# Ronald Fisher

## Quick Facts

Intro | English statistician, evolutionary biologist, geneticist, and eugenicist |

A.K.A. | Ronald Aylmer Fisher, R. A. Fisher, Ronald A. Fisher |

Was | Mathematician Scientist Geneticist Statistician |

From | United Kingdom |

Type | Biology Mathematics Science |

Gender | male |

Birth | 17 February 1890, London, East Finchley |

Death | 29 July 1962, Adelaide (aged 72 years) |

## Biography

Sir Ronald Aylmer Fisher FRS (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. This helped to create the new Darwinist synthesis of evolution known as the modern evolutionary synthesis. He was also a prominent eugenicist in the early part of his life.

He worked at Rothamsted Research for 14 years from 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", 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". 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."

## Personal life

Fisher was born in East Finchley in London, England, one of twins with the other being still-born and grew up the youngest with three sisters and one brother. From 1896 until 1904 they lived at Inverforth House in London, where English Heritage installed a blue plaque in 2002, before moving to Streatham. His mother, Kate, died from acute peritonitis when he was 14, and his father, George, then lost his business as a successful partner in Robinson & Fisher, auctioneers and fine art dealers, 18 months later.

Lifelong poor eyesight caused his rejection by the British Army for World War I, but also developed his ability to visualize problems in geometrical terms, but not in writing mathematical solutions, or proofs. He entered Harrow School age 14 and won the school's Neeld Medal in mathematics. In 1909, he won a scholarship to Gonville and Caius College at the Cambridge University.

Fisher worked for six years as a statistician in the City of London and taught physics and maths at a sequence of public schools, and at the Thames Nautical Training College, and Bradfield College where he settled with his new bride, Eileen Guinness, with whom he had two sons and six daughters. In 1919 he began working at Rothamsted Research.

His fame grew and he began to travel and lecture widely. In 1931, he spent six weeks at the Statistical Laboratory at Iowa State College where he gave three lectures per week, and met many American statisticians, including George W. Snedecor before returning again in 1936. In 1937, he visited the Indian Statistical Institute in Calcutta, and its one part-time employee, P. C. Mahalanobis, often returning to encourage its development, being the guest of honour at its 25th anniversary in 1957 when it had 2000 employees.

His marriage disintegrated during World War II and his oldest son George, an aviator, was killed in combat. His daughter and one of his biographers, Joan, married the noted statistician George E. P. Box. In 1957, a retired Fisher emigrated to Australia where he spent time as a senior research fellow at the Australian Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Adelaide, where he died in 1962, with his remains interred within St Peter's Cathedral.

## Academic career

Fisher gained a scholarship to study Mathematics at the University of Cambridge in 1909, gaining a First in Astronomy in 1912. In 1915 he published a paper *The evolution of sexual preference* 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. 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 and quantitative genetics, which demonstrated that natural selection could change allele frequencies in a population, resulting in reconciling its discontinuous nature with gradual evolution. Joan Box, Fisher's biographer and daughter says that Fisher had resolved this problem in 1911.

Between 1912 and 1922 Fisher recommended, analyzed (with flawed attempts at proofs) and vastly popularized Maximum likelihood.

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.

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. Fisher's method 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. 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."

In Table 1 of the work, he gave the more precise value 1.959964.

*The Genetical Theory of Natural Selection* was first published in 1930 by Clarendon Press and is dedicated to Leonard Darwin. A core work of the neo-Darwinian modern evolutionary synthesis, it helped define population genetics, which Fisher founded alongside Sewall Wright and J. B. S. Haldane, and revived the idea of sexual selection, neglected since Darwin's death. Commonly cited in biology books, it outlines many important concepts, such as:

- Parental investment, is any parental expenditure (time, energy etc.) that benefits one offspring at a cost to parents' ability to invest in other components of fitness,
- Fisherian runaway, explaining how the desire for a phenotypic trait in one sex combined with the trait in the other sex (for example a peacock's tail) creates a runaway development of the trait.
- Fisher's principle, which explains why the sex ratio is mostly 1:1 in nature.
- Reproductive value which implies that sexually reproductive value measures the contribution of an individual of a given age to the future growth of the population.
- Fisher's fundamental theorem of natural selection, which states that "the rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time."
- Fisher's geometric model, an evolutionary model of the effect sizes on fitness of spontaneous mutations proposed by Fisher to explain the distribution of effects of mutations that could contribute to adaptative evolution.
- Sexy son hypothesis, which explains why females choose promiscuous, unreliable fathers for their children in the hope of having similar sexy sons who give them lots of grandchildren.
- Mimicry, a similarity of one species to another that protects one or both
- Dominance, a relationship between alleles of one gene, in which the effect on phenotype of one allele masks the contribution of a second allele at the same locus.
- Heterozygote advantage which was later found to play a frequent role in genetic polymorphism.
- Demonstrating that the probability of a mutation increasing the fitness of an organism decreases proportionately with the magnitude of the mutation and that larger populations carry more variation so that they have a greater chance of survival.

In 1933 he became Professor of Eugenics at University College London until 1939 when the department was dissolved.

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". In this book Fisher also outlined the Lady tasting tea, now a famous design of a statistical randomized experiment which uses Fisher's exact test and is the original exposition of Fisher's notion of a null hypothesis.

The same year he also published a paper on fiducial inference 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.

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. Out of this also came the Fisher–Kolmogorov equation.

In 1938 the Fisher–Yates shuffle was described by Fisher and Frank Yates in their book *Statistical tables for biological, agricultural and medical research*. 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".

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.

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 In the same year 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.

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. Later authors have claimed Fisher's analysis was flawed, proposing various statistical and botanical explanations for Mendel's numbers. In the same year, Fisher cofounded the journal *Heredity* with Cyril Darlington and in 1949 he published *The Theory of Inbreeding.*

In 1950 he published "Gene Frequencies in a Cline Determined by Selection and Diffusion" 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, 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.

During this time he also worked on mouse chromosome mapping; breeding the mice in laboratories in his own house.

Fisher publicly spoke out against the 1950 study showing that smoking tobacco causes lung cancer, arguing that correlation does not imply causation. 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."

He gave the 1953 Croonian lecture on population genetics.

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. My efforts to understand this Fisher compromise led me to the likelihood principle".

He is also known for the following theories:

- Linear discriminant analysis is a generalization of Fisher's linear discriminant
- Fisher information, see also scoring algorithm (also known as Fisher's scoring) and Minimum Fisher information, a variational principle which, when applied with the proper constraints needed to reproduce empirically known expectation values, determines the best probability distribution that characterizes the system.
- F-distribution arises frequently as the null distribution of a test statistic, most notably in the analysis of variance
- Fisher–Tippett–Gnedenko theorem Fisher's contribution to this was made in 1927
- Fisher–Tippett distribution
- Von Mises–Fisher distribution
- Inverse probability, a term Fisher uses in 1922, referring to "the fundamental paradox of inverse probability" as the source of the confusion between statistical terms that refer to the true value to be estimated, with the actual value arrived at by the estimation method, which is subject to error.
- Fisher's permutation test
- Fisher's inequality
- Sufficient statistic, when a statistic is
*sufficient*with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter". - Student's t-distribution became well-known through Fisher, who called the distribution "
*Student'*s distribution" and referred to the value as*t*. - Fisher's noncentral hypergeometric distribution, a generalization of the hypergeometric distribution, where sampling probabilities are modified by weight factors.

### Eugenicist

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 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 fewer 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.

### The Race Question

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.

### Personal beliefs

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." 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". In a 1955 broadcast on Science and Christianity, he said:

## Recognition and legacy

Fisher was elected to the Royal Society in 1929. He was made a Knight Bachelor by Queen Elizabeth II in 1952 and awarded the Linnean Society of London Darwin–Wallace Medal in 1958.

In 1950, Maurice Wilkes and David Wheeler used the Electronic Delay Storage Automatic Calculator to solve a differential equation relating to gene frequencies in a paper by Ronald Fisher. This represents the first use of a computer for a problem in the field of biology. The Kent distribution (also known as the Fisher–Bingham distribution) was named after him and Christopher Bingham in 1982 while Fisher kernel was named after Fisher in 1998.

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.

## Quotations

- "Natural selection is a mechanism for generating an exceedingly high degree of improbability."