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When bacteria survive an antibiotic or a virus, it is tempting to think the attack made them change. NCERT's Class 12 evolution chapter says otherwise: resistant variants are selected, not created. The experiment that showed this for bacteria used a clever piece of statistics. This post explains the question Salvador Luria and Max Delbrück asked, why the spread of their counts settled it, and walks through a worked example you can check with Class 11 statistics.
Who were Luria and Delbrück?
Salvador Luria was born in Turin, Italy, on 13 August 1912 and died in Lexington, Massachusetts, on 6 February 1991, according to his Nobel facts page. Max Delbrück was born in Berlin on 4 September 1906 and died in Pasadena, California, on 9 March 1981, according to his facts page. With Alfred Hershey they shared the 1969 Nobel Prize in Physiology or Medicine "for their discoveries concerning the replication mechanism and the genetic structure of viruses". Both facts pages note that in 1943 they used statistics to show that bacteria, like larger organisms, change through mutation.
Their paper, Mutations of Bacteria from Virus Sensitivity to Virus Resistance, appeared in Genetics in November 1943. A footnote splits the work neatly: "Theory by M. D., experiments by S. E. L." Delbrück had moved into theoretical physics as a graduate student at Göttingen, according to his Nobel biography, and worked for Lise Meitner in Berlin before turning to biology.
What was the question?
The paper begins with something every microbiologist had seen. Add a virus to a bacterial culture and it clears as the bacteria die. Wait longer and it often turns cloudy again, because a resistant variant grows. They worked with the bacterium Escherichia coli B and a virus they called α.
Where did the resistant cells come from? The paper sets out two camps. One view was that contact with the virus induced resistance in a few cells. The other was that resistant mutants had already arisen by chance, before any virus was added, and the virus simply killed everything else.
Counting the survivors once cannot tell these apart. Both predict some survivors.
Why does the spread of counts decide it?
Luria and Delbrück's insight was to look at how the counts vary across many identical cultures.
If the virus induces resistance, every cell has the same small chance of surviving at the moment of testing. Counts across cultures would vary like random samples, with the variance about equal to the average.
If mutations happen at random during growth, timing matters. A mutation early in one culture's growth leaves a large family of resistant cells; most cultures have a late mutation or none. A few cultures should have huge counts and most should have very few.
The paper compares this to "the operation of a (fair) slot machine", where most plays return little and, rarely, "the jackpot is hit".
They also ran a control: many samples from a single culture. Those counts varied only as much as sampling predicts, with variance close to the mean, so their plating method was not adding noise.
Worked example: two sets of counts
These are sample numbers made up to show the logic, not the paper's data. Each set has 10 counts of resistant colonies.
Set A, ten samples from one big culture: 10, 22, 15, 21, 12, 17, 16, 13, 19, 15.
Mean = 160 ÷ 10 = 16.
Squared deviations: 36, 36, 1, 25, 16, 1, 0, 9, 9, 1; sum = 134.
Variance = 134 ÷ 10 = 13.4, close to the mean, as random sampling predicts.
Set B, ten separate cultures each grown from a few cells: 0, 1, 0, 3, 0, 107, 2, 0, 5, 42.
Mean = 160 ÷ 10 = 16, the same as set A.
Squared deviations: 256, 225, 256, 169, 256, 8,281, 196, 256, 121, 676; sum = 10,692.
Variance = 1,069, about 67 times the mean.
Same average, completely different spread. Set B is the signature of random mutations happening before the test. The median of set B is only 1.5, which shows how two jackpot cultures drag the mean up.
Common slips:
Comparing only means. Both hypotheses can give the same average; the variance is what differs.
Confusing the two kinds of repeat. Samples from one culture test the counting method. Separate cultures test the biology.
Thinking "appears after exposure" means "caused by exposure". The virus reveals resistant cells by killing the rest.
Where does this meet your syllabus?
NCERT's Class 12 Biology chapter on evolution notes that resistant microbes appear within months or years when we use antibiotics, and calls evolution "a stochastic process based on chance events". Its exercises ask you to explain antibiotic resistance in terms of Darwinian selection. The fluctuation test is the classic experimental evidence behind that answer. For the variance formula, see our guide to mean and variance, and for the distribution that describes random sampling, our post on Siméon Poisson.
What can a student take from their way of working?
Find the measurement that separates the ideas. Averages could not decide; spread could.
Let different skills meet. Delbrück's theory and Luria's experiments together answered a question neither could have settled alone.
Look twice at messy results. Inconsistent data can carry the very information you need.
If you can follow the logic but stumble on the variance arithmetic, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
Next step: replace the 107 in set B with 7 and recompute the variance to see how much one jackpot culture changes the picture.
