The Rise of Chance in Evolutionary Theory: A Pompous Parade of Arithmetic

By Charles H. Pence

The Rise of Chance in Evolutionary Theory: A Pompous Parade of Arithmetic explores a pivotal conceptual moment in the history of evolutionary theory: the development of its extensive reliance on a wide array of concepts of chance. It tells the history of a methodological and conceptual development that reshaped our approach to natural selection over a century, ranging from Darwin’s earliest notebooks in the 1830s to the early years of the Modern Synthesis in the 1930s. Far from being a “pompous parade of arithmetic, as one early critic argued, evolution transformed during this period to make these conceptual and technical tools indispensable.

This book charts the role of chance in evolutionary theory from its beginnings to the earliest days of modern evolutionary theory, making it an ideal resource for evolutionary biologists, historians, philosophers, and researchers in science studies or biological statistics.

• Analyzes contributions of key historical figures and assesses how and why these “foundational conclusions were reached by original evolutionary biologists, including Darwin, Galton, Pearson, and more
• Describes the journey of the role of chance in evolutionary theory and illuminates our contemporary understanding
• Presents the historical narrative in a non-technical way, focusing on the conceptual structure of evolutionary theory

• Language: English
• Publisher: Academic Press
• Release date: Nov 25, 2021
• ISBN: 9780323912921

Charles H. Pence

Charles H. Pence is Chargé de cours (Assistant Professor) at the Institut supérieur de philosophie, and director of the Center for the Philosophy of Science and Society (CEFISES) at the Université catholique de Louvain, Belgium. Previously, he was Assistant Professor and Director of the LSU Ethics Institute at Louisiana State University. He is the author of 2 books and over 20 articles and book chapters on the philosophy and history of evolutionary theory. His work centers on the integrated philosophy and history of biology, with a particular focus on the introduction and contemporary use of concepts of chance and methods of statistics in evolutionary theory.

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Chapter 1: Chance governs the descent of a farthing: Charles Darwin

Abstract

In the process of developing the theory of evolution by natural selection, Charles Darwin was forced to reckon with concepts of chance as they entered into contemporary understanding of the history of life. For him, natural selection is a mere tendency, not an exceptionless law of nature, and our ignorance of the precise causes of variation gives rise to what Darwin would call indefinite variation. This creates a tension for Darwin, who does his best, consistent with his fundamental commitment to a Newtonian ideal for science, to hedge and contain the impact of chance on evolution, especially by emphasizing the extent to which natural selection acts as a non-chancy constraint on chance’s effects.

Keywords

Charles Darwin; Chance; Statistics; Adaptation; Natural selection

If I am as muzzy on all subjects as I am on proportions & chance,—what a Book I shall produce!

Darwin, letter to John Lubbock, 14 July 1857

It is April of 1901, 19 years after the death of Charles Darwin, and Karl Pearson cautiously writes to Francis Galton. Along with W. F. R. Weldon and Charles Davenport, he has recently begun to hatch plans to launch the first journal entirely dedicated to the statistical study of biology, Biometrika, and he hopes for Galton’s help—perhaps a position on the editorial board, an article for the first number of the journal as a send off, even a contribution toward the guarantee fund (Pearson, 1901a)? If the journal, he says, can survive the risk of infantile mortality, we will live on (Pearson, 1901b). A few months later, with Galton’s help (and his financial backing) secured, Pearson turns to the matter of situating the statistical study of evolution within its history. I have been looking at one or two of Darwin’s books, he writes to Galton, to see if he anywhere emphasises the value of statistical enquiry. I can find nothing, and yet I feel quite certain he realised its value by undertaking, as he did, the long series of experiments in cross- and self-fertilisation of plants. Surely, somewhere, Pearson pleads, there must be an apt remark as to the need of statistical method in solving evolution problems (Pearson, 1901c)?

Galton has no good news. He writes that he well remembers discussing the matter of statistics with Darwin, but I doubt if he ever thought very much or depended much on statistical inquiry in his own work (Galton, 1901a). Before Pearson can respond, he adds that, having spoken to Darwin’s children Francis and Leonard, their views about their father’s attitude toward statistics are the same as mine, except that Frank’s was more strongly expressed. I fear you must take it as a fact that Darwin had no liking for statistics. They even thought he had a ‘non-statistical’ mind, rather than a statistical one (Galton, 1901b). Pearson replies, clearly crestfallen. Many thanks for your inquiries, he laments, which I fear means we can find no statement of a definite kind. Darwin’s view of statistics, Pearson muses through rose-colored glasses, must amount to a general realization "that the root of evolution lay in the largeness of the numbers dealt with" (Pearson, 1901d).

While we may no longer be able to write to Francis Darwin for confirmation, Pearson has the right idea—any study of the role of chance and statistics in evolutionary theory must begin with Darwin himself. As Pearson correctly sees, Darwin was not, and could not have been, entirely ignorant of the role of chance and the utility of something like statistical inference in his development and subsequent elaboration of evolution by natural selection. But this leaves much room for interpretation. Indeed, one of the most striking differences between the evolutionary theory that we read in Darwin’s work and the evolutionary theory of a 21st century textbook is a shift in the importance of statistical methodology and the roles for chance that are implied by its use. Darwin introduces natural selection in a rich context alongside a whole host of other topics, ranging from biogeography to embryology to paleontology, over the course of some 490 pages. And he does so with barely any reference to mathematics whatsoever (for an extensive survey of these few uses, see Sheynin, 1980). A contemporary textbook on evolutionary theory, on the other hand, makes it only three pages without a graph, and is describing mathematical models for phylogenetic inference by page 28 (Futuyma, 2005).

Understanding this shift is precisely the goal of this book. How did we move from an essentially non-statistical, non-mathematical theory of evolution, with only a few circumscribed roles for chance, to a thoroughly mathematized and statistical theory in which the interpretation of chance stands as one of the most significant philosophical issues? And what can this history tell us about evolution’s present and future?

But let’s begin at the beginning.

Darwin before the Origin

Scholars studying Darwin have, perhaps more than in the case of any other major figure in the history of science, a vast wealth of correspondence, notebook, draft, and manuscript materials on which to draw. We can thus trace, in minute detail, the development and maturation of Darwin’s idea of evolution. At the very beginning of Darwin’s career, as he sets off to make a name for himself as the ship’s naturalist aboard HMS Beagle (in fact, little more than a rich, intellectual companion for the captain, whose predecessor had committed suicide at sea), he is a fairly typical, young English scientist. His interests focus on geology and natural history, and perhaps his most significant influence on both scores is Charles Lyell. Lyell’s picture of the natural world gives pride of place to the harmony evidenced by the economy of nature, prodded by the occasional, yet ordered and regular, creation of new species. Darwin’s first work on species may thus be profitably read as a series of breaks with his friend and mentor, as he abandons the tenets of Lyell to craft his own view, particularly in his notebook writings of 1837 and 1838.

This much is a fairly well known story, and to detail all of its contours (along with Darwin’s debts to other authors in this era, especially German Romantics like Alexander von Humboldt) would be the project of several books (the interested reader may consult Ospovat, 1981; Hodge, 1983; Sloan, 1986; or Hodge, 2009, among many others). What is less well understood is the early development of Darwin’s views of chance prior to the publication of his opus magnum. As we survey this period with chance as our focus, what we will find are fewer such breaks than he makes with Lyell on most other subjects. Lyell’s own view—as should be clear from its emphasis on natural law, balance, and harmony—leaves precious little room for the working of chance in nature. While Darwin refashions his understanding of the creation, dispersal, modification, and relations of species over these years (each of which constitutes no small feat, much less all of them at once), chance remains for him an issue he does not quite know how to handle. The tension that emerges in this early period, constituting as it does a sort of unwelcome, doubtful guest in Darwin’s theorizing, continues to loom large in his thought for the rest of his life.

As Darwin departs on the Beagle at the end of 1831, he carries with him the first volume of Lyell’s Principles of Geology (inscribed as a gift from the ship’s captain), the other volumes to arrive via post in the next few years of the voyage. Twenty-four months later, and shortly after the third volume was sent, Darwin’s Lyellian bent is so well known that his sister Catherine writes to him that I hear that your Theory of the Earth is supposed to be the same as what is contained in Lyell’s 3d Vol. (Darwin, 1833). What, then, is Lyell’s view, which forms Darwin’s point of departure for all of his initial thoughts on the origin and extinction of species? To begin, we must understand the focal species problem for Lyell. Lyell is a deeply committed uniformitarian—he argues, that is, that all natural phenomena that are now visible on the earth are the result of the same set of causes that still operate today (floods, volcanoes, earthquakes, and the like), acting at effectively the same intensity as they always have, back through an immeasurably vast geological past. For prior uniformitarians such as Hutton, this sufficed: the earth is a static and perfectly balanced creation from time immemorial, exemplifying the best features of divine providence. But by Lyell’s day, any such uniformitarianism was confronted with the problem of extinction. While life on earth has broadly looked the same as it does now (with many major groups appearing to have been similar back to the deepest fossil layers known at the time), the species which constitute it have not. The earth has changed enough to render it uninhabitable for some forms—think woolly mammoths wandering the forests of North America—but not so much as to violate the broader precepts of uniformitarianism.

Lyell therefore needs to introduce just the right amount of variability into the natural order, and he does so by pointing to one major cause of species destruction, and a second major, compensating cause of species creation. The destroyer is the redistribution of climatic patterns, along with biological competition. There is no contradiction with a general uniformitarian view if the pattern of climate, while retaining essentially the same overall features across geologic time, has modified its distribution across the globe. New land will emerge, old land erode and subside, and with these developments (all observable as well, for still operating in the present) will undoubtedly come climatic differences. These changes will result, in turn, in alterations to inter-species relations. Species will go extinct, as the finely tuned conditions necessary for their existence disappear (or move outside their range) and they fall victim to competition. To retain long-term balance, we must offset the destruction of species with a creative force. For this, Lyell proposes that species are created as single individuals or pairs (as needed), at such times and in such places as to enable them to multiply and endure for an appointed period, and occupy an appointed space on the globe (Lyell, 1832, p. 2:129). The production of novel species (presumably divine, although Lyell is tacet on the details here), at a slow and steady pace, is a thus an admissible, if difficult to observe, cause of change, in just the same way as erosion or subsidence are in geology. In areas where geographic isolation occurs, this theory will even will reproduce the appearance of centres of creation—areas like South America which appear to have a larger share of tailor-made organisms, because the species being created there at the usual rate are unable to migrate away from the site of their creation (Lyell, 1832, p. 2:131). This cause being added to our uniformitarian arsenal, we have all that we need, Lyell thinks, in order to account for the phenomena we observe—and without proposing anything like Lamarck’s radical hypotheses concerning species transformation.

The young Darwin, therefore, starts his work on the species question from a theory of the earth that does its best to downplay the role of chance. It is the fixed and uniform character of natural law that is on display here, the finely tuned balance of the economy of nature propagating itself steadily onward into the future. While new species are assumed to be divinely created, this, too, is subsumed under the broader banner of uniformitarian causation—there is no caprice or arbitrariness in their creation. Darwin’s own theorizing for many years leaves this minimization of chance broadly intact, even as he begins to modify some of Lyell’s core tenets. His first departure comes as he attempts to integrate his geological and biological findings from the Beagle voyage—particularly patterns of extinction which seem to have taken place in the absence of the kinds of environmental changes that Lyell emphasized—with Lyell’s account of how species are destroyed. Drawing an analogy between species and individual organisms, Darwin considers a picture on which species are not only continually created like individuals, but also have fixed, maximum durations or lifespans just as individual organisms do (Hodge, 1983). This is, however, only an effort to square Lyell’s overall view with the South American fossil record as Darwin interprets it. Darwin has yet to loosen his grip on the perfection and balance of the economy of nature, nor to make any further room for the play of chance:

If the existence of species is allowed, each according to its kind, we must suppose deaths to follow at different epochs, & then successive births must repeople the globe or the number of its inhabitants has varied exceeding[ly] at different periods. — A supposition in contradiction to the fitness which the Author of Nature has now established.b

(Darwin, 1835, fol. 2v)

Darwin is thus still a committed, if at this point slightly heterodox, Lyellian, for whom the distribution of species still shows, most of all, the harmonious and roughly stable character of the natural order. Adding a second cause for the disappearance of species makes no dramatic change in this regard.

Two years later, opening a notebook containing his current ideas on the species question, Darwin writes what is commonly taken to be the first strong evidence of transformism or transmutationism in his thought, as hypotheses concerning the evolution of species were most commonly then called (at the beginning of Notebook B, Darwin, 1837; though see Hodge, 1983, p. 80, for skepticism concerning the extent to which this work is really transformist). While he begins to consider here the notion that species might change over time, he does not yet alter, in any significant way, his philosophical approach—he is still on the hunt for regular, clockwork laws of life, as Lyell called them, that would fulfill the same role as Lyell’s dual causes for species creation and destruction. Drawing his now-famous, first ever tree of life diagram, he realizes that a tree-like structure in which species give rise to similar species by the accumulation of small variations, combined with a principle of divergence over time driving clusters of organisms on the tree apart, will produce the pattern of similarities and differences, species and higher taxa arranged as groups within groups, that we have come to expect from taxonomic study since Linnaeus.

Hence if this is true, [it will be the case] that the greater the groups the greater the gaps (or solutions of continuous structure) between them. – for instance, there would be [a] great gap between birds and mammalia, Still greater Vertebrate and Articulata, still greater between animals & Plants.

(Darwin, 1837, pp. B42–3)

Even this skeletal process of differentiation and divergence already bears some of the features of Darwin’s mature works. It proceeds, he says, from three elements which mirror his later presentation of evolution by natural selection—from infinite variations, from the species all coming from one stock, and from obeying one law, here the principle of divergence (Darwin, 1837, p. B43). But the details, of course, are still unspecified (in particular, the mechanism of natural selection as the driver for adaptation is nowhere to be found), and Darwin worries whether or not there will be sufficient evidence for his newly fledged picture. Heaven know[s] whether this agrees with Nature, he writes. "Cuidado" (Darwin, 1837, p. B44).

But even as Darwin begins to more seriously move away from the views of Lyell, embarking upon a project to construct a picture of the natural world in which observed taxonomic structure is a product only of the regular interaction of the laws of nature, he still is not making much, if any, room for chance. The passages above were written around the middle of July 1837, and as he writes the remainder of the B notebook over the ensuing year, all its uses of chance refer only to something like a law of large numbers. (To take just one example, at two points Darwin considers how unlikely it is that any currently extant organism will have offspring still living dozens of generations into the future (Darwin, 1837, pp. B41, B146).) He then enters a long period of slow theoretical work, in which it is difficult to locate any major landmarks (Hodge, 2009, pp. 53, 64). His focus widens during this time, as he starts to consider the impact of the evolution of species on the understanding of humans, including our mental and behavioral faculties, and on religious doctrine. He also begins thinking about how to package what he now calls my theory as a publishable piece of public science, re-reading Sir John Herschel’s Preliminary Discourse on the Study of Natural Philosophy in October of 1838 and taking from it a wealth of advice on how to build a causal theory that would satisfy all the tenets of the Newtonian philosophy of science of his day (Pence, 2018). Chance makes one brief appearance here, but only in the metaphysical notebook M, as Darwin uncharacteristically grapples with the question of free will. [W]e may easily fancy there is such a thing as free will, he writes, as we fancy there is such a thing as chance. — chance governs the descent of a farthing, free will determines our throwing it up. — equall true the two statements (Darwin, 1838a, p. M27). Not exactly an attempt at offering a detailed analysis of the concept, nor indicative of it being particularly important to his thought.

A month later, however, we see that chance remains a conundrum. Darwin is contemplating the transmission of habits across generations—important, he thinks, for the understanding of sexual behavior in humans, a topic to which he would return at length in the Descent of Man—and he notes that the distinction between habits and instincts parallels nicely that between two sources of variation in heredity:

An habitual action must some way affect the brain in a manner which can be transmitted. – this is analogous to a blacksmith having children with strong arms. – The other principle of those children, which chance? produced with strong arms, outliving the weaker ones, may be applicable to the formation of instincts, independently of habits.

(Darwin, 1838b, p. N42)

That is, in the same way that heredity comprises both the inheritance of acquired characters from parents and the generation of novel characters by chance, we should see in species such as humans (with complex patterns of behavior) both the inheritance of acquired behavioral habits as well as the generation by chance of behaviors produced by novel instincts.

One can, however, almost feel the revulsion with which Darwin has underlined the word chance in the passage above, which is emblematic of his approach toward the concept throughout this early period. He realizes, it seems, that the generation of variation appears chancy to the outside observer—connected, in some way, to both environmental change and to the habits and characters of parents, to be sure, but by connections too loose and tenuous to be amenable to direct study. But how else to describe it? What kind of explanation could be offered here that was satisfactory, by the lights of both Darwin’s biology and his philosophy of science? In some form or another, this question would lurk in the background of Darwin’s thought from the mid-1830s until his last works.

It is clear, however, that there is no answer to these questions in Darwin’s early notebooks. The role of chance—as with most of Darwin’s most important contributions to the study of life on earth—enters gradually, piecemeal, as he puzzles out the correct interpretation of the data he collects from the natural