Mutation fixation is an evolutionary process culminating in the loss of polymorphisms, also known as fixed alleles. That is, a locus for which two or more alleles are present within a population is converted, through loss of all but one allele, to a locus at which only a single allele is present within the population. In practice, fixation is not necessarily reduction to just a single allele but instead represents an overwhelming prominence within a population of just one allele at a given locus (e.g., all other alleles present may be maintained there at low levels solely by drift and mutational generation).
The potential for an existing mutation to become fixed is a function of the fitness benefits associated with the mutation, the fitness of competing alleles, and various stochastic processes. Stochastic processes leading to mutation fixation are drift but also selection. Selection that leads to fixation of the most fit allele, of course, is a deterministic rather than stochastic process. Especially in more clonal populations, however, selection results in fixation of the fittest genotype rather than necessarily the fittest allele. Due to this selection acting on genotypes, less fit alleles can become fixed as they hitchhike along with more fit alleles that are found at different loci than the actual allele (or alleles) being selected, a process known as periodic selection (see "Natural Selection"). Drift similarly can give rise to alleles that are fixed, via random processes, for reasons that are more independent of their fitness. All else held constant, fitter alleles have a greater potential to become fixed. A population geneticist's ability to predict which allele will become fixed at a given locus declines, however, as a function of the effective size of a population, that is, as drift overwhelms selection in smaller populations. In clonal populations, the fixation of beneficial mutations can be delayed not only by drift but also by periodic selection as well as by a process known as clonal interference, something we'll get to subsequently.
One can also speak of the fixation rates of mutations, or alleles. That is, how long until a given allele becomes or is expected to become fixed within a population along with the rate at which fixation events occur within a population over all loci. I will not delve further into these rates in an absolute sense, though note that it can be helpful to consider relative rates (Rand, 2008) . Thus, we can expect in general that mutation rates at a given locus will be greater than the rates at which mutations will lead to polymorphisms, since mutations are often lost due to selection or drift while mutations must survive plus increase in frequency before a polymorphism can be declared. Furthermore, we can assume that rates of mutation then polymorphism will be greater than rates of mutation then polymorphism then fixation. Thus for a given allele: Mutation likelihood > mutation then formation of polymorphism likelihood > mutation then polymorphism then fixation likelihood. The likelihood of polymorphism and then fixation also will be greater the greater the fitness benefit supplied by a new mutation and lower the greater the associated detriment. Of many mutations, in other words, few will survive (thereby contributing to a polymorphism) and fewer still will become fixed within a population.
While I speak of fixation of mutations, more properly above I am describing the fixation of alleles. Speaking of "fixation of mutations" is a simply a convenient means of codifying evolutionary progress, that is, the origin, rise, and then fixation of one allele at the expense of one or more other alleles. As these steps imply, one should always keep in mind that in order for a mutation to become fixed it must first be generated. Hence, the first limitation on mutation fixation is its presence in a population, which, as noted, is limited by a combination of population size, mutation rates, and a species' evolutionary history. The latter, also as noted, can be represented in terms of how many mutational steps are necessary to give rise to a specific allele. That is, what degree of constraint, in terms of both strength of selection and mutation rates, that a current genotype imposes on the generation of a given novel genotype (historical contingencies).
The second limitation on the fixation of a mutation, initial survival, will occur at the point of first occurrence of an allele (or genotype). This is because absolute numbers of mutated alleles are initially low at the point of allele generation (i.e., such as equal to one) and therefore the likelihood of allele loss due to stochastic processes (drift) initially will be quite high. A newly generated allele alternatively can increase in frequency due to stochastic processes. An allele's increase in frequency, though and as noted, is more assured if an allele has a selective advantage. This selection acts on genotypes, however, which is different from selection acting instead on individual alleles, meaning that a beneficial allele found in the same genome as a detrimental allele may display a lower potential to survive than if that detrimental allele were not also present. An allele's relative advantage also can be lost via the arrival of additional alleles in competing individuals, alleles giving rise to similar fitnesses, as we will consider in terms of a process known as clonal interference. Once fixed, and even before then, an allele thus can be vulnerable to replacement by additional, newly arising alleles. Alternatively, a population may display a balanced polymorphism at a given locus. A balanced polymorphism by definition is a sustained failure of any one allele to achieve fixation.