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NCERT's Class 12 chapter on evolution lists genetic drift as one of five factors that upset Hardy-Weinberg equilibrium, in a sentence or two. Behind that sentence is the work of an American geneticist who turned "chance" into numbers you can calculate. This post covers who Sewall Wright was, what his 1931 paper showed, a worked example of drift with Class 11 probability, and what students can take from how he worked.
Who was Sewall Wright?
The Royal Society's memoir, Sewall Wright, 21 December 1889 – 3 March 1988, gives his dates. Early in his career he studied inbreeding in guinea pigs for the United States Department of Agriculture, published as The effects of inbreeding and crossbreeding on guinea pigs in 1922. In the same year he published Coefficients of inbreeding and relationship, a way of putting a number on how closely related two individuals are.
His great 1931 paper gives his address as the University of Chicago. He later moved to the University of Wisconsin, where, according to Who Was Who, he was Professor Emeritus of Genetics from 1960. He received the US National Medal of Science; the citation reads "for original and sustained contributions to the mathematical foundations of the theory of evolution and for basic contributions to experimental and biometrical genetics".
With R. A. Fisher and J. B. S. Haldane he is counted among the founders of population genetics. Our posts on Haldane's maths of selection and Fisher's design of experiments cover the other two. Wright's particular contribution was to take chance seriously.
What did the 1931 paper show?
Evolution in Mendelian populations runs to more than sixty pages in the journal Genetics. Its summary lists what can change the frequency of a gene: recurrent mutation, migration, selection of various sorts and, in Wright's words, "far from least in importance, mere chance variation". He stressed that the number that matters is the effective number of breeders, N, which he noted is usually much smaller than the actual number of adults.
His summary then gives the key result. After a large population is reduced to a small one, genes become fixed or lost by chance, each at a rate of about 1/4N per generation, so that the fixation process as a whole runs at about 1/2N.
Finally he compared population structures. In a very small population there is nearly complete fixation, little variation and little effect of selection. In a very large freely mixing one, gene frequencies settle so close to equilibrium that there is almost no evolution under steady conditions. Fastest of all, he argued, is a large population divided into small, partly isolated local groups, where chance and selection keep shifting the groups in different directions. A 2016 commentary in Genetics by Nicholas Barton, Sewall Wright on Evolution in Mendelian Populations and the "Shifting Balance", revisits this idea under the name it later took, the "shifting balance".
Worked example: how strong is drift?
Each generation, the genes passed on are a random sample of the parents' genes. A population of N diploid individuals passes on 2N copies of each gene. The probability tools here are from Class 11 and 12.
Problem 1. A tiny population has N = 5 and allele A at frequency 0.5, so 2N = 10 gene copies. If each copy in the next generation is drawn at random, what is the chance that A is lost in one generation?
Each copy is "not A" with probability 0.5, so all 10 are not A with probability 0.5¹⁰ = 1/1,024 ≈ 0.001.
A becomes fixed with the same probability, so the chance of either outcome in a single generation is about 2 in 1,024, or 0.2 percent.
Problem 2. How big is a typical step? The standard deviation of the new frequency is √(pq ÷ 2N).
N = 5: √(0.25 ÷ 10) = √0.025 ≈ 0.16. The frequency could easily jump from 0.50 to 0.34 or 0.66.
N = 500: √(0.25 ÷ 1,000) ≈ 0.016. A typical step is ten times smaller.
Problem 3. Use Wright's rate. If variation is lost at about 1/2N per generation, then after t generations about (1 − 1/2N)ᵗ of it remains. For N = 10 and t = 10: (1 − 1/20)¹⁰ = 0.95¹⁰ ≈ 0.60, so about 40 percent is gone in ten generations. For N = 1,000 the same calculation gives about 0.995, a loss of half a percent.
Common mistakes:
Confusing drift with selection. In Problem 1 neither allele is better; the change is pure chance.
Using individuals instead of gene copies. Diploid organisms carry two copies each, so the sample size is 2N.
Using the census size. Wright warned that the effective number of breeders is usually much smaller than the head count.
NCERT also mentions the founder effect, where a few individuals start a new population. The maths above shows why: a founding group is a small sample. Our guide to evolution for NEET puts drift alongside the other factors.
What can a student take from his way of working?
Wright moved between careful breeding records and abstract mathematics, and each kept the other honest. He also refused to treat chance as noise to be ignored; he measured it. When a textbook calls something "random", ask how big the randomness is and what it depends on.
If the binomial probability steps above felt rushed, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning, so you can follow each stage.
Try it now: toss ten coins, record the number of heads as a frequency, then use that frequency to toss again, and see how quickly you reach all heads or all tails.
