Under the influence of Malthus’s law of population growth: Darwin eschews the statistical techniques of Aldolphe Quetelet

Abstract

Charles Darwin, James Clerk Maxwell, and Francis Galton were all aware, by various means, of Aldolphe Quetelet’s pioneering work in statistics. Darwin, Maxwell, and Galton all had reason to be interested in Quetelet’s work: they were all working on some instance of how large-scale regularities emerge from individual events that vary from one another; all were rejecting the divine interventionistic theories of their contemporaries; and Quetelet’s techniques provided them with a way forward. Maxwell and Galton all explicitly endorse Quetelet’s techniques in their work; Darwin does not incorporate any of the statistical ideas of Quetelet, although natural selection post-twentieth century synthesis has. Why not Darwin? My answer is that by the time Darwin encountered Malthus’s law of excess reproduction he had all he needed to answer about large scale regularities in extinctions, speciation, and adaptation. He didn’t need Quetelet.

Introduction

In the epigraph Fisher blames two generations of theoretical biologists, from Darwin on, for ignoring Quetelet’s statistical techniques and hence harbouring confusions about evolution and natural selection. He is right to imply that Darwin and his contemporaries were aware of the core of Quetelet’s work. Quetelet’s seminal monograph, Sur l’homme, was widely discussed in Darwin’s academic circles. We know that Darwin owned a copy (Schweber, 1977). More importantly, we have in Darwin’s notebooks two entries referring to Quetelet’s work on the cause of a large-scale global phenomenon where each year more boys were born than girls. The first entry is written sometime between April and July 1838. Darwin writes, ‘Find out from the Statistical Society—where M. Quetelet has published his laws about sexes relative to age of Marriages’ (Barrett, Gautrey, Herbert, Kohn, & Smith, 1987, p. 324). The second is written sometime after October 16, 1838: ‘In the Athenaeum Numbers 406, 407, 409, Quetelet papers are given, & I think facts there mentioned about proportion of sexes, at birth & causes’ (ibid., p. 379). So, even if Darwin did not read Sur l’homme directly it is likely (though not certain) that he read its review in the Athenaeum. There is no doubt that Darwin eventually became familiar with Quetelet’s work in statistics: the smoking gun is an essay that Darwin writes in 1873, entitled ‘On the males and complemental males of certain cirripedes, and on rudimentary structures’, where he discusses Quetelet’s laws of variation (Darwin, 1873).

As for Darwin’s contemporaries, Fisher is wrong to imply they were not aware of the importance of Quetelet’s work. There is little question about his impact on James Clerk Maxwell and on Darwin’s cousin, Francis Galton. Both read the extensive review of Quetelet’s achievements in statistics in John Herschel’s 1850 essay in the Edinburgh Review (then ‘Anonymous’). Both were profoundly affected by it (Porter, 1986, Gillispie, 1963, Brush, 1976, Hacking, 1990). Maxwell, following Quetelet via Herschel, takes his basic assumption that the aggregate description of the numerous collisions between individual molecules in a gas fit the regular distribution patterns of gas laws already known at the time (Brush, 1976, p. 186). Galton’s central postulate in Hereditary Genius that drives his theory of inheritance is derived explicitly from deliberating upon Quetelet’s use of Gaussian bell-shaped curves (Hacking, 1990, p. 184, who provides quotations from Galton on his reflections on Quetelet).

So, Darwin, Galton, and Maxwell were all exposed to Quetelet’s early advocacy of statistics, and Galton and Maxwell were aware that they had something to learn in this field; yet Darwin was apparently unaware. This is not entirely surprising. Karl Pearson once inquired to Darwin’s sons, Frank and Leonard, whether their father was aware that the theory of natural selection is applicable to statistical analysis. Frank and Leonard’s response was that their father had a ‘non-statistical’ mind (Porter, 1986, p. 135). Yet, if we take seriously the idea, put forward by late nineteenth and early twentieth century evolutionary thinkers as Pearson, Fisher, along with Sewall Wright and J. S. B. Haldane, among others, that modern natural selection theory is essentially a statistical theory (pioneered by Quetelet, according to Fisher, 1953), then a larger question arises about the difference between Darwin’s version of natural selection and its modern day statistical correlate. A key difference, I think, is found when we reflect on the methodological difference between the quasi-statistical thinking of Thomas Robert Malthus and Quetelet’s pioneering statistical techniques. As I will argue, once Darwin got hold of Malthus’s thinking, especially about the consequences of the doctrine of excessive reproduction, Darwin had no more need of Quetelet and his techniques. Yet, if Darwin had carefully read Quetelet’s critique of Malthus’s doctrine of excessive reproduction instead of relying on a rather misleading or (at best) opaque review of Quetelet in the Athenaeum, then Darwin would have had to grapple with a serious argument in favor of eschewing Malthus and begin to adopt a statistical mind.