Mutationism (more appropriately called “mutation-selection theory”) refers to the theory that mutation has a creative power in evolution and genetic variation is caused by discrete elements rather than by continuous variation as proposed by Charles Darwin. Darwin believed that evolution occurs by a slow process of evolutionary change of continuous variation.
The re-discovery of Mendelian genetics challenged Darwin's theory
At the dawn of the 20th century, geneticists learned that discontinuous variations could arise by mutation and be inherited to offspring through stable non-mixing genetic factors. The rules of inheritance of these factors constitute Mendel’s laws. A more important discovery from the evolutionary point of view was that slight variations in quantitative traits emerge every generation but the "fluctuating variations" on which Charles Darwin built his theory were not necessarily inherited. This was shown in a series of breeding experiments by Wilhelm Johannsen. From mixtures of different true-breeding varieties of beans of different sizes, selection could be used to sort out different varieties, but selection within pure lines would not produce evolutionary changes.
This result was interpreted as a threat to the "Natural Selection" theory of Darwin, who argued in The Origin of Species that
"Natural selection can act only by the preservation and accumulation of infinitesimally small inherited modifications, each profitable to the preserved being; and as modern geology has almost banished such views as the excavation of a great valley by a single diluvial wave, so will natural selection, if it be a true principle, banish the belief of the continued creation of new organic beings, or of any great and sudden modification in their structure." (Ch. 4, Origin of Species)
Darwin knew that discontinuous variations or "sports" occurred and that their effects were heritable, but he argued that such changes would not be important in evolution because evolution occurs gradually according to the doctrine of natura non facit salta (see gradualism). In Darwin's theory, infinitesimal hereditary variation arises in response to the effect of "altered conditions of life" on "the sexual organs." Whenever conditions change, adaptation may happen because natural populations were thought to contain all sorts of variations.
Though mutationism is generally associated with Mendelian genetics and genic mutation, the school of thought known today as "mutationism" began in the 1890s (prior to the re-discovery of Mendel’s laws) with the studies of William Bateson  and Hugo De Vries  on naturally occurring discontinuous variations. Their thoughts concerning the role of discontinuity in evolution drew on earlier ideas of William Keith Brooks, Francis Galton, and Thomas Henry Huxley.
The "mutationist" view began by abandoning Darwin's idea of gradual evolution and proposing instead the concept that variation emerges by rare events of mutations. This view was expressed in the writings of key founders of genetics, including Thomas Hunt Morgan, Reginald Punnett, Wilhelm Johannsen, Hugo de Vries, William Bateson and others. The mutationists believed that mutation creates innovative characters and natural selection is a process of preservations of advantageous mutations.
A common misconception is that the mutationists denied selection. Instead, mutationists such as Morgan simply understood its role differently. In the following passage, Morgan (writing in 1916 ) displays a clear understanding of the concept of the probability of fixation of a new mutation, which might be deleterious, neutral, or advantageous:
"If through a mutation a character appears that is neither advantageous nor disadvantageous, but indifferent, the chance that it may become established in the race is extremely small, although by good luck such a thing may occur rarely. It makes no difference whether the character in question is a dominant or a recessive one, the chance of its becoming established is exactly the same. If through a mutation a character appears that has an injurious effect, however slight this may be, it has practically no chance of becoming established. If through a mutation a character appears that has a beneficial influence on the individual, the chance that the individual will survive is increased, not only for itself, but for all of its descendants that come to inherit this character. It is this increase in the number of individuals possessing a particular character, that might have an influence on the course of evolution."
Morgan resisted calling this process "Natural Selection" because it differed so much from Darwin's view. Later Nilsson-Ehle (1909) and East (1910) showed that this is indeed the case with several quantitative characters in plants.
Demise of Mutationism and Rise of the Modern Synthesis
While the mutationist view was very popular in the first 3 decades of the 20th century, it was replaced eventually by Neo-Darwinism or the synthetic theory of evolution. In 1902 G. Udny Yule argued that a trait reflecting effects of multiple Mendelian characters could show a normal distribution. Nevertheless, the synthesis of Mendelian genetics and Darwinism later put forth by Wilhelm Weinberg (1908) and R. A. Fisher (1918) did not develop immediately  for various reasons: it could be doubted that natural selection was sufficiently powerful to act on infinitesimal differences; it could be doubted that natural populations had enough heritable variation to support a Darwinian view; a common (erroneous) belief at the time (following Francis Galton's notion of regression to the mean) held that even heritable fluctuating variations could not lead to large or qualitative changes; and some advocates of Darwinism, such as Karl Pearson, refused to accept Mendelian genetics. A key conceptual innovation of the Modern Synthesis, crucial for its acceptance, was the "gene pool" concept, which argued that natural populations "maintain" abundant heritable variation through a combination of recombination, mixis, recessivity, heterosis and balancing selection.
At the time of the Darwin centennial in Cambridge in 1909, Mutationism and Lamarckism were contrasted with Darwin's “Natural Selection” as competing ideas; 50 years later, at the University of Chicago centennial  of the publication of The Origin of Species, mutationism (like Lamarckism) was no longer seriously considered.
Nevertheless, after another 50 years, evolutionary biologists are re-considering the mutationist view.
Contemporary status of mutationism
With the arrival of molecular biology, scientists studying "molecular evolution" began to suggest mutational explanations for patterns such as genomic nucleotide composition, and eventually it became a characteristic of the field of molecular evolution to emphasize the role of mutation in evolution.  Contemporary interest in mutationism is revealed by articles in mainstream research journals that advocate mutationist ideas, referring to Goldschmidt's concept of the Hopeful Monster, or using the label "mutationism"  or "neo-mutationism". Phrases such as "new mutations" or "mutation-driven evolution" also indicate a departure from the "shifting gene frequencies" view of neo-Darwinism, in which evolution consists of establishing a new multi-locus equilibrium for the frequencies of pre-existing alleles, without new mutations.
These contemporary writings suggest that mutation plays a role in evolution that was proposed by the "mutationists" but rejected in the Modern Synthesis. A key aspect of this role is how single mutations can have huge effects that drive evolution, a result that is difficult to argue from retrospective analyses, but that appears clearly in laboratory evolution experiments, such as those of Lenski and colleagues. According to Takahata,
"Unlike neo-Darwinism, which regards mutation as merely raw material and natural selection as the creative power, Nei's mutationism assumes that the most fundamental process for adaptive evolution is the production of functionally more efficient genotypes by mutation (especially birth and death of duplicated genes) and by recombination."
Another aspect of this role, discussion of which is restricted largely to trade journals in molecular evolution and genomics, is that patterns of diversity and rates of change reflect systematic biases in mutation. Stoltzfus and Yampolsky  list examples in which mutation-biased evolution is either a plausible hypothesis or the received view. In a recent comprehensive treatment of mutation-driven evolution, however, Nei  does not consider that such codon usage bias is particularly important. Rather, he believes that nucleotide or genomic sequence is subject to strong sequence constraints for the genome to be functional but that occasionally this functional constraint is broken and leads to the formation of innovative characters. This process of genomic constraint and constraint-breaking mutation has operated from the time of origin of life to the evolution of human. He also believes that evolution does not necessarily occur by the struggle for life but by production of new niche-filling variants.
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