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Was regression to the mean really the solution to Darwin’s problem with heredity?

Essay Review of Stigler, Stephen M. 2016. The Seven Pillars of Statistical Wisdom. Cambridge, Massachusetts: Harvard University Press


Statistical reasoning is an integral part of modern scientific practice. In The Seven Pillars of Statistical Wisdom Stephen Stigler presents seven core ideas, or pillars, of statistical thinking and the historical developments of each of these pillars, many of which were concurrent with developments in biology. Here we focus on Stigler’s fifth pillar, regression, and his discussion of how regression to the mean came to be thought of as a solution to a challenge for the theory of natural selection. Stigler argues that the purely mathematical phenomenon of regression to the mean provides a resolution to a problem for Darwin’s evolutionary theory. Thus, he argues that the resolution to the problem for Darwin’s theory is purely mathematical, rather than causal. We show why this argument is problematic.

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  1. An important debate concerning the relation between mathematical and causal explanations in the philosophy of biology literature is the debate over whether explanations of population change that refer to natural selection and random drift are causal or mathematical explanations (e.g. Walsh et al. 2002; Shapiro and Sober 2007). We will not discuss how our analysis of Stigler's views relates to this debate.

  2. An alternative interpretation of this chapter is that Stigler describes two distinct problems: "Darwin's problem" being the maintenance of sufficient variation in natural populations and "Galton's version of Darwin's problem" being the problem of the apparent conflict between intergenerational variability and stable variation. We thank an anonymous referee for this suggestion. We prefer our reading of the chapter and note that in the section "The Solution to Darwin's Problem", Stigler describes only one problem, which is the problem we focus on here. The alternative interpretation does not fundamentally affect our argument, which is concerned with Galton's solution for the problem of the apparent conflict between intergenerational variability and stable variation in natural populations.

  3. It is important to note that this is Stigler's argument, not necessarily Galton's. We are not providing an interpretation of Galton's work in this paper, but rather analyze Stigler's interpretation in his analysis of Galton's work.

  4. From this point on, whenever we speak of mathematical explanations we mean pure mathematical explanations. That is, explanations that are mathematical rather than causal.

  5. These authors take explanations for population changes that appeal to natural selection or drift to be mathematical and not causal because these changes "can be explained by referring to the deductive consequences of statistical models, independent of considerations of causation" (Ariew et al. 2015, p. 636). They note that to be explanatory, it is not sufficient that the explanandum will simply be deduced from the mathematical facts. The mathematical facts need to also provide counterfactual information, by telling us "how things would have been different in various counterfactual situations" (Ariew et al. 2015, p. 655).

  6. The argument made here by Stigler, namely that regression to the mean solved Darwin's problem, did not appear in his earlier works on Galton and Darwin's problem (e.g. Stigler 2010). We thank an anonymous referee for pointing this out.

  7. This line of thought is compatible with recent work by Andersen (forthcoming) who suggests that mathematical and causal descriptions should be thought of as complementary explanations of phenomena.


  • Andersen H (forthcoming) Complements, not competitors: causal and mathematical explanations. Br J Philos Sci

  • Ariew A, Rice C, Rohwer Y (2015) Autonomous-statistical explanations and natural selection. Br J Philos Sci 66(3):635–658

    Article  Google Scholar 

  • Hacking I (1990) The taming of chance, vol 17. Cambridge University Press, New York

    Book  Google Scholar 

  • Hacking I (2016) Logic of statistical inference. Cambridge University Press, New York

    Google Scholar 

  • Keller EF (2003) Making sense of life: explaining biological development with models, metaphors, and machines. Harvard University Press, Cambridge

    Google Scholar 

  • Lamm E (2013) Theoreticians as Professional Outsiders: The Modeling Strategies of John von Neumann and Norbert Wiener. In: Harman Oren, Dietrich MichaelR (eds) Outsider scientists: routes to innovation in biology. University of Chicago Press, Chicago, pp 291–312

    Google Scholar 

  • Lange M (2013a) What makes a scientific explanation distinctively mathematical? Br J Philos Sci 64(3):485–511

    Article  Google Scholar 

  • Lange M (2013b) Really statistical explanations and genetic drift. Philos Sci 80(2):169–188

    Article  Google Scholar 

  • Mayo DG (1996) Error and the growth of experimental knowledge. University of Chicago Press, Chicago

    Book  Google Scholar 

  • Shapiro L, Sober E (2007) Epiphenomenalism–the Do’s and the Don’ts. In: Machamer PK, Wolters G (eds) Thinking about causes: from greek philosophy to modern physics. University of Pittsburgh Press, Pittsburgh

    Google Scholar 

  • Sober E (1980) Evolution, population thinking, and essentialism. Philos Sci 47(3):350–383

    Article  Google Scholar 

  • Sober E (2008) Evidence and evolution: the logic behind the science. Cambridge University Press, New York

    Book  Google Scholar 

  • Stigler SM (2010) Darwin, Galton and the statistical enlightenment. J R Stat Soc Ser A (Stat Soc) 173(3):469–482

    Article  Google Scholar 

  • Walsh DM, Lewens T, Ariew A (2002) The trials of life: natural selection and random drift. Philos Sci 69(3):429–446

    Article  Google Scholar 

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Adam Krashniak’s work was kindly supported by The Interuniversitry Ph.D. Program in the History and Philosophy of the Life Sciences, supported by the Humanities Fund of the Israeli Council of Higher Education. The work of Ehud Lamm is supported by Israeli Science Foundation Grant 1128/15.

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Correspondence to Ehud Lamm.

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Krashniak, A., Lamm, E. Was regression to the mean really the solution to Darwin’s problem with heredity?. Biol Philos 32, 749–758 (2017).

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  • Francis Galton
  • Regression to the mean
  • Mathematical explanations
  • Biology and statistics
  • Evolution and inheritance