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Sir Ronald Aylmer Fisher FRS^{[2]} (17 February 1890 – 29 July 1962), who published as R.A. Fisher, was an English statistician, and biologist, who used mathematics to combine Mendelian genetics and natural selection, helping to create a new Darwinist synthesis of evolution known as modern evolutionary synthesis, as well as a prominent eugenicist in the early part of his life.
He began working at Rothamsted Research in 1919, where he developed the analysis of variance (ANOVA) to analyse its immense data from crop experiments since the 1840s, and established his reputation there in the following years as a biostatistician. He is known as one of the three principal founders of population genetics. He outlined Fisher's principle as well as the Fisherian runaway and sexy son hypothesis theories of sexual selection. He also made important contributions to statistics, including the maximum likelihood, fiducial inference, the derivation of various sampling distributions among many others.
Anders Hald called him "a genius who almost single-handedly created the foundations for modern statistical science",^{[3]} while Richard Dawkins named him "the greatest biologist since Darwin. Not only was he the most original and constructive of the architects of the neo-Darwinian synthesis. Fisher also was the father of modern statistics and experimental design. He therefore could be said to have provided researchers in biology and medicine with their most important research tools, as well as with the modern version of biology's central theorem."^{[4]} and Geoffrey Miller said of him "To biologists, he was an architect of the 'modern synthesis' that used mathematical models to integrate Mendelian genetics with Darwin's selection theories. To psychologists, Fisher was the inventor of various statistical tests that are still supposed to be used whenever possible in psychology journals. To farmers, Fisher was the founder of experimental agricultural research, saving millions from starvation through rational crop breeding programs."^{[5]}
Fisher gained a scholarship to study Mathematics at the University of Cambridge in 1909, gained a First in Astronomy in 1912.^{[6]} In 1915 he published a paper The evolution of sexual preference^{[7]} on sexual selection and mate choice. He published The Correlation Between Relatives on the Supposition of Mendelian Inheritance in 1918, in which he introduced the term variance and proposed its formal analysis.^{[8]} He put forward a genetics conceptual model showing that continuous variation amongst phenotypic traits measured by the biostatisticians could be produced by the combined action of many discrete genes and thus be the result of Mendelian inheritance. This was the first step towards the establishment of population genetics, which demonstrated that natural selection could change allele frequencies in a population, resulting in reconciling its discontinuous nature with gradual evolution.^{[9]} Joan Box, Fisher's biographer and daughter says that Fisher had resolved this problem in 1911.^{[10]}
Between 1912 and 1922 Fisher recommended, analyzed (with flawed attempts at proofs) and vastly popularized Maximum likelihood.^{[11]}
In 1919 he was offered a position at the Galton Laboratory in University College London led by Karl Pearson, but instead accepted a temporary job at Rothamsted Research in Harpenden to investigate the possibility of analysing the vast amount of data accumulated since 1842 from the "Classical Field Experiments" where he analysed the data recorded over many years and published Studies in Crop Variation in 1921. In 1928 Joseph Oscar Irwin began a three-year stint at Rothamsted and became one of the first people to master Fisher's innovations.
His first application of the analysis of variance was published in 1921.^{[12]}
Fisher's article On a distribution yielding the error functions of several well known statistics (1924) presented Pearson's chi-squared test and William Gosset's Student's t-distribution in the same framework as the Gaussian distribution and where he developed Fisher's z-distribution a new statistical method, commonly used decades later as the F distribution. He pioneered the principles of the design of experiments and the statistics of small samples and the analysis of real data.
In 1925 he published Statistical Methods for Research Workers, one of the 20th century's most influential books on statistical methods.^{[13]} Fisher's method^{[14]}^{[15]} is a technique for data fusion or "meta-analysis" (analysis of analyses). This book also popularized the p-value, and it plays a central role in his approach. Fisher proposes the level p = 0.05, or a 1 in 20 chance of being exceeded by chance, as a limit for statistical significance, and applies this to a normal distribution (as a two-tailed test), thus yielding the rule of two standard deviations (on a normal distribution) for statistical significance.^{[16]} The 1.96, the approximate value of the 97.5 percentile point of the normal distribution used in probability and statistics, also originated in this book.
"The value for which P = .05, or 1 in 20, is 1.96 or nearly 2 ; it is convenient to take this point as a limit in judging whether a deviation is to be considered significant or not."^{[17]}
In Table 1 of the work, he gave the more precise value 1.959964.^{[18]}
The Genetical Theory of Natural Selection was first published in 1930 by Clarendon Press. A core work of the neo-Darwinian modern evolutionary synthesis,^{[19]} it helped define population genetics, which Fisher founded alongside Sewall Wright and J. B. S. Haldane, and revived the idea of sexual selection,^{[20]} neglected since Darwin's death. Commonly cited in biology books, it outlines many important concepts, such as:
In 1935, he published by The Design of Experiments, which was "also fundamental, [and promoted] statistical technique and application... The mathematical justification of the methods was not stressed and proofs were often barely sketched or omitted altogether .... [This] led H.B. Mann to fill the gaps with a rigorous mathematical treatment in his treatise".^{[13]}^{[31]} In this book Fisher also outlined the Lady tasting tea, now a famous design of experiments statistical randomized experiment which uses Fisher's exact test and is the original exposition of Fisher's notion of a null hypothesis.^{[32]}^{[33]}
The same year he also published a paper on fiducial inference^{[34]}^{[35]} and applied it to the Behrens–Fisher problem, the solution to which, proposed first by Walter Behrens and a few years later by Fisher, is the Behrens–Fisher distribution.
In 1936 he introduced the Iris flower data set as an example of discriminant analysis.^{[36]}
In his 1937 paper The wave of advance of advantageous genes he proposed Fisher's equation in the context of population dynamics to describe the spatial spread of an advantageous allele and explored its travelling wave solutions.^{[37]} Out of this also came the Fisher–Kolmogorov equation.^{[38]}
In 1938 the Fisher–Yates shuffle was described by Fisher and Frank Yates in their book Statistical tables for biological, agricultural and medical research.^{[39]} Their description of the algorithm used pencil and paper; a table of random numbers provided the randomness.
Although a prominent opponent of Bayesian statistics, Fisher was the first to use the term "Bayesian".^{[40]}
He was the first to use diffusion equations to attempt to calculate the distribution of allele frequencies and the estimation of genetic linkage by maximum likelihood methods among populations.^{[41]} In 1950 he published "Gene Frequencies in a Cline Determined by Selection and Diffusion"^{[42]} on the wave of advance of advantageous genes and on clines of gene frequency, being notable as the first application of a computer, the EDSAC, to biology. He developed computational algorithms for analyzing data from his balanced experimental designs,^{[43]} with various editions and translations, becoming a standard reference work for scientists in many disciplines. In ecological genetics he and E. B. Ford showed how the force of natural selection was much stronger than had been assumed, with many ecogenetic situations (such as polymorphism) being maintained by the force of selection.
In 1943 , along with A.S. Corbett and C.B. Williams he published a paper on Relative species abundance where he developed the logseries to fit two different abundance data sets^{[44]}
In 1947, Fisher used a Pearson's chi-squared test to analyze Mendel's data and concluded that Mendel's results with the predicted ratios were far too perfect, suggesting that adjustments (intentional or unconscious) had been made to the data to make the observations fit the hypothesis.^{[45]} Later authors have claimed Fisher's analysis was flawed, proposing various statistical and botanical explanations for Mendel's numbers.^{[46]}
Fisher publicly spoke out against the 1950 study showing that smoking tobacco causes lung cancer, arguing that correlation does not imply causation.^{[47]} To quote his biographers Yates and Mather, "It has been suggested that the fact that Fisher was employed as consultant by the tobacco firms in this controversy casts doubt on the value of his arguments. This is to misjudge the man. He was not above accepting financial reward for his labours, but the reason for his interest was undoubtedly his dislike and mistrust of puritanical tendencies of all kinds; and perhaps also the personal solace he had always found in tobacco."^{[2]}
He gave the 1953 Croonian lecture on population genetics.^{[48]}
Debabrata Basu, the Indian statistician, met Fisher in the winter of 1954–1955; he wrote in 1988, "With his reference set argument, Sir Ronald was trying to find a via media between the two poles of Statistics – Berkeley and Bayes.^{[49]} My efforts to understand this Fisher compromise led me to the likelihood principle".^{[50]}
He is also known for the following theories:
In 1910 he joined the Eugenics Society at Cambridge, whose members included John Maynard Keynes, R. C. Punnett, and Horace Darwin. He saw eugenics as addressing a pressing social and scientific issues that encompassed both genetics and statistics. During World War I Fisher started writing book reviews for the Eugenic Review and volunteered to undertake all such reviews for the journal, being hired for a part-time position. The last third of The Genetical Theory of Natural Selection focussed on eugenics, attributing the fall of civilizations to the fertility of their upper classes being diminished, and used British 1911 census data to show an inverse relationship between fertility and social class, partly due, he claimed, to the lower financial costs and hence increasing social status of families with less children. He proposed the abolition of extra allowances to large families, with the allowances proportional to the earnings of the father. He served in several official committees to promote Eugenics. In 1934, he resigned from the Eugenics Society over a dispute about increasing the power of scientists within the movement.
He opposed UNESCO's The Race Question, believing that evidence and everyday experience showed that human groups differ profoundly "in their innate capacity for intellectual and emotional development" and concluded that the "practical international problem is that of learning to share the resources of this planet amicably with persons of materially different nature", and that "this problem is being obscured by entirely well-intentioned efforts to minimize the real differences that exist". The revised statement titled "The Race Concept: Results of an Inquiry" (1951) was accompanied by Fisher's dissenting commentary.^{[60]}
Fisher was born to Kate and George, a successful partner in Robinson & Fisher, auctioneers and fine art dealers, in East Finchley in London, England, one of twins but his elder twin was still-born^{[61]} and grew up the youngest with three sisters and one brother.^{[62]} From 1896 until 1904 they lived at Inverforth House in London, and English Heritage installed a blue plaque in 2002 to mark this. They then moving south of the river to Streatham.^{[25]} His mother died from acute peritonitis when he was 14, and his father then lost his business 18 months later.
Due to the lifelong poor eyesight which meant he was unable to join the British Army in World War I, he learnt mathematics without paper and pen, which developed his ability to visualize problems in geometrical terms, but not in writing proper derivations of mathematical solutions, especially proofs. He amazed his peers with his ability to conjecture mathematical solutions without justifying his conclusions by showing intermediate steps. He won the Neeld Medal (a competitive essay in mathematics) at Harrow School age 16 and developed a strong interest in biology, and especially evolutionary biology. In 1909, he won a scholarship to the Gonville and Caius College at the University of Cambridge. On graduating in 1912, his tutor told him that despite his aptitude for scientific work and mathematical potential his disinclination to show calculations or to prove propositions rendered him unsuited for a career in applied mathematics, which required greater thoroughness, giving him a "lukewarm" recommendation, stating that if Fisher "had stuck to the ropes he would have made a first-class mathematician, but he would not."^{[63]}
Fisher worked for six years as a statistician for the City of London. He took up teaching physics and mathematics at a sequence of public schools, at the Thames Nautical Training College and Bradfield College, where, with his new bride, 17 year old Eileen Guinness, with whom he had two sons and six daughters, and her sister, they became subsistence farmers, with a large garden and animals, surviving on very little and living through the last two years of the war without using food coupons.^{[64]} In 1919 he began working at Rothamsted Research.
Leonard Darwin was a great supporter of Fisher. When Fisher was elected to the Royal Society in 1929, Darwin congratulated him. Fisher replied on 25 February 1929, "I knew you would be glad, and your pleasure is as good to me almost as though my own father were still living." Darwin always treated Fisher with tact and generosity. Some years before, after a disagreement, Fisher had resigned from the Royal Statistical Society. Darwin regretted the development and engineered Fisher's re-entry by making him the gift of a life-time subscription to the society. (Letters of 25 and 27 June.) Fisher's 1930 book The Genetical Theory of Natural Selection is dedicated to Darwin. After Darwin's death in 1943 at the age of 93, Fisher wrote to Darwin's niece, Margaret Keynes, "My very dear friend Leonard Darwin... was surely the kindest and wisest man I ever knew". Leonard was the last surviving as well as the longest lived of Charles Darwin's 10 children.
In 1933 he became Professor of Eugenics at University College London (UCL), but in 1939 UCL dissolved the eugenics department, ordering all of the animals to be destroyed. Fisher was dispatched back to Rothamsted with a much reduced staff. In 1943, he took the Balfour Chair of Genetics where the Italian researcher Luigi Luca Cavalli-Sforza was recruited in 1948, establishing a one-man unit of bacterial genetics. Fisher continued his work on mouse chromosome mapping; breeding the mice in laboratories in his own house.^{[65]} In 1947, Fisher cofounded the journal Heredity with Cyril Darlington and in 1949 he published The Theory of Inbreeding.
His fame grew and he began to travel and lecure widely. In 1931, he spent six weeks at the Statistical Laboratory at Indian Statistical Institute in Calcutta, and its one part-time employee, P. C. Mahalanobis, often returnings to encouraging its development, being the guest of honour at its 25th anniversary in 1957 when it had 2000 employees.^{[66]}
His marriage disintegrated during Adelaide, where he died in 1962, with his remains interred within St Peter's Cathedral.^{[69]}
According to Yates and Mather, "His large family, in particular, reared in conditions of great financial stringency, was a personal expression of his genetic and evolutionary convictions."^{[2]} Fisher was noted for being loyal, and was seen as a patriot, a member of the Church of England, politically conservative, as well as a scientific rationalist. He developed a reputation for carelessness in his dress and was the archetype of the absent-minded professor. H. Allen Orr describes him in the Boston Review as a "deeply devout Anglican who, between founding modern statistics and population genetics, penned articles for church magazines".^{[70]} In a 1955 broadcast on Science and Christianity,^{[2]} he said:
In 1950, M. V. Wilkes and Wheeler used EDSAC to solve a differential equation relating to gene frequencies in a paper by Ronald Fisher.^{[72]} This represents the first use of a computer for a problem in the field of biology. Fisher–Bingham distribution was named after him in 1982 while Fisher kernel was named after Fisher in 1998.^{[73]} The R. A. Fisher Lectureship is a prize of a lecture given yearly in North America that was established in 1963. On April 28, 1998 a minor planet, 21451 Fisher, was named after him.^{[74]}
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