Paleontology and Darwin’s Theory of Evolution: The Subversive Role of Statistics at the End of the...

Published in Journal of the History of Biology November 2015, Volume 48, Issue 4, pp 575–612 https://link.springer.com/article/10.1007/s10739-015-9402-y

Paleontology and Darwin’s Theory of Evolution: The Subversive Role of Statistics at the End of the 19th Century

Abstract: This paper examines the subversive role of statistics paleontology at the end of the 19th and the beginning of the 20th centuries. In particular, I will focus on German paleontology and its relationship with statistics. I argue that in paleontology, the quantitative method was questioned and strongly limited by the first decade of the 20th century because, as its opponents noted, when the fossil record is treated statistically, it was found to generate results openly in conflict with the Darwinian theory of evolution. Essentially, statistics questions the gradual mode of evolution and the role of natural selection. The main objections to statistics were addressed during the meetings at the Kaiserlich-Königliche Geologische Reichsanstalt in Vienna in the 1880s. After having introduced the statistical treatment of the fossil record, I will use the works of Charles Léo Lesquereux (1806-1889), Joachim Barrande (1799-1833), and Henry Shaler Williams (1847-1918) to compare the objections raised in Vienna with how the statistical treatment of the data worked in practice. Furthermore, I will discuss the criticisms of Melchior Neumayr (1845-1890), one of the leading German opponents of statistical paleontology, to show why, and to what extent, statistics were questioned in Vienna. The final part of this paper considers what paleontologists can derive from a statistical notion of data: the necessity of opening a discussion about the completeness and nature of the paleontological data. The Vienna discussion about which method paleontologists should follow offers an interesting case study in order to understand the epistemic tensions within paleontology surrounding Darwin’s theory as well as the variety of non-Darwinian alternatives that emerged from the statistical treatment of the fossil record at the end of the 19th century.

Keywords: Statistics, Paleontology, Data, Fossil Record, Quantity, Melchior Neumayr.

“Wie ich bei einer früheren Gelegenheit auseinandergesetzt habe, ist es vor allem die statistische Methode der Geologie und Paläontologie, welche gegen die Descendenzlehre Argumente geliefert hat.”

Melchior Neumayr

In his textbook Die Stämme des Thierreiches (1889), the German paleontologist Melchior Neumayr

(1845-1890) asserted that the task of paleontology “is to demonstrate that all of the animals and plants

evolved from one or a few basic forms by gradual transformation, and to seek the causes which have led to

this procedure” (Neumayr 1889)1. Neumayr thus understood evolution as a process of gradual, steady, and

slow diversification and organization of living organisms from a common origin. He believed that is the job

of paleontology to demonstrate this constant and gradual process and to elucidate its causes with evidence

from the fossil record. However, Neumayr’s statement was challenged during the last decades of the 19th and

the beginning of the 20th centuries. Few paleontologists questioned the validity of evolution, i.e. the

modification of organisms over time, but most disagreed on its mode and mechanisms. In German-speaking

circles, most of these objections centered around the mathematical treatment of paleontological data.

1 All translations are mine unless otherwise noted.


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This paper analyzes the contested role of statistics2 in paleontology at the end of the 19th and the

beginning of the 20th centuries. I will focus particularly on German paleontology and its relationship with

statistics. Until the later part of the 19th century, a quantitative approach to the fossil record was popular

among German paleontologists, including Heinrich Georg Bronn (1800-1862) and Friedrich Sigismund

Leuckart (1794–1843). This approach was derived from Kameralwissenschaft, i.e. the science of public

administration, which applied surveys and censuses to amass quantitative data that could be analyzed and

depicted in tables. This general approach to quantitative state administration acquired a specifically

biological meaning through Alexander von Humboldt’s botanical arithmetic.3 Statistics were consequently

used to depict biological patterns and processes in deep time and to provide the basis for arguments about the

history of life. I will argue that in paleontology, the quantitative method was evaluated and strongly limited

by the first decade of the 20th century because—as its opponents asserted—a statistical treatment of the fossil

record was found to generate results openly in contrast with the Darwinian theory of evolution4. Statistics

questioned the gradual mode of evolution—particularly the assumption shared by many paleontologists (as

Neumayr) that steady, slow and gradual change is the only correct exemplification of evolution—and the

role of natural selection. For example, by statistically treating the fossil record, the Austrian paleontologist

Theodor Fuchs (1842-1925) argued that the development of the organisms did not follow “a continuous and

uniformly progressive change” as Charles Darwin (1809-1882) suggested, but it is characterized by a long

timespan of “relative calm with shorter periods of transformation [relativer Ruhe mit kürzeren Epochen der

Umwandlung]” (Fuchs 1880) or based on his tabular representation of the coal formations of North America,

Charles Léo Lesquereux (1806-1889) claimed that there were no intermediate forms between the extinct

fossils types and the following ones (Lesquereux 1860a).

Many leading German paleontologists successfully argued that paleontology could not accept the

results of these statistical analyses because Darwin’s theory provided an essential biological foundation to

2 During the entire 19th century, paleontologists conceived statistics exactly as Gottfried Achenwall (1719–

1772) used it: a descriptive and comparative study of particular objects presented in a specific area. 3 See for instance (Browne 1983). 4 As Melchior Neumayr noticed it, the statistical approach did not necessarily challenge the Darwinian model,

but rather it happened that proponents of statistical approaches came to this conclusion. In fact, the statistical approach is not intrinsically in tension with Darwinian theory of evolution as the paleobiological revolution of the 1970s has shown. See above and the conclusion of this paper.


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develop paleontology’s autonomy as a discipline (i.e. to free it from geology). The great German

paleontologist Karl Alfred von Zittel had a prominent role in rejecting the statistical approach to the fossil

record in his two works, Handbuch der Palaeontologie (1876) and Grundzüge der Palaeontologie

(Palaeozoologie) (1895). Zittel argued that fossils should be understood as data which could individually aid

morphological reconstructions and studies of biological function that supported the Darwinian theory, rather

than as a source of abstracted generalized information for numerical analysis as his teacher, Bronn, had

urged5. Hence, the mathematical treatment of the fossil record was strongly opposed by several German

paleontologists in favor of descriptive and morphological investigations.

The crux of the matter, as Neumayr put it, was that

“If we compare the results [obtained by various geologists and paleontologists] regarding the theory of evolution, we find that […] the results formulated are essentially different depending on the applied research method. Those who seek to establish series of forms [Formenreihen] by comparing closely related species of the common genera, or those who seek to detect changes through morphological pathways almost obtain always a result favorable to the Darwinian theory of evolution. We find an opposite result—not always but in the majority of cases—where a more or less purely statistical treatment is applied [eine mehr oder weniger rein statistische Behandlung angewendet wird].” (Neumayr 1889)

On the one hand, support for Darwinian evolution is found among paleontologists working in a comparative

morphological tradition in order to arrive at a series of forms [Formenreihen]6. Opposition to Darwin is

found among those paleontologists who use the comparison between numbers and statistics as their main

method. This opposition is not based on the distinction between geology and paleontology, but is concerned

with the proper use of mathematical methods within the paleontological sciences. Since Neumayr was a

direct student of Albert Oppel (1831–1865), Wilhelm Heinrich Waagen (1841-1900) and Karl Alfred von

5 The German paleontologist Otto Jaekel (1863-1929) asserted that “After Karl Alfred v. Zittel had critically

looked through all the material of our science and uniformly ordered it, as Linnaeus did with living organisms, paleontology at least put on children’s shoes for independent movement” (Jaekel 1907).

6 In 1869, Wilhelm Heinrich Waagen found a method to globally reading the fossils in order to show the genetic relationships among them. These genetic relationships are named series of forms [Formenreihen]. Waagen took the name from Franz Martin Hilgendorf’s works (1839–1904). Through this epistemic practice Waagen was able to point out that evolution is a gradual Darwinian process of descent with modification. As the paleontologist Carl Diener (1862-1928) affirms, the series of forms [Formenreihen] provides important insight into the causes of the evolution. One of these is natural selection: “The task for Paleontology is to seek the genealogical series of forms [Formenreihen]. Their members seem to be so closely temporally linked, that the series of forms may be considered as evidence for the gradual transmutation of one species into one as required by the theory of natural selection [von der Selektionstheorie geforderte].” (Diener 1910) Therefore the fossil record meant as a member of a Formenreihe offers the evidence for the evolution theory, its mode and its causes. See (Tamborini 2015a; Waagen 1869).


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Zittel (1839-1904), he chose to follow the former ‘Darwinian’ method: he tried to develop Formenreihen

based upon morphological identifications, actively rejecting the quantitative approach.

This paper reconstructs the debate surrounding the use of statistics during the last decades of the 19th

century. I will consider the arguments for and against the quantitative methods raised particularly in the

German-speaking community. These were addressed mostly during the meetings at the Kaiserlich-

Königliche Geologische Reichsanstalt in Vienna around 1880. The geological institute was established in

Vienna in 1849 and it was one of the main centers for geology and paleontology in Europe (Bachl-Hofmann

1999; Schübl 2010). However, this debate went beyond Vienna. The work of two paleontologists in the

United States perfectly illustrates both the assumptions behind the statistical method, and as its potential

pitfalls. I will use the works of Charles Léo Lesquereux and Henry Shaler Williams (1847-1918) to illustrate

the statistical treatment of data that German paleontologists such as Neumayr objected to so strongly.

Besides the discussion about which method paleontologists should follow, what is particularly

interesting about the Vienna debate is that it offers an interesting case study in order to understand the

epistemic tensions within paleontology surrounding Darwin’s theory at the end of 19th century as well as the

variety of non-Darwinian alternatives that emerged from the statistical treatment of the fossil record. On the

one hand, there were paleontologists such as Heinrich G. Bronn, Joachim Barrande (1799-1833), Charles

Léo Lesquereux, Henry Shaler Williams, and Theodor Fuchs who challenged the view of evolution proposed

by Darwin. Employing a broadly statistical analysis of the fossil record, they questioned whether evolution is

a slow, gradual, and steady phenomenon that operates only by means of natural selection. Consequently,

they proposed different mechanisms in order to understand how biodiversity has changed through geological

time. For example, Williams asserted that “evolution of fundamental characters [is] relatively rapid and this

rapid evolution [is] difficult to account for by any working of natural selection” (Williams 1895) and

therefore he championed orthogenetic evolution.

On the other hand, Melchior Neumayr and Karl Zittel defended Darwin’s theory. They supported

Darwin because he gave the theory of evolution a stable foundation for promoting the importance of

paleontology as biological discipline: “so long as there was no stabile belief in the variation of species the

importance of paleontology could not be so exceptional as it is today” (Neumayr 1889). Hence, for the sake


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of saving the disciplinary autonomy of paleontology and its pivotal role Neumayr and Zittel were

particularly suspicious of any non-Darwinian mechanism of evolution. It is important to stress that the

statistical approach does not necessarily oppose the Darwinian position; rather, it is a contingent historical

fact that, in the later 19th and early 20th centuries, opponents of Darwinism found support for their view in

quantitative analysis of fossil data (in part because of limitations to available data at the time). This in turn

led paleontologists with strong commitments to Darwin to reject those quantitative methods, often by

questioning whether fossil data was of sufficient quality to justify a statistical approach. As a result, in the

minds of many paleontologists statistical treatments became associated with anti-Darwinian positions, but

the contingency of this state of affairs is underlined by the fact that, a century later, statistical approaches

were convincingly mustered by paleontologists to support broadly Darwinian arguments, as the conclusion

of this paper will discuss. Nonetheless, my analysis provides important context for understanding debates

surrounding the various non-Darwinian theories that proliferated in paleontology during the late 19th and

early 20th century. Furthermore, this paper reveals an ironic twist in the subsequent development of

paleontology: while the morphological approach supported by 19th century Darwinist paleontologists would

be established in Germany during the first decades of the 20th century, it became associated with the

decidedly non-Darwinian school of orthogenesis or “Typostrophism” promoted by Karl Beurlen (1901-

1985), Otto Schindewolf (1896-1971), and others.7 In contrast, the quantitative method, which flourished

after the Modern Evolutionary Synthesis in the work of neo-Darwinian American paleontologists such as

G.G. Simpson (1902-1984) and Norman Newell (1919-2004), would eventually constitute the backbone of

the American paleobiological revolution of the 1970s (Sepkoski 2012a).

The paper will begin by briefly surveying the use of mathematics in paleontological sciences during

the 19th century. Next, I will explore the Vienna debate on the rejection of statistics circa 1890. Having

illustrated how the mathematical treatment actually works by studying Bronn, Lesquereux, Barrande, and

Williams’ investigation, I will then deal with Neumayr’s criticisms to show why and to what extent the use

7 See (Reif 1983).


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of statistics was questioned. The final part of this paper focuses on the legacy of the statistical approach,

which stimulated a discussion about the epistemic status8 of fossil data in paleontology.

Statistical Treatment of Data: an Introduction

Paleontology was long established in Germany, before Darwin’s theory, as an approach to examining the

fossil record for evidence about the development of life over time. Generally, this took the form of statistical

analysis: Heinrich G. Bronn was probably the most influential paleontologist to apply mathematical

techniques to examine biological patterns and processes. The “weight of his education” (Fleck 1929) played

an essential role in this choice. In fact, Bronn’s training and appointment at university of Heidelberg was in

Kameralwissenschaft. From his study of public administration he learnt the importance of treating data as a

record of data9.

Bronn’s quantitative approach inspired many contemporary paleontologists to approach the fossil

record as a statistical ensemble. It is therefore important to deal with Bronn’s practice to understand this

important “style of reasoning” (see, for instance, Hacking 2002). Bronn’s starting point was taxonomical and

morphological: in order to correctly investigate how diversity has changed over deep time, the paleontologist

has to assess his data for accuracy and sources of bias. For example, Bronn noticed that many authors had

classified the same specimen under different taxonomical entries and this misidentification could generate a

flawed starting point for further quantitative analyses. This was not an insignificant issue because a small

difference in the temporal position of the fossils or an error in their taxonomic identification could bias the

results of any statistical analysis performed on them. Thus, he determined that the existing fossil record,

collected by generations of previous paleontologists, needed to be revised and standardized. In order to

accomplish this preliminary task, Bronn conducted a major taxonomic revision of paleontological data,

which he published as the massive Nomenclator paleontologicus (1849), in which all plant and animal

fossilized species so far unearthed were alphabetically listed.

8 It is important to stress though that although the actions of the paleontologists taken into account in this paper

are described as epistemic, the subject matter of their debate was ontological. In fact, this debate was based upon a classical ontological question: what is the fossil record? I thank the anonymous referee for having pointed out this.

9 Concerning this point, I would like to recall Car August Ludwig von Schlözer’s (1725-1809) maxims: “statistics is history without motion; history is statistics in motion” (quoted in (Desrosières 1998)). This approach toward statistics and history has indubitably marked Bronn’s thought.


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Bronn’s approach thus took taxonomic revision as an essential starting point for further statistical

analysis: “my intention”, wrote Bronn, “is to list and enumerate every species according to its definite name

and its correct genus” (Bronn 1849a). Once the valid taxonomic categories had been established, he

reasoned, standardized morphological criteria could be applied to the placement of new specimens in the

existing fossil record. For this reason, in addition to listing the taxonomic name, Bronn’s Nomenclator

provided references to the appropriate literature to identify the morphological features of each genus listed.

For example, the figure 1 shows a typical page of Bronn’s Nomenclator paleontologicus: it lists all the

species and individuals of the genus Lyriodon together with the literature necessary to recognize and classify

their morphological features. Hence, Bronn’s quantitative approach began with a correct identification of

taxa based upon a wide use of existing paleontological literature. In addition to taxonomic and

morphological identification, Bronn also included other “metadata” useful for further classification of his

data, such as locality information. For example, the entry for the species angulatus includes the letter “n” to

symbolize that it was found in the Lower Jurassic.


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Figure 1 typical page of Bronn’s Nomenclator paleontologicus.

The information presented in the Nomenclator paleontologicus was, however, only the starting point for

Bronn’s further quantitative analysis. In fact, Bronn presented an entirely reconfigured version of his

taxonomic catalog as a collection of numerical data in a companion volume to the Nomenclator. In the

Enumerator paleontologicus (1849), he chronologically and systematically tabulated the fossils listed in the

Nomenclator stressing how many and in which places they were found: by transposing the taxonomic list to

the temporal and spatial format of the table, Bronn reconceptualized his data as a statistical history of

changes in biodiversity and biogeography over deep time. The figure 2 reproduces one of the over 745 tables

presented in the Nomenclator paleontologicus. It lists all the known species of the genus Lyriodon by sorting


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them according to the stratigraphic location in which they were found. The tabular visualization of the fossil

record allowed the paleontologist to easily count how many species and genera appeared on the earth’s

surface (87 in this case).

Figure 2 An example of Bronn’s tabular data.

By relying on Bronn’s lists and tables, the paleontologist could consequently pose and answer

important questions about the history of life: Bronn invented a new discipline for the purpose of

mathematically tracing and narrating historical patterns from his tabular data. Called paläontologische Statik,

this aimed to give numerical and quantitative treatment to the fossils previously tabulated and listed. For

instance, Bronn calculated the geographical distribution of genera and species (figure 3) or depicted the


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pattern of diversity of some genera stressing whether their development was gradual and linear or rapid and

abrupt (figure 4).

Figure 3 Bronn’s table of geographical distribution.

Figure 4 Bronn’s table of development and distribution of various genera.

Hence, Bronn conceived the fossil record as a record of data (Sepkoski 2012b): it was meant as a

discrete numerical unity which enabled narration of a complete history of past events. By virtue of a

quantitative reading, Bronn identified biological patterns and even proposed general biological laws (though

he was careful to qualify these as being probabilistic rather than certain) (Bronn 1841-1849). Although he


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sympathized with the Darwinian theory of evolution (see for instance Bronn’s translation of the Origin of

Species (Darwin 1860)), Bronn’s laws were not in agreement with Darwin’s mechanism (Rupke 2005;

Glidoff 2008; Junker 1991; Baron 1961; Querner 1985; Nyhart 1995).

Bronn, however, was not the only naturalist who used this method10: Christian Keferstein (1784-

1866), Friedrich Sigismund Leuckart (1794–1843), Hermann Hoffmann (1819-1891), and Rudolf Wagner

(1805-1864) developed a statistical treatment of natural data as well based upon a similar, albeit less

sophisticated, practice. Their statistical approach was grounded on the simple idea that by numerically

comparing the number of collected fossils with that of living organisms, the naturalist could acquire a degree

of knowledge about the development of life over time. By visualizing their data in tables, all these naturalists

tried to develop a quantitative method for discovering the laws of the geographic distribution of the species

within the history of the earth: first, they compared the pattern of distribution of the fossils with the current

dispersion of the specimens; second, they identified a degree of regularity behind the distribution of the

records in the different epochs. For example, Leuckart asserted that after rigorous investigation the number

of fossilized plants and animals has been in constant increase from the time of their creation. That means that

the complexity of the organisms has been increasing since their origin: “there is infinitely more species and

variety among living beings in present creation than in the prehistoric world”. (Leuckart 1835) Or by

accomplishing a statistical treatment of data, Bronn was able to compare the number of the plant and animal

fossils, count the total number of families, and find the ratio between families and species (Bronn 1858,

1848, 1831).

Hence, during the first half of the 19th century, the fossil record was often used as raw material to

narrate the history of earth. The statistical treatment revealed, in quantitative terms, how the structure of the

organisms and the complexity of the former world have changed. Additionally, statistical analyses were used

to enumerate the diversity and disparity of the forms of life in the earth11. These methods were extremely

10 Many paleontologists used the statistical method during the 19th century. For instance, Martin J. Rudwick in

his “Charles Lyell’s Dream of a Statistical Paleontology” (1978) deals with Charles Lyell (1797-1875) and Barthelemy de Basterot (1800-1887) and provides valuable considerations about their statistical methods (Rudwick 1978).

11 Among others, I would like to recall the name of Christian Keferstein (1784-1866). He was a “commendable researcher and prolific writer” (Mayer, 1977) in the field of geognosy and mineralogy. In his Die Naturgeschichte des Erdkörpers in ihren ersten Grundzügen (1834), he drew up an alphabetic list of all the fossil record discovered. He


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simple: first, one collected fossils; second, one arranged in a tabular form these collected fossils; third, one

made numerical comparison between them so as to reveal patterns of distribution; fourth – and most

demandingly – one tries to discover the biological process behind these patterns.

However, as Bronn noted, a crucial question arose from this approach: “if we attempt to institute a

comparison between the distinguishable fossil beings and the present creation, what is the present creation?

Does it consist of 100,000 or 200,000 species of animals, of 70,000 or 150,000 species of plants? And how

many genera does it contain? What is a species? And what indeed is a genus?” (Bronn 1849b) Thus a

comparison between fossil species and living species is problematic. Even if the paleontologist is

simultaneously a great botanist and an excellent zoologist, he will commit errors. Bronn was warning the

zoological community of the risks related to such quantitative investigations. At the same time, however, he

was convinced that paleontologists could overcome doubts connected with the statistical approach to

paleontology by anticipating potential shortcomings12. He argued that the quantitative paleontological

enterprise should not be abandoned: “We are not bound to wait for [the solution of the problems raised]”, on

the contrary we should keep in mind “when instituting this comparison that all the imperfections just

mentioned attach to this comparison.” (Ibid.)

Bronn’s point was that through a comparison of data, paleontology, or broadly speaking natural

history, could discover trends and patterns despite the imperfections attached to comparative methods and to

the notion of the fossil record. But how can this comparison be done? How can the paleontologist secure his

discipline from all the imperfections and errors that inevitably seem to belong to it? The answer lies in the

training of the paleontologist’s skill. On the one hand, the paleontologist has to improve his skills to avoid

errors in narrating the correct history of the earth; on the other, he needs to reconsider the imperfections of

the fossil record in order to acknowledge them, i.e. he has to reconsider the features of the fossil record thus

providing a new definition of this epistemic object. I will argue that a statistical treatment of data enables

reconsideration of the epistemic nature of the fossil record. Nevertheless, paleontologists did not take

advantage of this method between 1859 and the beginning of 20th century. Instead of developing and refining

divided those data into the species and genera and for each of them he listed the number of found fossils and living species.

12 In order to criticize the statistical method, Neumayr will use the same argument reaching though conclusions different from Bronn.


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it, they put it aside to save the biological basis for paleontology, namely the Darwinian theory of evolution,

which meant focusing instead on descriptive morphological research. According to Zittel, Bronn’s student in

Heidelberg, by describing the morphological features of the fossil record, the paleontologist provided a rich

collection of facts, which can be used to support the Darwinian theory of evolution. Hence, by developing a

morphological approach Zittel successfully aimed at emancipating paleontology from geology – pushing

paleontology toward biology.

The Statistical Treatment of the Fossil Record

The research into patterns of fossil distribution constituted a hot topic within the paleontological

sciences of the 19th century. This was a method commonly employed within the geographical and botanical

sciences. As Janet Browne shows in The Secular Ark (1983), “botanical arithmetic was to natural history

what mathematics was to the study of electromagnetism, heat” (Browne 1983). The link between botanical

arithmetic and paleontological data was Leopold von Buch (1774-1853). In 1825, Buch published

Physikalische Beschreibung Kanarischen Inseln, the first part of which is entitled Statistical overview of the

Canaries. It gives an overview of the surface, population, and density of the island assisted by the statistical

employment of data and tables. Buch’s book did not offer particular paleontological insights; however, his

status as an authority in geological sciences meant that his methods captured the attention of his colleagues13.

In practice, geologists and paleontologists followed Buch’s example. During the entire 19th century,

geologists used tables and statistical tools to survey the objects of a particular locality. The aim of these

works was mainly to take a census of the lithological and paleontological formations of a specific area. A

few exceptions, such as the previously cited works of Bronn and Leuckart, were able to direct the aim of

survey towards a more biological target, developing their statistical analysis of the history of life without any

evolutionary or Darwinian assumptions. However, the statistical tradition did continue after the publication

of Darwin’s Origin of Species in 1859. For instance, Leo Lesquereux’s reflections show us how statistics

was used to investigate the features of the evolution of life in deep time. Neumayr was perfectly aware of

13 As Zittel remarks “Leopold von Buch was rightly regarded as the greatest geologist of his time. He had

studied in every domain of geology; he was familiar with a large part of Europe. Wherever he went, he willingly and freely communicated his own knowledge to others, and ever rejoiced to be able to assist by his money or his influence any one in whom he detected a true devotion to science.” (Zittel 1901)


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Lesquereux’s analyses, since these were discussed during the meetings at the Geologische Reichsanstalt in

Vienna. Neumayr addressed his criticisms therefore also to Lesquereux’s results.

Lesquereux was one of the most important paleobotanists of the 19th century. Although he was born

in Switzerland, he received his scientific education in America, thanks to Louis Agassiz’s friendship.

Lesquereux took part in numerous surveys in Pennsylvania and the American Midwest, contributing to the

identification of numerous plant species, and wrote a series of papers on Some questions concerning the coal

formations of North America between 1859 and 1863. In a letter to George Maw on February 28th, 1863,

Darwin recognized the significance of these papers: “almost the best papers I have ever read on Coal are

some lately published in late numbers of Sillimans American Journal by Lesquereux.— They would be

worth your reading & you will like them all the better, as they give the ‘Origin of Species’ a few little

unpleasant kicks.—” [italics mine] (Buckhardt 1999) These little unpleasant kicks are the result of

Lesquereux’s statistical treatment of the fossil record.

In the second part of this series of papers, it was Lesquereux’s explicit aim to “merely expose the

facts that appear surely ascertained by a long and careful exploration of the coal fields of North America,

leaving the naturalist-philosopher to take from these facts any conclusion that may appear just to him.”

(Lesquereux 1860b) To accomplish this, he attempted to discover the relationship between the plants in

America and Europe found in the same geological formations. Following the practice established by Bronn,

he listed the number of species peculiar to America, to Europe and in common to both in a table.


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Figure 5 Table of genera of Coal plants presented in America, Europe or in both of them. Taken from (Lesquereux 1860b)

By a simple comparison of data, Lesquereux showed the relations between the American fauna and the

European one: from 654 species identified, about 160 were present in America and 350 in Europe. Although

the number of species is greater in Europe, we can find in America “peculiar forms or types, which are not

seen in Europe”. Next, Lesquereux extended this numerical analysis to understand the stratigraphical

composition of the formation. By correlating the different layers and the diverse ratios, he noticed a decrease

in number of some species of trees: “As fast as these species of trees decrease in number, the ferns mostly of

small size invade the coal-fields. They become predominant and show the greatest number of species at the

base of the Mahoning sandstone.” (Lesquereux 1860a) This statement is based upon a stratigraphical

correlation of the strata with their numerical relations; at first glace it appears to be a merely stratigraphic

observation. However, Lesquereux immediately stressed its evolutionary meaning. As he wrote to Darwin, “I

was just engaged in a general examination of the fossil Flora of the coal measures of North America and

could not but try to test the value of some of your systematic conclusions in applying them to what I saw of

the vegetation of this ancient world.” (Lesquereux 1864) The numerical distribution of these two species


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offers the perfect test bench for the Darwinian theory of evolution: “Both genera [of plant, namely

Lepidodendron and Lycopodites] appear or at least disappear at the same time, and are replaced by typical

forms, which have no analogy whatever with them.” (Lesquereux 1860a) After many observations,

Lesquereux concluded that

“The distribution of the ferns in the coal-measures is equally contrary to the supposition of a change of species by successive variations. They appear, it is true, grouped together, in a kind of relation between contemporaneous species; but we do not see, either before or after any of them, a trace of an intermediate form between the lost types and the following ones.” [italics mine] (Ibid.)

By means of a simple mathematical relation applied to tabular data, Lesquereux showed a

mechanism of development which was not in line with Darwin’s theory: there were no intermediate forms

between the extinction of the Lepidodendron and Lycopodites and the appearance of the ferns.

Lesquereux’s statistical practice was analogous to Bronn’s paleontological statics. First, the Swiss-born

paleobotanist revised his taxonomic data based on a careful evaluation of morphological differences between

groups. Second, he tabulated the classified species to visualize both their quantity and stratigraphic location.

This step was essential because a change in number of species found in two contiguous strata would have

implied a morphological, i.e. evolutionary, change. Third, he worked with these discrete tabular data to

illustrate and explain patterns of global and local diversity through geological time. It was through statistical

tabulation that Leusquereux found, for instance, that there were no intermediate forms between certain

successive plant taxa, allowing him to argue therefore that it is “useless […] to argue on the distribution of

the coal-flora as resulting from successive variations of species and of genera” (ibid.) as Darwin claimed.

Leusquereux’s study not only revealed a difficulty related to the gradualism of the Darwinian theory,

but through a mathematical treatment of data, it specifically questioned the explanatory power of natural

selection:

“Moreover, the numerous species of Neuropteris and Pecopteris appear at coal No.3 and 4 in the middle of the coal-measures, and do not ascend higher, while those species which should be considered as originators or parents and consequently ought to be destroyed (from the law of selection) by their offspring, continue to predominate to the top of the coal-measures” (Ibid.)


17

Lesquereux therefore addressed his doubts to both the mode and mechanism of Darwin’s theory. This was

possible by treating the fossil record as a record of data within a broader statistical framework: tables and

statistics enabled broader biological investigations.

Similarly, by using statistical tools, the contemporary French geologist Joachim Barrande (1799–

1883) arrived at even more radical conclusions: he was “intellectually by far the most dangerous opponent of

evolution” (Marcon 1883). Barrande presented his result in twenty-one quarto volumes entitled Systême

silurien du centre de la Bohême (1852-1894). In this work, he described and classified all the fossils of the

Bohemian Silurian basin portraying its stages and structures. The supplement to the first volume was

extensively discussed at the Kaiserlich-Königliche Geologische Reichsanstalt (Neumayr 1889; Tietzte 1873)

because Barrande numerically compared the Paleozoic with Triassic fauna to question the validity of

Darwinian evolution. By means of tables and statistics, he calculated the number of the fossilized species

found in every geological period:

Figure 6 Tabular representation of the number of fossilized species found in different geological periods. The periods are listed according to the numbers of fossilized species found and not chronologically.

Barrande used this simple statistical survey to challenge the Darwinian mechanism of evolution. The

data show, in fact, that there is no gradualism at all. On the contrary, the “greatest diversity can be found at

the beginning and at end of the entire considered geological period” (i.e. in the Silurian and Tertiary),

whereas it decreased towards the Permian. He concluded this survey asserting that “the cause of the

accumulation of these animal forms in two contrasting epochs remains inexplicable even in the light of all

the [biological] theories”. However, since paleontologists clearly observe and tabulate the apparently

irregular distribution of forms and can therefore numerically analyze the relative degree of organization and

distribution of the fossilized animals, “we”, wrote Barrade, “are forced to recognize that the influence of

secondary causes, such as the natural selection had to be more or less insignificant” (Barrande 1872).

Barrande claimed thus that the tabular data and quantitative analyses highlight features of the fossil record


18

that are inconsistent with the Darwinian model of evolution. Furthermore, based on numerical data, he

asserted that mutations are only special cases of variations within species: they play no role in the formation

of new species. This last result was openly in contrast with the Darwinian framework adopted by several

paleontologists. In fact, by distinguishing the changes in time (mutations) from the transformation in space

(variations), Waagen claimed that evolution was a slow and gradual process exactly as Darwin had theorized

it (Waagen 1869).

Both Barrande and Lesquereux—and Bronn before them—showed, therefore, that the statistical

method can generate results which contest Darwin’s theory. As Neumayr would lament, this happens “not

always, but in the majority of cases” and unfortunately “it cannot be denied that the results obtained by this

method seem to have an overwhelming evidence at least at first blush.” (Neumayr 1889) The statistical

approach to the fossil record has an apparently stunning evidential value; nevertheless, it was strongly

discouraged, since it undermined the status of paleontology as an autonomous biological science. In the next

section, I will analyze the main assumption behind the quantitative treatment of the fossil record. I will argue

that the results of statistical treatment of fossils can be considered valid only if the fossil record is seen as a

complete set of data. Only if fossils constitute reliable and complete data, can they be inserted into a

mathematical framework. Hence, the statistical treatment of the fossil record not only generated results in

contrast with the Darwinian theory of evolution, but also encouraged proponents of statistical paleontology

to challenge the pervasive assumption that the fossil record itself is an incomplete data set.

On the Presumed Incompleteness of the Paleontological Tradition

In his investigations, Bronn set bio-stratigraphical charts whereby the fossil record can be read. Bronn’s

paleontological statics, i.e. a statistical treatment of paleontological data, was considered an intrinsically

valid means of reading the fossil record. This reading, however, could be accomplished only if the fossil

record was thought to be patchy but not misleading or biased. Fossils are, in fact, imperfect and incomplete

material objects that require integration with other disciplines in order to be used fruitfully. Bronn’s practice

was thus a reaction to the imperfection of the material object called the fossil record. In fact, as Bronn wrote

in Untersuchungen über die Entwickelungs-Gesetze der organischen Welt während der Bildungs-Zeit

unserer Erd-Oberfläche (1858), “the earth crust is a great book which pages are incomplete, broken, jumbled


19

up and faded before us; we need to organize them and to search to supplement what is missing. The alphabet,

in which the book was written, was long unfamiliar to us; we had misunderstood it and began first to

decipher and comprehend it as we began to look for the key in our present nature” (Bronn 1858) 14. This was

a very common attitude. For instance, both Charles Lyell (1797-1875) and Darwin considered the fossil

record as incomplete and imperfect (Sepkoski 2012a): as Darwin wrote, “I look at the natural geological

record, as a history of the world imperfectly kept, and written in a changing dialect; of this history we

possess the last volume alone, relating only to two or three countries. Of this volume, only here and there a

short chapter has been preserved, and of each page, only here and there a few lines.” (Darwin 1964)

The American paleontologist Henry Shaler Williams 15 advocated the statistical method in

paleontology at the end of the 19th century and conceived the fossil record oppositely. In his textbooks,

Geological Biology (1895), Williams affirmed that regarding the question “‘What are fossils?’ the concise

answer is: “Fossils are traces of organisms buried in the rocks” that “chiefly represent the hard parts of

organisms” (Williams 1895). At first glance, this statement seems quite obvious and intuitive: it is, in fact,

quite well known that the materials from which animal fossils are derived consist mostly of the hard-parts of

animals. This was the main source of embarrassment for paleontological investigations. However, Williams

was not highlighting this epistemic fault, he was emphasizing, rather, the qualities of the fossil record:

“Fossils represent organisms, but almost universally they represent the hard parts of living organisms; hence the most valuable lessons to be learned from fossils must be derived from the study of the hard parts of organisms. These hard parts are the parts which have attained definite and fixed form during the life development of the individual.” (Ibid.)

Although the fossil record represents only the hard parts of organisms, they are the visible final results of a

process of evolution and, as such, reliable sources for biological investigations. Williams went further

stressing the differences between the soft and hard parts as presented in the fossil record: “soft parts, or

organs, are adjustable to changing exterior conditions, but its hard parts are already adjusted, and, therefore,

they are an expression of the working adjustment of the species, to the conditions of its environment, at the

14 English translation in (Sepkoski 2012b). 15 Henry Shaler Williams had graduated from Yale in 1868 and taught at Cornell University till 1892. In that

year, he succeeded James Dwight Dana (1813–1895) at Yale till 1904. See (Brice 2000).


20

particular time in which it lived.” (Ibid.) The weaknesses of paleontological data are therefore

simultaneously strengths: the hard parts represented in the fossil record are a reliable source for studying the

line of biological development16 with geological time, since “the hard parts […] represent the royal line of

succession for the geological ages.”(Ibid.)

This point is essential because it influences what can be done with the fossil record and, a fortiori,

paleontology. The argument is not limited to Williams’s thought alone, but has a global validity: many

supporters of the quantitative treatment of the fossil shared it, especially those who took part in the meetings

at the Austrian Federal Geological Office [kaiserlich-königliche Geologische Reichsanstalt]. The

paleontologist Theodor Fuchs was a supporter of the statistical method and endorsed exactly the same

position: he strongly defended the mathematical treatment of data and the related completeness of the fossil

record. In fact, in a meeting at the Geologischen Reichsanstalt, he vehemently endorsed the statistical

treatment of the fossil record against his colleague Neumayr. A section of the meeting of the Austrian

Federal Geological Office on 16th December 1879 is dedicated to Fuchs’ talk on die präsumirte

Unvollständigkeit der paläontologischen Ueberlieferung [On the Presumed Incompleteness of the

Paleontological Tradition]. Fuchs began by asserting that if the incompleteness of the paleontological

tradition [Ueberlieferung] corresponded to reality, then “we would have to completely abstain to consider

general issues, such as those raised by Darwinian doctrine, in the light of paleontology” (Fuchs 1879). If we

dub paleontological data and experience as incomplete, then not only is there no room for paleontology

within the evolutionary theory, but also the Darwinian theory of evolution could not be validated by

paleontology. On the contrary, Fuchs asserted that paleontological flora and fauna “is, in some parts,

extraordinarily complete [data]”.

To prove this point, Fuchs stressed the importance of maintaining a distinction between the hard and

soft parts of organisms. The fossil record contains two kinds of organisms: on the one hand, we have very

early organisms with only soft parts; on the other, organisms with resistant [widerstandskräftige] hard parts

that must be treated as fossils from later eras [Fossilien der Nachwelt]. The former set of data is only

16 As Williams wrote, “the history of organisms, which we particularly trace in the study of fossils, is not the

history of imperfect organisms struggling towards perfection, but it is the history, for each age and epoch, of the perfected adjustment of the organisms of the time to the particular conditions of environment in which they lived.” (Williams 1895)


21

fragmentary; whereas, the latter set, within the paleontological tradition, is “extremely complete” [äusserst

vollständige]. Given the difference in the nature and kinds of data preserved, Fuchs made his point about the

completeness of the paleontological Ueberlieferung by showing that the number of fossils gathered is

representative of the former world. To drive his point home, he carried out a quantitative and statistical

comparison using the collected data17. For instance, “Appelius found in the Tyrrhenian Sea 337 species of

Mollusca. Of these 337 species, he was able to identify 300 also in the quaternary Panchina of Livorno and

therefore one could study the fauna of the Tyrrhenian from those fossils.” [Italics mine] (Ibid.)

Hence fossils, which contain hard parts, accurately represent the former world and can be correctly

used to draw conclusions about evolution. If the Darwinian theory is correct as concerns those organisms

with soft parts—as for instance jellyfish, insects, and birds—then it should be likewise for those with

primarily hard parts such as corals or mollusks.18

Both Fuchs and Williams shared a common argumentative approach: they needed the fossil record to

advocate its own completeness and its reliability, as is necessary for further statistical treatment. If ‘raw’

paleontological data is already biased, then a statistical treatment has no epistemic validity at all. Although

both paleontologists stressed and defended the reliability of the fossil record, they used slightly different

techniques. Williams used the soft/hard part distinction to emphasize the reliability of paleontological data

for aiding evolutionary processes. His argumentative tactics can be drawn in this way: given that i) the fossil

record chiefly represents the hard parts of organisms and ii) the hard parts of organisms are “an expression of

the working adjustment of the species”, it follows from i) and ii) that iii) the reliability of the fossil record is

rescued. Fossils directly testify to the mechanism of evolution and therefore the paleontologist can put them

into a statistical framework. In this way, Williams stressed that both vertebrate and invertebrate paleontology

can say something about the theory of evolution. Fuchs, on the contrary, recognized this capacity only in

invertebrate paleontology. By carefully distinguishing between the chemical components of the organism, he

argued that “corals, sea urchins, shells show [the Darwinian principles] as well”.

17 Unfortunately, only a few of them are reported in the printed version of the talk. 18 As Fuchs explicitly asserts: “if the Darwinian principles are correct, then that can be shown by corals, sea

urchins, shells and so forth show as well.”


22

The degree of reliability of the fossil record is thus fundamental, and the ability of paleontology to

speak about evolutionary theory depends upon it: the quality of the data has more epistemic weight in a

science that is at first glance merely quantitative. It is thus not surprising that the nature and the quality of the

fossil record prompted a rather heated debate during those years. To summarize, the fundamental issue at

stake concerns the nature of the fossil record: is the fossil record incomplete, patchy, and biased? The

supporters of the quantitative method were willing to give a new ontological status to the allegedly

incomplete and imperfect fossil record so that it could be employed in a statistical framework by literally19

reading it: the fossil record is an extraordinary complete datasets. The opponents, on the other hand, stressed

the incomplete nature of the fossil record to prevent their further statistical analysis. The nature of the fossil

record was the central point of discussion in the meetings of the Viennese geological institute, and the

outcome of these discussions had a profound influence further development of paleontological methods in

German-speaking paleontology.

In a meeting on 13th January, 1880, the paleontologist Rudolf Hoernes20 spoke in opposition to

Fuchs’ concept of the fossil record. Hoernes’s talk was an answer to Fuchs’ claim regarding the

completeness of the fossil record. He immediately underlined the matter of the debate, identifying that

Fuchs’s paper was, in reality, an attack on the Darwinian theory of evolution and should be read as an

“introduction of a larger campaign against the Descendenzlehre”. Fuchs — Hoernes asserted — had tried to

make his point and to contradict the Darwinian theory on the basis of distorted and poorly interpreted

statistical facts. Therefore, Hoernes questioned the validity of Fuchs’ investigation by pointing to his biased

assumptions. For instance, he asserted that if the interpretation of the external hard parts is based on isolated

bones, then it “is quite uncertain and in no way can replace the knowledge of the whole organism” (Hoernes

1880). Or again, “no one will dare today to assert, with all certainty, the full identity of twenty diluvial

hoofed animals with the living ones merely because their hard parts show a large agreement”. Hoernes’

conclusion was that the statistical analysis could neither prove nor save the quality of the fossil record.

19 See p. 25. 20 Rudolf Hoernes (1850-1912) was an Austrian paleontologist, the youngest son of the famous paleontologist

Moritz Hoernes (1815-1868). In 1856, Moritz Hoernes published a short paper in Jahrbuch der Kaiserlich-Königlichen Geologischen Reichsanstalt about Die fossilen Mollusken des Tertiärbeckens von Wien. In this paper, Moritz Hoernes accomplished one of the first gradual phyletic series of the Cancellaria cancellata.


23

Furthermore, taxonomic problems were directly connected with a poverty in the paleontological material;

therefore paleontological data were, in principle, biased and statistical methods should be avoided.

Four years later, Hoernes shored up this point in his textbook Elemente der Palaeontologie (1884).

As he tells us in his introduction, paleontology deals with fossils and aims to discuss their biological

relationships, their temporal and spatial distribution and their genetic relationships. However, “the

achievement of the ideal purpose of paleontology is significantly stopped and hindered by the

incompleteness and imperfection of the material with which it deals.” (Hoernes 1884) The incompleteness

and imperfections of the fossil record strongly hinder the achievement of paleontology’s ideal aims. This

situation is not temporary: paleontological evidence has been and will always be characterized

incompleteness and imperfection21. Acknowledging that the paleontological record is incomplete, the

paleontologist is thus subject to error in his judgments and classifications and therefore “who wants to

correctly judge the relationship between evolutionary theory and paleontology, must, above all, give account

on the flaws and deficiencies [Mängel] inherited in the paleontological material.” (Hoernes 1911) The

paleontologist has to keep in mind the degree of imperfection related to his material: the statistics Fuchs

proposed are useless and can be used neither to prove the completeness of the fossil record nor to establish

evolutionary patterns. On the contrary, the main aim of paleontology is identifying the series of forms

[Formenreihen], which are signs of the gradual and Darwinian process of evolution.

The debate about the completeness of the fossil record is therefore an essential step in the

development of the notion of paleontological data and in the rejection of statistics. Williams and Fuchs both

stressed that the fossilized sample of life of the past is as significant as it appears: the gaps in the fossil

record should not be seen as evidence of the incompleteness of the paleontological data. On the contrary,

Hoernes and many other German paleontologists22, vigorously emphasized the incompleteness of the fossil

21 Concerning this point, Hoernes changed his mind between the talk given in Vienna (1880) and the

publication of the textbook (1884). In the proceedings of meeting, he wrote that “it is therefore a task of the geologists and paleontologists to combat the incompleteness of the fossil record by extending and deepening their studies”. That means that, in principle, the paleontologist will obtain soon or later a higher degree of reliability for his data. Four years later Hoernes affirmed that “paleontological tradition must always remain incomplete, even when larger parts of the earth's surface will be explored geologically as is the case today” (Hoernes 1880).

22 I would like to recall Neumayr’s statement that “if one, as it usually happens, proceeds without any regard to the extraordinary incompleteness of the material and almost blindly accepts the accuracy of the numbers, whose incompleteness and inaccuracy is obvious, then a proof based upon it is a absolutely inadmissible and it leads to most severe errors”. See also (Rolle 1863, 1866).


24

record: by stressing data’s incompleteness, they aimed to discredit the use of fossils in a statistical

framework saving thus the disciplinary autonomy of biology.

Geological Biology

A second example of the statistical challenge to Darwin’s theory can be seen in the work of Henry

Shaler Williams’ Geological Biology (1895). As mentioned, Williams used a statistical approach to

paleontology and contested the Darwinian model of evolution. While Neumayr was perfectly aware of

Bronn, Barrande, and Lesquereux’s investigations, Williams’ studies were published after Neumayr’s death

in 1890. Nevertheless, Williams’ analyses provided an excellent example of how the statistical treatment of

the data worked in practice between the end of the 19th and the beginning of the 20th century in the United

States and are a continuation of the approach that Neumayr opposed. His method would leave a mark on the

development of American paleontology: George Gaylord Simpson (1902-1984) would embrace a

quantitative approach following Williams’ principle, “With statistics in hand we may hope to understand

better the laws of evolution as affected by and related to the varying conditions of environment and time.”

(Williams 1903b) Unlike Williams, though, Simpson would use statistics to support Darwin’s model of

evolution.

Furthermore, Williams’ analyses offered important details to illustrate the variety of non-Darwinian

alternatives that emerged from the statistical treatment of the fossil record at the end of the 19th century. By

using tables and statistics, Lesquereux had pointed out the absence of intermediate forms and the marginal

role of natural selection, Fuchs argued that evolution did not follow “a continuous and uniformly progressive

change” (à la Darwin), and Barrande questioned the validity of the Darwinian model of evolution in toto.

Williams not only challenged the role of natural selection, but also claimed that orthogenesis could better

explain the data listed in tables and depicted in graphs.

Williams’ practice again followed Bronn’s mode of quantitative analysis. First, he classified the

fossils according to their morphological features. For example, according to the morphological features of

their brachidium he divided the brachiopods in Atrypidae, Spiriferidae, and Athyridae. This morphological

identification was essential in order to avoid errors in the further treatment. Second he arranged fossil taxa in

tabular form in order to “help to give a notion of the time-relations of the forms under discussion” (Williams


25

1895). For instance, the previously classified brachiopods are now arranged in a tabular form to illustrate

their geological range and development (figure 7).

Figure 7 An example of Williams’s table. It lists the geological range of the families and subfamilies of the Helicopegmata as well as the number of its genera (Williams 1895).

This first tabularization allowed the paleontologists to infer some biological conclusions about the

development of the Helicopegmanta. For instance, Williams pointed out that “the total life-range of all the

representatives of the group extends over eleven periods of the time-scale” and that “all of the family

differentiation was attained in, we may say, the first decade of the life of the suborder”. Third, following

Bronn’s practice, Williams rearranged the tabular data into a graphical form and by numerically comparing

their values he tested the Darwinian model of evolution. For example, by analyzing the figure 8 Williams

noticed that rapid evolution characterized the suborder Helicopegamata.


26

Figure 8 Williams’ table that express in graphic form the rate of expansion of the family, subfamily, and generic characters of the Helicopegmata. It shows a rapid and early expression of the differences in structure of the Helicopegmata.

Hence, Williams discovered a mode of evolution that is not strictly Darwinian: he argued that evolution is a

relatively rapid processes and this rapidity is difficult to account for merely by the action of natural selection.

As Williams put it, “the law of natural selection, suggested to explain the evolution [as] an extremely slow

rate of modification, but uniform and continuous of the history itself point to the reality of rapid strides at

critical points” (Williams 1895). In The Correlation of geological Faunas: a Contribution to Devonian

Paleontology (1903), Williams went on arguing against the Darwinian model of evolution:

“Relatively speaking, the variability is almost in proportion to the vigor and abundance of reproduction of the individuals. Here at once we see a means of rapid evolution. If a species varies and the variation is augmented by favorable conditions of livelihood, the change from one environment to another necessitates the modification of some of the species almost immediately, and the variability of the fauna will be strongly expressed when migration of the species takes place.” [Italics mine] (Williams 1903a)

Hence, by statistically treating the fossil record, Williams asserted that evolution could be rapid or even

abrupt under favorable conditions of livelihood, and that this rapidity poses difficulties for the supporters of

natural selection. The quantitative approach is thus essential to come up with biological explanations. In fact,

only by arranging the fossil record in tabular form and mathematically operating with it was Williams able to

graphically visualize a different mode of evolution: “if now we reduce the facts of generic differentiation to


27

graphic form, we find that the sudden or rapid differentiation is a fact, and is not due to imperfect evidence”

(ibid.). Williams concluded,

“the facts we have examined do not support the hypothesis that the chief factor in organic evolution is either external environment or natural selection. […] The facts examined—and we believe that fuller examination of other statistics, both fossil and recent, will support—show that evolution is rather an intrinsic law of all organisms, and is to be discovered in the phenomena of variation, which appear to be constantly active, rather than in any accidental operations dependent upon the conditions the same conditions of external environment.” [italics mine] (Ibid.)

Hence, Williams’ conclusion is in opposition to the Darwinian model of evolution: evolution is rapid

and guided by an intrinsic law, not gradual and slow and by means of natural selection. This conclusion is

mainly due to the examination of record of data arranged in tabular and graphical form. Indeed, the graphical

representation enabled him to visualize a mode and tempo of development in tension with Darwin’s theory.

Williams came up with biological explanations in disagreement with Darwin since he, like Fuchs,

emphasized that the record of data arranged in tables or graphs is as significant as it appears. Therefore, they

endorsed a literal23 reading of the fossil record based upon quantitative relations among numbers. This is

particularly interesting because it introduces a new feature of paleontological data: the gaps in the fossil

sequence function as data just as does the morphological information obtainable from a single fossil

specimen. That means that the paleontologist should also take the absence of fossils into account: if only 20

species had been gathered in a specific area, the paleontologist must assume this number is consistent for his

biological investigations of that area. By stressing this point, Williams strongly influenced the further

development of paleontology at Yale. The professor of vertebrate paleontology at Yale, Richard Swann Lull

(1867-1957), and Lull’s student George Gaylord Simpson each stressed exactly this point, in their works

Organic Evolution (1917) and Tempo and Mode in Evolution (1944), respectively. For instance, Simpson

asserted that “incompleteness of the paleontological record is an essential datum and that it, as well as the

positive data, can be studied with profit” (Simpson 1944). Hence, the paleontologist should no longer distrust

the reliability of the sample. This stands openly against the assumption that Darwinian evolution will

necessarily be reflected by a completely continuous, gradual line of evolutionary descent. 23 As David Sepkoski put it in a literal reading: the fossil record, “with all its notorious gaps and

inconsistencies, was taken at face value as a reliable document. There never were, in other words, any missing pages or volumes: the discontinuities in the record existed because the history of life is discontinuous.” (Sepkoski 2012a)


28

As I have shown by discussing Lesquereux and Barrande, the statistical treatment of the fossil record

threated paleontology's status within biology because its results did not agree with what (Darwinian)

biologists wanted to hear, namely that evolution is a gradual, slow, and steady process by means of natural

selection. If, in fact, the fossil is used as a valid source of investigation for statistical analysis, its mostly anti-

Darwinian results should also be accepted. The risk, then, was that paleontology would be ostracized from

biology, and in fact that is precisely what happened to paleontologists like Henry Fairfield Osborn (1857-

1935) and Henry Williams who openly advocated non-Darwinian mechanisms. Hence, Neumayr, Zittel,

Hoernes and following them the majority of German paleontologists were convinced that paleontology could

provide not only the “direct analytical proofs for the gradual modification of organisms, but also for its

further theoretical development” (Neumayr and Paul 1882). Thus, by embracing the Darwinian model of

evolution paleontology acquired an autonomous room for biological knowledge.

Neumayr’s Reaction: the Rejection of the statistical Treatment of Data

The statistical treatment of fossils generated data and conclusions that were mostly in opposition to the

Darwinian theory. This opposition is more dangerous than it appears at first glance. Indeed the foremost

matter at issue here was not the validity of Darwin’s theory of evolution. What was at stake was rather the

autonomy of paleontology as a discipline. The Darwinian theory had given paleontologists the required

support to free their discipline from geology and stratigraphy and consequently to enter study of the fossil

record into the biological curriculum24. Hence, statistics undermined both the autonomy and status of

paleontology and so should not be utilized. The debate between Fuchs, Hoernes and Neumayr within the

geologische Reichsanstalt centers on this: statistical analyses are subversive, since they can be used against

Darwinian theory and, as such, should not be utilized in paleontology. As I have mentioned in my

24 Karl Zittel asserted at the 6th International Geological Congress in Zürich (1894) that “paleontology has long

ceased to be exclusively at the service of geology as theory of Leitfossilien. It has gradually grown into an independent branch of biological sciences and takes part in every biological movement and current” (Anonymous 1897). The International Geological Congress was indeed the right place to express his convictions about the nature of paleontology: it is a branch of biology and it is no longer a geological discipline. Darwin’s theory paved the way for the new disciplinary status announced by Zittel because it ensured paleontology a different space of knowledge: “paleontology provides numerous and very significant proofs for the benefit of the [Darwinian] theory of evolution” (Zittel 1895). Hence, it is not a case that no statistics are presented in Zittel’s Handbuch and on the contrary statistics are widely used in stratigraphic investigations. About the disciplinary context of paleontology in German speaking area see (Tamborini 2015a, Under review).


29

introduction, Neumayr put forward this conclusion even in his textbook to make the new generations of

paleontologists aware.

One week after the aforementioned talk at the geologische Reichsanstalt, Fuchs gave another

presentation. It was entitled Über einige Grunderscheinungen in der geologischen Entwickelung der

organischen Welt [About some basic phenomena in the geological evolution of the organic world]. This talk

was intended as a continuation of the arguments expressed the week before, namely that paleontologists

could obtain “certain principles” concerning the geological development of the organic world through

statistical treatment of the fossil record. These principles, Fuchs said, are “in direct contradiction with

Darwinian school.” (Fuchs 1880)

The first point he raised in this new talk is that the development of the organisms does not follow “a

continuous and uniformly progressive change” (Ibid.), but it is characterized by a long timespan of “relative

calm with shorter periods of transformation [relativer Ruhe mit kürzeren Epochen der Umwandlung]”

(Ibid.). This conclusion is very similar to that proposed by Williams25 and endangered paleontology’s status

within Darwinian sciences. Conversely, Neumayr was strongly convinced that, as according to Darwin,

evolution is the development of organisms from “basic forms by gradual transformation [Grundformen

durch allmälige Umgestaltung]”26 by means of natural selection (Neumayr 1889).

Neumayr could not approve Fuchs’ conclusions since statistics completely undermines the

Darwinian biological core of paleontology:

“those paleontologists, who base their conclusions on the numerical relations [Zahlenverhältnisse] of species and genera in the successive fauna or in the individual types, classes, orders in addition to the modality of their appearance and spread of new groups of forms, those which in a word use a more or less purely statistical method, they usually come to the results that the species are constant. [...] On the other hand, we usually find favorable results to Darwinian doctrine, where the paleontologists use the procedure of comparative anatomy, as for example in the work of Gaudry, Gegenbauer, Huxley, Kovalevsky, Rütimeyer and others”. (Neumayr 1878)

25 The metaphysical assumptions behind it are though different. Fuchs did not argue under the influences of

orthogenetic theories. 26 He is even more explicit: “after having analyzed different Formenreihen, I am convinced about the gradual

nature of transmutation”. (Neumayr 1889)


30

As Neumayr affirmed in many meetings of the geologischen Reiehsanstalt and in his textbook Die Stämme

des Thierreiches, the conflict between defenders and opponents of the Darwinian theory stemmed from the

question of statistics: users of the statistical method suggested the expulsion of Darwinian results from

paleontological research. There is no union at all between paleontology and Darwin, or to put it otherwise,

between paleontology and the biological sciences if the paleontologist unconditionally uses statistics.

Therefore, statistics should be carefully used and the paleontologist has to learn under which conditions he

can carry out a quantitative treatment of the fossil record. A secure integration is however always practicable

if the paleontologist draws Formenreihen. Series of forms in fact, provide the evidence for the Darwinian

theory of evolution.

To limit the validity of statistics and to promote the construction of Formenreihen, Neumayr

developed a comparative analysis of the sources of error related to both methods. This analysis aimed to

ascertain which method was worth pursuing. Unsurprisingly, he asserted that the Formenreihen offered far

fewer sources of error than did numerical relations [Zahlenverhältnisse]. Neumayr proposed this argument

also in his Die Stämme des Thierreiches in a section dedicated to the opponents of the theory of evolution27.

His argument was based upon a) the availability and reliability of the data used in each methods, and b) the

possibility of detecting and correcting possible errors during the application of the methods to the collected

data.

Concerning the Formenreihen, the paleontologist has the materials for their realization clearly in

front of him: he only has to collect and classify the fossil record. However, he may be mistaken about a

particular morphological judgment. Although “a mistake is possible in particularly difficult cases or in

clumsy handling, the method itself does not give rise to errors, it may be referred as a very safe method”

(Neumayr 1889). This method is therefore very safe and reliable. The control during its application can also

be done simply: using the morphological method, it is easily possible “to discover the source of error”

(ibid.). On the contrary, the statistical method is characterized by incomplete and unreliable material and “it

is hard to succeed in balancing all the defects and flaws even by very carefully considering all sources of

error” (ibid.).

27 Symbolically Neumayr considered opponents only those paleontologists who use statistics.


31

Neumayr’s conclusion was that the statistical method has to be laid aside until our knowledge about

the nature fossil record can be more complete28. Only in this way can the epistemic status of paleontology be

preserved.

Conclusion

This paper has shown the contested role of statistics in paleontology between the final decades of the

19th and the beginning of the 20th centuries. The aim of a statistical treatment of the fossil record is to draw

the numerical relations between the various zones entombed in rock layers. I have characterized this method

and argued that it was criticized by German paleontologists because it generated results that contradicted the

Darwinian theory of evolution. Essentially, the statistical method questioned the gradual mode of evolution,

its tempo, and the role of natural selection. By presenting the fossil record in tabular and graphical form,

several paleontologists contested whether evolution is a gradual, steady, and slow process by means of

natural selection. This threated Darwinism, but not other alterative theories of evolution. In fact, by amassing

quantitative data Bronn, Barrande, Lesquereux, Fuchs, and Williams endorsed different mechanisms in order

to explain how biodiversity changed through geological time.

These results were refused not because Zittel, Neumayr, and colleagues considered Darwin’s theory

as an infallible dogma, but rather because statistics undermined the role of Darwinian ideas in promoting

paleontology as a biological discipline. The earlier statistical program of Bronn and others was replaced by a

purely morphological approach, which Neumayr and his colleagues believed would allow paleontology to

present itself as an autonomous and biological science. Hence, besides the reconstruction of the

methodological debate concerning which approach is worth pursing in paleontology, my analysis shows the

epistemic tensions between paleontology and biological sciences at the end of the 19th century. In fact, the

paleontologists who rejected the statistical approach were keen on emancipating their discipline from

geology and stratigraphy. They saw in Darwin’s theory the correct means to establish paleontology finally as

an independent and biological science: “Darwin's conception of the origin of species could not fail to

28 This means until we will be able to establish, “whether gaps exist in the sequence of faunas and to what

extent we know the population in each individual temporal period. Only then it will be possible to determine for all formations, as done here for Jurassic, […] under which condition [the absence of fossils] can be used as an argument against the Descendenzlehre” (Neumayr 1889).


32

enhance the interest of palaeontology. That study was realised to be no longer merely descriptive and

comparative, or the means of bringing useful material to the sciences of botany and zoology, but a branch of

knowledge to be studied for its own intrinsic interest. [italics mine]” (Zittel 1901) In this view, paleontology

has a space within biological science inasmuch as it collects facts and evidence supporting the theory of

evolution: “with Darwin begins the modern period of palaeontological research.” (Ibid.) It is thus a

morphological discipline which seeks to reconstruct the morphological features of the fossil record into a

linear series of forms, thus illustrating the gradual process of evolution by means of natural selection. This

practice ensured to paleontology an academic space of autonomy: paleontological professorships were

established in Munich29 (1867) and Vienna (1873) in order to pursue this morphological aim. The debate at

Kaiserlich-Königliche Geologische Reichsanstalt epitomized therefore an important branching point in the

growth of paleontology: in the end what was at stake was the conflict between two opposing ideas of the

nature of paleontology as a science. The future paleontological agenda was set in these years: German

paleontologists conceived paleontology as a taxonomical discipline which deals with morphological data,

American paleontologists studied the tempo and mode of evolution by developing the statistical treatment of

data introduced by Williams and colleagues at Yale.

Secondly, although many paleontologists advocated a morphological approach only because it

supported in turn Darwin’s theory, they abandoned the Darwinian framework as soon as paleontology

obtained an autonomous space for knowledge. In fact, German morphological paleontology allied itself with

neo-Lamarckian theories during the first decades of the 20th century30. This was one of the consequences

derived from the paleontological agenda set at the end of the 19th century: as the Swiss paleontologist Karl

Hescheler (1868-1940) asserted, “when most paleontologists express a judgment about the causes of the

origin of new species based upon the nature of their [morphological] data, they end up immediately with

Lamarckism.” (Hescheler 1904) Conversely, the statistical approach would play a pivotal role in the

formation of American paleobiology: John Maynard Smith welcomed paleontology back to the evolutionary

29 Although there was already a professorship of Geognosie, Bergbaukunde, and Hüttenkunde [geognosis,

science of mining, and metallurgy] in Munich in 1843, the first professorship of paleontology was established in 1867. It was hold by Zittel.

30 The causes of this transition still need to be investigated in-depth. For useful introductions see (Tamborini 2015b; Bowler 1996; Reif 1986, 1983).


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‘high table’ on the basis of the results obtained from a quantitative treatment of data (Smith 1984; Sepkoski

2012a). This was possible because several American paleontologists developed techniques to reframe into a

Darwinian framework the patterns emerged from tables and graphs. They namely investigated the tempo and

mode in evolution in order to show that the patterns emerged from a quantitative analysis of the fossil record

have validity31 within Darwinism (Simpson 1944; Eldredge and Gould 1972). Hence, a question can be

legitimately posed: what does it mean to be a Darwinist? How has this notion changed over time?

Thirdly, the Vienna debate shows that not statistics per se are incompatible with Darwinism, but

rather that statistics reveal patterns, which are not in line with Darwinism. Therefore, this debate calls

attention to the nature of paleontological data. The opponents of the statistical approach argued that the fossil

record couldn’t be treated statistically because the data are incomplete. Conversely, the advocates of the

quantitative approach asserted that if the fossil record is seen as a reliable source, then it could be used in

statistical procedures. Thus, the central debate was whether numerical data were a valid indication of true

patterns in the history of life, not whether particular theories of evolutionary mechanism were more or less

compatible with particular methods: since some paleontologists did not support Darwinism, they were more

incline to accept the validity of the numerical data, whereas Darwinist paleontologists were predisposed to

challenge the validity of anything that called their theory into question. Bronn and others chose to downplay

the uncertainty of their data, while their opponents chose to highlight it. Both sides had reasonable arguments

to make and, in the end, the debate was not about the paleontological method, but rather about the

reasonableness of inferences drawn from the chosen data. Hence, my analysis shows that this was a time

when the validity of fossil data was an open question: what we see happening is that individual

paleontologists were drawn to one or the other side of the debate depending on whether the data supported

their chosen interpretation. That pattern has, to a certain extent, continued right up to the present day: for

example, in debates about punctuated equilibrium advocates of the hypothesis claim that their data is robust

and sufficient to support a punctuated model of evolution (Eldredge and Gould 1972), while opponents

challenge the validity of that data on a variety of grounds. Opponents of punctuated equilibrium do not,

31 It is interesting to notice that Eldredge and Gould revisited the tempo and mode in evolution not only to

validate the patterns that emerged from the fossil record, as Simpson did, but also to give them a broader autonomy and value. (See Eldredge and Gould 1972; Gould and Eldredge 1977)


34

however, challenge the validity of any kind of data analysis; they simply object that the data used to support

this theory is not good enough.

With the rejection of the statistical method by the first decades of the 20th century, the quality of the

fossil record became a hot topic in paleontology. However, it was American paleobiology, rather than the

German morphological tradition, which started to reflect on the epistemic limits and virtues of their data.

From the beginning of the 20th century onwards, paleontologists started asking themselves how the

imperfections of the fossil record can be overcome so that the past can be fruitfully studied. The apogee of

this inquiry coincided with the American ‘paleobiological revolution’ (Sepkoski 2012a; Sepkoski and Ruse

2009). Indeed, the result of this revolution was that the traditional meaning of data as individual

morphological entities appeared to be inadequate to study the diversity of life over time: the paleontologist

slowly acquired a deeper awareness of the epistemic possibilities contained in the fossil record. The

consequence of this awareness was the construction of a new form of data which overcame the imperfections

of the fossil record: paleobiological data became statistical samples. Hence, the meaning of fossils is not only

in their individual morphological features, but also in the role they play collectively as data in the statistical

reconstruction of the history of life. This change was possible since the champions of the paleobiological

revolution could utilize statistical practices to constitute and correct the biased nature of their data: tests of

significance and rarefaction analyses, rather than pictographical descriptions, became the essential tools to

overcome the incompleteness of the fossil record and to merge the quantitative approach and its allegedly

anti-Darwinian results with the Darwinian theory of evolution. The application of statistical tests to the

biased sample of the past was therefore an important turning point in the development and adoption of a

quantitative approach. This application went hand in hand with a definition of a space of empirical

knowledge much broader in comparison with that defined by the advocates of the quantitative approach of

the 19th century. As a result, paleontological data became reliable entities: the fossil record might “be patchy,

but it is not necessarily misleading.” (Sepkoski and Ruse 2009)


35

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