The Hardy-Weinberg theory of genetic equilibrium predicts that changes in the frequency of genetic alleles and genotypes should result only from external disturbances, as these frequencies should otherwise exist as constants - that is, in equilibrium. (Such disturbances include selective reproduction, genetic mutation, natural selection, genetic drift, and the side-effects of extremely small populations.) Five key assumptions inform this theory: the equilibrium should hold provided that all mating is effectively randomized, that alleles are not altered through genetic mutation, that populations do not migrate or exchange individual reproducing members with other populations of the same species, that the population is extremely large (mathematically speaking, it should be infinite), and that natural selection does not impose a preference for certain alleles or traits over others.
The equilibrium theory aims to explain, ultimately, why some populations evolve new traits while others do not. Effectively, if the assumptions of the theory are satisfied, then the theory predicts the population in question will not experience evolution. In practice, species in nature do not satisfy all of these conditions, and therefore at least some degree of evolution usually occurs.
Genetic equilibrium will not hold - that is to say, genetic changes will occur - if mating is not random. The effects of this are easiest to see in the outcomes of what amounts to long-term human experiments in artificial selection, ranging from goldfish to house pets (dogs and cats) to domesticated livestock. If mating is not random, then - presumably - it is the result of some factor relating to genetics. In this case, genes which favour that factor will gradually be selected out over others, resulting in a change in the frequency of genes in the population. Suggesting that only people with blue eyes should reproduce, for example, will gradually lead to an increase in the proportion of blue-eyed people in the population.
Coupled with the necessity for random mating are two further sub-assumptions: the entire adult or breeding population participates in the mating process, and, on average, all of the breeding pairs produce an equal number of offspring.
NO GENETIC MUTATION
In current evolutionary theory, most new traits ultimately occur because of small genetic mutations. Once a mutation resulting in a new trait has occurred, that new trait will exist to some extent in the population. If at some future date it gains a survival advantage over those who lack the trait, then what began as an isolated mutation can become the dominant characteristic of a population.
Obviously, therefore, an equilibrium likely will not exist if mutations are occurring commonly, because the genetic changes resulting from those mutations may spread throughout the population, altering genetic frequencies.
Sometimes, a species contains a population dispersed over a single region, so that, at least in theory, any one member has a decent chance of mating with any other (thus satisfying the requirement for random mating above). In practice, however, many species contain relatively isolated populations, with occasional migration or changes in membership between them. This process of migration or exchange violates the equilibrium principle for the individual populations, because it has the potential to introduce new genes from the outside.
Like mutation, external introduction of new genes would represent a likely opportunity for genetic frequency to change.
NO NATURAL SELECTION
One final reason that genetic frequency changes would be driven by evolutionary needs would be a change in the external environment, leading some traits to be preferred over others. In order for a genetic equilibrium to exist, however, populations must be living in stable environments in which, given the existing set of genetic possibilities for reproduction, no one particular allele or trait has a clear survival advantage over any other. Where survival advantages exist, those genes will gradually be expressed more than others.
Finally, and perhaps most impossibly, the Hardy-Weinberg equilibrium theory assumes that the population in question is effectively infinite. This is essential because the smaller a population gets, the more likely that one individual or small group will, for various reasons, end up having a disproportionate impact on genetic frequency. To move from the abstract to the particular, this is effectively the reason humans ban incest: an extremely small population, breeding only internally, will often develop genetic changes, and these changes will usually be negative.
This may be seen in certain natural species as well. The near-extinction of the plains buffalo in North America, for example, has resulted in a surviving population which is genetically very fragile, because all current buffalo are genetically descended from an extremely small ancestral population rescued by the Canadian and U.S. governments. Even more bizarrely, perhaps, Tasmanian devils are so genetically identical that they are currently suffering from a contagious tumour, which spreads through contact between stricken animals because their immune systems are unable to recognize other devils' body tissues as foreign. Eventually, the only devils to survive - if any do - will be those with a markedly different genetic makeup.