# Sewall Green Wright

### Born: 21 December 1889 in Melrose, Massachusetts, USA

Died: 3 March 1988 in Madison, Wisconsin, USA

**Sewall Green Wright**'s parents were Philip Green Wright and Elizabeth Quincy Sewall who were cousins. We should record right at the beginning of this article at Wright later dropped his middle name so was known simply as

**Sewall Wright.**Philip Wright was an economist and in 1892 he moved with his family to Galesburg, Illinois, to join the faculty at Lombard College where he taught mathematics, astronomy, surveying, and English composition in addition to economics.

Sewall had two brothers Quincy Wright and Theodore Paul Wright; they were all gifted children. He was educated at home until he was eight years old and by the time he entered school in 1897 he had read his father's mathematics books, learning how to extract cube roots. (How many mathematicians today know how to extract cube roots?) He was fascinated by mathematical models and calculating, learning arithmetical methods from his mother. He had also read much natural history, influenced by his mother, and at the age of seven had written a pamphlet on natural history, with chapters on marmosets, ants, dinosaurs, chicken gizzards, and astronomy. Completing eight years of schooling in five, he entered Galesburg High School in 1902, graduating in 1906. In his final year in High School he read Darwin's *Origin of the Species*. He then entered Lombard College where the intention of studying chemistry.

The next five years spent at Lombard College saw him move away from chemistry and instead he studied mathematics, reaching differential and integral calculus, and surveying in classes taught by his father. He worked during one summer vacation in South Dakota on the Chicago, Milwaukee and St Paul Railroad where he used the mathematical skills he was learning at College. In his final year he was influence by some fine teaching to become interested in biology and after graduating from Lombard College in 1911 with a B.S. he moved to the University of Illinois for graduate work in biology. Wright had already some experience in such research having studied at the Carnegie Institution of Washington Station for Experimental Evolution at Cold Spring Harbor during the summers of 1911 and 1912. He graduated with a master's degree from the University of Illinois in 1912. Ernest William Castle visited the University of Illinois in Wright's final year and after, interviewing Wright, offered him an assistantship at Harvard's Bussey Institution. There he studied for his doctorate which was awarded in 1915 for his dissertation on the inheritance of coat colours of guinea pigs. He developed new mathematical methods in this study.

For ten years, from 1915 to 1925, Wright worked for the United States Department of Agriculture. An important method which he had worked out by 1918 was a new statistical approach called path analysis. He applied this in many different situations in the following years. He married Louise Lane Williams, a genetics teacher at Smith College, in 1921; they had three children, Richard Wright, Robert Wright, and Elizabeth Quincy Wright. Wright took up a post at the University of Chicago in 1926 which he held until he retired in 1955. During this time he held two visiting professorships; he was Hitchcock Professor at the University of California Berkeley during 1943 and Fulbright Professor at the University of Edinburgh during session 1949-1950.

Wright is famed for his work on evolution, in particular in the use of statistical techniques in the subject. In 1942 he published the Gibbs lecture that he had delivered in the *Bulletin of the American Mathematical Society*. Opatowski writes in a review:-

Another paper by Wright which shows his mathematical approach to the subject isThis sixteenth Gibbs lecture is a review of the prominent work done by the author in the last twelve years towards the establishment of a mathematical theory of evolution. Hardy's formula, a mathematical consequence of Mendel's inheritance mechanism, requires the persistency of the relative frequency of genes in each set of alleles of an indefinitely large random breeding population free from evolutionary agents. Therefore the change of this frequency(called briefly the gene frequency q)is a measure of the evolution of the population. As a consequence of biologically plausible hypotheses compatible with the requirements of mathematical simplicity the change of q per generation is[found]. ... Introducing[an]approximation, the author succeeds in deriving an explicit expression of the distribution function of the gene frequencies satisfying the conditions of a statistical equilibrium(constant mean and constant variance). The distribution curve ... clearly the slight effect of selection in small populations.

*The differential equation of the distribution of gene frequencies*which he published in 1945. He derives differential equations which are satisfied by the probability density function of the distribution of gene frequencies under certain conditions. For example he considers: stationary distribution of gene frequencies; steady flow due to mutation pressure from gene frequency 0 to gene frequency 1 or vice versa; and nonstationary states.

In 1950 Wright gave the Galton lecture at University College, London. In this lecture, which was later published as *The genetical structure of populations*, he systematically applied his method of path coefficients to problems of population structure in a variety of situations such as: random mating and inbreeding; statistical properties of populations; the inbreeding coefficient *F*; hierarchic structure; natural populations; the island model of structure; isolation by distance; population structure in evolution; ecologic opportunity; and evolution in general. He also presented a number of mathematical appendices in the paper: the method of path coefficients; general coefficients of inbreeding; properties of populations as related to *F*; the inbreeding coefficient of breeds; regular systems of mating; and isolation by distance.

Fisher and Wright had differing views on the mechanism and importance of natural selection. Their disagreement began in the late 1920s and became increasingly bitter leading to a split among evolutionists. Turner looks at this dispute in [10] and explains what divided these two leaders in mathematical population genetics:-

After retiring from Chicago, Wright joined the faculty of the University of Wisconsin as Leon J Cole Professor of Genetics. He worked for five years until his second retirement in 1960 but he continued to undertake research up to his death at the age of 98. His four volume masterpieceFisher achieved a synthesis in which mutation was awarded a minimal role by being required to deliver variation to the selective machinery in the most finely divided state that was imaginable. His opposition to Sewall Wright's proposals that random drift was a creative force when allied to selection was a natural outgrowth of this philosophy. Fisher maintained that as a general proposition he believed in the essentially stochastic nature of causation, and the indeterminacy of the future. His opposition to the creative role of stochastic process in evolution arose therefore not from a belief in determinism, but from a belief in the sole power of natural selection to create order and adaptation.

*Evolution and the Genetics of Populations*appeared between 1968 and 1978 (that is when he was between the ages of 80 and 90).

Crow writes in [7] about Wright's teaching:-

As to his character, Crow writes [7]:-He was a conscientious teacher, and spent many hours in the classroom and in the laboratory, which he ran himself. ... His lectures invariably ran far over the allotted time.

Wright received many honours such as the Weldon Medal from the Royal Society (London) in 1947 and their Darwin Medal in 1966. From the National Academy of Sciences (United States) he received the Elliott Award in 1947 and the Kimber Award in 1956. In 1966 he was awarded the National Medal of Science. In all he received nine major medals or prizes and was awarded ten honorary doctorates.Socially, Wright was shy and retiring. He had no small talk and was hard to engage in conversation. But, paradoxically, when he did start to talk about something of interest - his childhood, his experience on the railroad surveying team, his ancestors, guinea pigs, evolution, genetics, politics - he could, and would, talk at length. ... He was always gentle, yet he defended his views forcefully and he stated them fully. ... In regard to his time, he was generous to a fault.

**Article by:** *J J O'Connor* and *E F Robertson*

**August 2005**

**MacTutor History of Mathematics**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Wright_Sewall.html]