Genetic change over time (evolution) occurs when the assumptions of the Hardy-Weinberg principle are violated. Violations from random mating include inbreeding (mating between relatives) and assortative mating (matings based on similarity or dissimilarity in phenotype). Inbreeding is expressed by the inbreeding coefficient, F. This ranges from 0 (no inbreeding) to 1 (complete inbreeding). The Hardy-Weinberg relationship can be modified to take inbreeding levels into account. This will give the genotype frequencies as AA = p2 ((1-F) + pF , Aa = 2pq(1-F) , and aa = q2 (1-F) + qF. Note that this reduces to the normal formula when F = 0, and that the heterozygote is not present when F = 1. Inbreeding is generally harmful because recessive conditions are increased in frequency. However, for research purposes, inbred lines of mice and plants have been valuable. Inbred crosses (e.g., between corn lines) have been advantageous in agriculture. Assortative mating can occur for traits like height.
Mutation can be a significant force in evolution over long time periods. Most mutations are thought to be neutral or deleterious. Beneficial mutations are thought to be quite rare. If the mutation rate is too high, the frequency of harmful mutations would be increased and this could lead to a higher rate of genetic disease. The level of harmful mutations is sometimes expressed using the term "genetic load".
Migration can lead to rapid changes in allele and genotype frequencies in populations. Genetic markers can be used to monitor this process. Even a low level of migration, over a long time, can make populations uniform in allele frequency.
Selection can lead to both changes in allele frequency and to maintenance of variation. The fitness of an individual, in a genetic sense, refers to their ability to survive and reproduce. Fitness (w) is commonly expressed relative to the most fit genotype. For example, when the most fit type is 1, a genotype with half the survival / reproductive success will have a fitness of 0.5, and a type that consistently fails to reproduce will have a fitness of 0. The selection coefficient (s) is 1 minus the fitness. A situation in which the heterozygote is the most fit type (heterozygote advantage) will maintain both alleles in a population. Some believe that this is a general explanation for how genetic variation is maintained in populations. In humans, sickle cell anemia is a well-studied example of this phenomenon. The heterozygote was more resistant to malaria than either homozygous type. The formula p/q = t/s is used to express the equilibirum frequency to which alleles will tend when the heterozygote is the most fit genotype. This applies where t is the selection coefficient for the homozygous genotype associated with the allele with frequency q, and s is the selection coefficient for the homozygous genotype associated with the allele with frequency p.
In addition to heterozygote advantage, other factors that could be contributing to maintenance of genetic variation in populations could include the neutral nature of many mutations, and the fact that many new mutations may only be deleterious in the homozygous state. Because being homozygous for rare alleles is extremely rare, there would be little selection against such alleles.
Genetic drift can be another factor leading to evolution. This refers to changes in allele frequency in small populations due to sampling effects. When associated with the founding of a new populations, it is referred to as "founder effect".
Mitochondrial DNA can be used to try to reconstruct evolution. This is an aspect of the field of "molecular evolution" .Mitochondrial DNA has advantageous properties for the study of evolution: small circular DNA about 16 kb in size in animals, inherited through the mother, no apparent recombination, DNA sequences change quickly in evolution, multiple copies (100-1000) per cell.
Human mitochondrial sequences have been compared. A tree of relationship of human mitochondrial (mt) DNA sequences has been developed. This tree has some interesting implications for human evolution. Greatest diversity was seen among African samples. Particular types are not exclusively associated with particular racial groups. The tree can be traced back to an apparent common ancestral molecule. The woman who carried this molecule has been referred to as "Mitochndrial Eve". The time since this common ancestor lived has been estimated at 142,500 to 285,000 years. This is based on an average of 95 mt DNA substitutions among the types, and estimates of 1500 to 3000 years per substitution. These estimates are based on the somewhat controversial idea of a "molecular clock" which changes at a fairly steady rate over time.