In modeling the outcome of change in allele frequency in a population in response to selection, we need to know something about (1) the nature and dynamics of the introduction of new alleles via mutation, (2) the interplay of mutation and selection for and against those mutants, and (3) the expression patterns of mutant alleles.  We've discussed the third of these, with respect to whether advantageous alleles are dominant, recessive, or show no dominance.  However, equally or even more important are the factors that account for the presence of new alleles, and the fate of new mutants in the face of selective and nonselective forces.
 
 

One surprising result that came from the first surveys of genetic variability in natural populations was the often large number of alternative alleles present at a given locus.  Lewontin and Hubby (1966) argued that the high levels of polymorphism they observed in allozyme studies of Drosophila could not be explained completely by the action of selection; Kimura and Crow (1964) similarly argued that these levels of polymorphism would create too much segregational load in populations.  Kimura (1968) showed that the rates of fixation of amino acid substitutions in mammals were 100 times higher (1 substitution every 2-3 years) than the maximum expected rate under selection.  In addition, Zuckerkandl and Pauling (1965) observed that the substitution rate in many proteins appeared relatively constant over time, which would not be expected under a selection model. 

Based on this apparently incongruous result, Kimura (1966+) developed the neutral theory of molecular evolution.  Kimura argued that the level of genetic variation present in natural populations could not be maintained by selection (based on their contribution to the individual's fitness).  Rather, he suggested that alternative alleles are usually selectively neutral, which would mean that their frequencies could not be the result of selection. 
 
 

Kimura envisioned polymorphism to be a balance between the generation of new alleles via mutation and the random extinction (or fixation) of alleles through genetic drift.  Under this model, polymorphism is transient and stochastic, and differences in allele frequency among populations need not be adaptive.  Certainly some alleles do confer a fitness benefit and are subject to selection.  The neutral theory argues only that the majority of alleles are neutral or nearly neutral. 

The neutral model also implies that, in a diploid species containing 2N alleles, the probability that an allele will become fixed is 1/2N.  Further, if the mutation rate per generation is u, then 2Nu represents the number of new mutants introduced into the population each generation.  Combining these predictions, Kimura argued that the rate at which new mutations become fixed in populations should be equal to (2Nu)(1/2N), which is equal to u.  That is, the rate of change should be constant over time, and independent of both selection and population size.  This leads to the concept of molecular clocks.

Also, ffrom the neutral model we should be able to calculate the equilibrium heterozygosity expected in a population at any one time.  To do this, we need to consider models of how mutations are generated in populations.
 

When we sample genetic variation in natural populations, we can readily estimate the expected heterozygosity for a single locus (assuming the locus is in Hardy-Weinberg equilibrium) as

We can then calculate the multilocus heterozygosity (H) as the mean of the single locus heterozygosities.  But we can also think of h in a different context, as follows: Given the number of possible mutations that can occur in a DNA sequence of a given length, we might assume that each mutational event creates a unique allele.  Conversely, we can assume that if two alleles are identical in state, then they are descendants of a single mutational event (ancestral allele) - identical by descent or autozygous.  These assumptions are the besic tenets of the infinite-alleles model. 

Under this model, homozygous genotypes must consist of two autozygous alleles.  To determine the homozygosity of the population (and by extension the heterozygosity), we need to calculate the probability that two alleles are identical by descent.  From that, we can derive the equilibrium homozygosity to be

Given that this is a measure of homozygosity, we can relate the two equations, giving 

The contrasting model to the neutral theory is the neo-Darwinian model, which arose out of the Modern Synthesis of the 1930s.  Here, any genetic polymorphism observed is assumed to be adaptive.  Thus, in the selectionist view, polymorphism is a balanced and stable consequence of natural selection.  Of course, the underlying assumption is that genetic variants differ in their fitness, providing a fitness gradient among phenotypes upon which selection can act.  The apparent advantage of heterozygosity is a situation that might (or might not) be attributable to a neo-Darwinian model; more likely, the extreme variability mainatined at self-recognition and immune system loci constitute good examples where multiple variant alleles each carry positive fitness consequences.

Nevertheless, a strict adaptationist argument goes even further.  Assume that we begin with a perfectly-adapted population, where each individual is homozygous for a single allele.  Against this background, any new variants introduced by mutation will by definition be deleterious, and thus opposed by selection.  In this case, any polymorphism observed represents the balance between the generation of new alleles via mutation and the purging of those alleles via selection.  This is know as mutation-selection balance, where 

Not that this argument for balancing selection to maintain the maximum possible (but not maximal) adaptedness is not the same as selection for gene substitution or polymorphism (which themselves are adaptive).
 

Regardless of whether mutations are neutral or carry fitness consequences, we still need to look at the interplay of forces behind the dynamics of genetic variation in populations.  Observed mutation rates are underestimates of the actual base substitution rate, but range around 10^-5 to 10^-6 mutants per gamete per generation.  Mutation rates per base per gamete are on the the order of 10^-9.  These rates vary greatly among DNA regions and taxa. 

Neverthless, if we assume a rate of 10-5, we would expect to see one mutant for a given gene out of every 10,000 gametes in a given generation.  Given the number of individual genes, each gamete would be expected to contain at least one new phenotypically detectable mutation.  As such, in a large population, we would expect a large number of new mutants each generation.

Most mutations are deleterious under any scheme and are quickly removed by selection.  In addition, contrary to the views of Goldschmidt, Fisher showed that we would only expect mutations of small phenotypic effect to ever be advantageous.  Nevertheless, there is still a large pool of mutations that should fall in the mildly deleterious to neutral to advantageous range.  Because the mutation pressure is low, and given the potential for back mutation, the rate of change in allele frequency due to mutation alone is low, both in one generation and cumulatively over many generations.  As such, we would never expect a population to reach mutational equilibrium. 
 

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