Journal of the History of Biology

, Volume 51, Issue 2, pp 259–281 | Cite as

How Fast Does Darwin’s Elephant Population Grow?

  • János PodaniEmail author
  • Ádám Kun
  • András Szilágyi


In “The Origin of Species,” Darwin describes a hypothetical example illustrating that large, slowly reproducing mammals such as the elephant can reach very large numbers if population growth is not affected by regulating factors. The elephant example has since been cited in various forms in a wide variety of books, ranging from educational material to encyclopedias. However, Darwin’s text was changed over the six editions of the book, although some errors in the mathematics persisted throughout. In addition, full details of the problem remained hidden in his correspondence with readers of the Origin. As a result, Darwin’s example is very often misinterpreted, misunderstood or presented as if it were a fact. We show that the population growth of Darwin’s elephant population can be modeled by the Leslie matrix method, which we generalize here to males as well. Darwin’s most often cited figure, about 19 million elephants after 750 years is not a typical outcome, actually a very unlikely result under more realistic, although still hypothetical situations. We provide a recursion formula suggesting that Darwin’s original model corresponds to a tribonacci series, a proof showing that sex ratio is constant over all age classes, and a derivation of a generating function of the sequence.


Darwin’s correspondence Leslie matrix Population growth The Origin of Species Tribonacci series 


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Plant Systematics, Ecology and Theoretical Biology, Institute of BiologyEötvös UniversityBudapestHungary
  2. 2.MTA-ELTE-MTM Ecology Research GroupEötvös UniversityBudapestHungary
  3. 3.MTA-ELTE Theoretical Biology and Evolutionary Ecology Research GroupEötvös UniversityBudapestHungary

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