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Evolution is often taught as a story: variation, struggle, survival. J. B. S. Haldane was one of the people who turned that story into arithmetic, so that you could ask how many generations a change would take. Late in life he left Britain, moved to India and became an Indian citizen. This post covers his mathematics of selection, with his own numbers worked through, and his years in Calcutta and Bhubaneswar.
Who was J. B. S. Haldane?
A 2012 article in the Indian Journal of Human Genetics by Krishna Dronamraju, who worked with Haldane in India, gives the outline. Haldane was born in Oxford on 5 November 1892. His father, the physiologist John Scott Haldane, involved him from childhood in experiments on gases, with father and son often acting as their own test subjects. He was educated at Eton and Oxford and graduated in classics in 1914; Dronamraju notes that he made major contributions to physiology, genetics, biochemistry and statistics without ever holding a degree in any science.
He became Reader in Biochemistry at Cambridge in 1923, then Professor of Genetics at University College London from 1933 to 1937 and Professor of Biometry there from 1937 to 1957.
What did Haldane show about natural selection?
Dronamraju describes his most important genetic work as a series of mathematical papers on the effects of natural selection, summarised in his book The Causes of Evolution (1932). With the work of R. A. Fisher and Sewall Wright, it became the foundation of population genetics.
One passage in the book shows the kind of result he got. Take a selective advantage of one in a thousand, so that 1,001 individuals of one type survive to breed for every 1,000 of the other. Haldane calculated that it would take 11,739 generations to raise a favoured dominant type from one in a million to one in two, but 321,444 generations to do the same for a favoured recessive type. His conclusion: selection is rapid when a population contains a reasonable proportion of recessives, but excessively slow when recessives are very rare.
Why are rare recessives so slow? A worked example. Suppose a recessive allele a has frequency q = 0.001, so p = 0.999. Under random mating:
Individuals showing the trait (aa) make up q² = 0.000001, one in a million.
Carriers (Aa) make up 2pq = 2 × 0.999 × 0.001 = 0.001998, about two in a thousand.
Carriers outnumber those showing the trait by 2pq ÷ q² = 2p ÷ q = 1,998 to 1.
Selection can only act on the trait it can see. Almost every copy of a rare recessive allele sits hidden in a carrier, so it changes frequency very slowly. A rare dominant allele, by contrast, shows itself in every carrier. Haldane gave an example from his own time: the black form of the peppered moth, which replaced the original form in industrial districts of England and Germany during the nineteenth century, is a dominant.
Dronamraju lists other contributions: he proposed the term centimorgan as a unit of map distance, prepared the first human gene map, between the genes for haemophilia and colour blindness on the X chromosome, and suggested that people carrying one copy of the thalassaemia gene might resist malaria better. Our post on Ronald Ross and malaria covers the disease itself.
Why did Haldane move to India?
According to Dronamraju, Haldane grew increasingly dissatisfied with the political situation in Britain during the 1950s and was drawn to India's politics under Nehru and its cultural and philosophical traditions. He had first visited India in 1915, recovering from wounds received in the First World War. P. C. Mahalanobis, director of the Indian Statistical Institute (ISI) in Calcutta, offered him a professorship, with a post for his wife, the geneticist Helen Spurway. In July 1957 he moved to India and became an Indian citizen.
What did he do in India?
At the ISI he built a research group in genetics. Dronamraju, who joined at the end of 1957, describes early projects: a study of hairy ears as a possible Y-linked trait, a survey of inbreeding in Andhra Pradesh that found 30.6% of 2,177 marriages were between relatives, and studies of colour blindness in Andhra Pradesh and Orissa. With A. K. Ray, Haldane studied families with a short fourth toe, published in 1965 as The genetics of a common Indian digital abnormality. Dronamraju reports that 206 people in 61 families in West Bengal and Orissa were studied, and the pattern fitted dominant inheritance with about 27% penetrance.
He later moved to Bhubaneswar; the Who Was Who entry describes him as Head of the Genetics and Biometry Laboratory of the Government of Orissa from 1962. He died of cancer in Bhubaneswar on 1 December 1964. Throughout, Dronamraju notes, he wrote popular science essays every week.
What can a student take from Haldane's way of working?
Learn enough mathematics for your subject. A classics graduate became a founder of population genetics because he could calculate. If you are aiming at biology, keep your algebra and probability strong.
Put a number on the claim. "Selection is slow for recessives" becomes convincing when it reads 321,444 generations against 11,739.
Study what is in front of you. In India he chose problems that India's own families and populations could answer.
Explain your work to everyone. His weekly essays kept science public.
For the related principle he built on, see our post on G. H. Hardy and the 1908 genetics letter. If you can follow the algebra but cannot picture allele frequencies shifting over generations, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Repeat the worked example with q = 0.01 and find how many carriers there are for each person who shows the trait. (Answer: 198.)
