v be the mutation rate per locus per generation, and assume that the mutational changes toward the positive and negative directions occur with equal frequencies (see Fig. 1). We are particularly concerned with the level of genetic variability and the pattern of allelic distribution at equilibrium that may be attained in a finite population when each gene is subjected to such a mutational change in addition to being subjected to random extinction and multiplication due to random sampling of gametes in reproduction.In one of our previous papers (4)

The following five principles were deduced from the accumulated evidence on molecular evolution and theoretical considerations of the population dynamics of mutant substitutions: (i) Recent development of molecular genetics has added a new dimension to the studies of evolution. Its impact is comparable to that of Mendelism and cytogenetics in the past. Accumulated evidence suggests (1-8) that, as causes of evolutionary changes at the molecular (genie) level, mutational pressure and random gene frequency drift in Mendelian populations play a much more important role than the orthodox view of neo-Darwinism could lead us to believe.In the present paper, we intend to enumerate some basic principles that have emerged from recent evolutionary studies of informational macromolecules. Of these, the first four are empirical, while the last one, which is theoretical, enables us to interpret the four empirical principles in a unified way.(i) For each protein, the rate of evolution in terms of amino acid substitutions is approximately constant per year per site for various lines, as long as the function and tertiary structure of the molecule remain essentially unaltered. In their influential paper on the evolution of "informational macromolecules,"