While some scientists had hinted that maybe neutral mutations were widespread, like Sueoka (1962), a coherent theory of neutral evolution was first formalized by Motoo Kimura in 1968, followed quickly by Jack L. King and Thomas H. Jukes' provocative article, "Non-Darwinian Evolution" (1969).
According to Kimura, when one compares the genomes of existing species, the vast majority of molecular differences are selectively "neutral." That is, the molecular changes represented by these differences do not influence the fitness of the individual organism. As a result, the theory regards these genomic features as neither subject to, nor explicable by, natural selection. This view is based in part on the degenerate genetic code, in which sequences of three nucleotides (codons) may differ and yet encode the same amino acid (GCC and GCA both encode alanine, for example). Consequently, many potential single-nucleotide changes are in effect "silent" or "unexpressed" (see synonymous or silent substitution). Such changes are presumed to have little or no biological effect. However, it should be noted that the original theory was based on the consistency in rates of amino acid changes, and hypothesized that the majority of those changes too were neutral.
A second assertion or hypothesis of the neutral theory is that most evolutionary change is the result of genetic drift acting on neutral alleles. A new allele arises typically through the spontaneous mutation of a single nucleotide within the sequence of a gene. In single-celled organisms, such an event immediately contributes a new allele to the population, and this allele is subject to drift. In sexually reproducing multicellular organisms, the nucleotide substitution must arise within one of the many sex cells that an individual carries. Then only if that sex cell participates in the genesis of an embryo and offspring does the mutation contribute a new allele to the population. Neutral substitutions create new neutral alleles.
Through drift, these new alleles may become more common within the population. They may subsequently be lost, or in rare cases they may become "fixed"--meaning that their substitution becomes a 'permanent' feature of the population.
According to the mathematics of drift, when looking between divergent populations, most of the single-nucleotide differences can be assumed to have accumulated at the same rate as individuals with mutations are born. This latter rate, it has been argued, is predictable from the error rate of the enzymes that carry out DNA replication--enzymes that have been well studied and are highly conserved across all species. Thus, the neutral theory is the foundation of the molecular clock technique, which evolutionary molecular biologists use to measure how much time has passed since species diverged from a common ancestor. While the mutation rate is not considered to be constant, diverse and more sophisticated clock techniques have emerged.
A heated debate arose on the initial publication of Kimura's theory, in which discussion largely revolved around the relative percentages of alleles that are "neutral" versus "non-neutral" in any given genome. Contrary to the perception of many onlookers, the debate was not about whether or not natural selection acts at all. Kimura argued that molecular evolution is dominated by selectively neutral evolution, but at the phenotypic level changes in characters were probably dominated by natural selection rather than sampling drift (Provine 1991).
After flirting with the idea that slightly deleterious mutations might be quite common (Ohta, 1973), Tomoko Ohta, Kimura's student, made an important generalisation of the neutral theory by including the concept of "near-neutrality" (Ohta, 1992, 2002), that is, genes that are affected mostly by drift or mostly by selection depending on the effective size of a breeding population. The neutralist-selectionist quarrel has since cooled, yet the question of the relative percentages of neutral and non-neutral alleles remains. Graur & Li (2000), go as far as to say; "There are only two predictions we are willing to make about the future of molecular evolution. The first concerns old controversies. Issues such as the neutralist-selectionist controversy or the antiquity of introns, will continue to be debated with varying degrees of ferocity, and roars of "The Neutral Theory Is Dead" and "Long Live the Neutral Theory" will continue to reverberate, sometimes in the title of a single article."
As of the early 2000s, the neutral theory is widely used as a "null model" for so-called null hypothesis testing. Researchers typically apply such a test when they already have an estimate of the amount of time that has passed since two species or lineages diverged--for example, from radiocarbon dating at fossil excavation sites, or from historical records in the case of human families. The test compares the actual number of differences between two sequences and the number that the neutral theory predicts given the independently estimated divergence time. If the actual number of differences is much less than the prediction, the null hypothesis has failed, and researchers may reasonably assume that selection has acted on the sequences in question. Thus such tests contribute to the ongoing investigation into the extent to which molecular evolution is neutral (Leigh 2007).