Tuesday, 11 July 2017

Horizons of Patrick Matthew (1831)

Thematic breaks and asides
The book On Naval Timber and Arboriculture; with Critical Notes on Authors who Have Recently Treated the Subject of Planting by Patrick Matthew (1831) is not one long argument. This is clear from its miscellany contents ranging from ship building over tree botany to matters of forestry and arboriculture (see here for an illustration of the structure of the book) and from the thematic breaks that occur between these contents. The biggest part of the book is made up of reviews of earlier publications on the matter of tree planting and growing, though savage and biased criticism would better describe it (see here, here, or here, for example).
   Furthermore, the book has neither been written continuously nor been produced smoothly. Posterity can gather this straight from the horse's mouth, because Matthew introduced various passages of his book with statements like:
  • "After throwing together several of our own observations [on the structure of vessels, the utility of British forest trees for naval timber, practical matters of nursing, planting, training, pruning etc.], we bethought ourselves of examining into the ideas and experience of recent writers on the same subject." (p. 138)
  • "Since writing the above, we have looked over some experiments by Messrs Barlow, Beaufoy, Couch, and others, on the strength of timber." (p. 221, see Barlow, 1826 and citations therein)
  • "After the preceding parts of this volume had gone to press, we received a copy of Cruickshank's Practical Planter." (p. 309)
  • "In taking a retrospective glance at our pages from the press, ..." (p. 388)
  • "Since this volume went to press, there has been some changes of scenery on the political European stage, ..." (p. 390)
(See also this Wikipedia entry on valuable information about the book's structure and production.)

Horizontal lines
While the thematic breaks in the contents tell us something about the miscellany topics of the book (see first paragraph) and Matthew's asides tell us something about his discontinuous writing and thinking (see second paragraph), there is a third intriguing feature of the book—horizontal lines interrupting the main text (horizontal lines that merely underline headings or sub-titles will be ignored). These text-interrupting horizontal lines occur at the pages 135, 221, 294, 358, 381, 390:


   The first thing to note about these horizontal lines is that they do not consistently mark thematic breaks, that is, some thematic breaks are accompanied by such a marker (e.g., pp. 221, 381, 390), but not all thematic breaks in the book are marked that way. For example, the complete thematic break at page 388 is not marked by a horizontal line. Here, Matthew ends his important addendum that is still relevant for the history of evolutionary ideas, today, and begins with a corrigendum about his figure at page 27 (part d of that figure) and about his directions for forming larch roots into knees. However, this break is not marked by a horizontal line or another conspicuous visual element (no heading or anything either). Instead, one line is merely left blank and the text simply continues with one of Matthew's asides (see middle page in the following image):

Equally unmarked thematic breaks occur elsewhere in the book as well.
   Second, the horizontal line at page 135 does not mark a thematic break, but rather a thematic elaboration. That is, after emphasizing the importance of the marine for the superiority of the British economy at pages 130-134, a horizontal line occurs at the top of page 135 and Matthew continues to elaborate that this importance of the marine for the British economy should be reflected in a direct political representation of the marine in the British parliament. [This elaboration contains another elaboration in the form of a footnote at page 135 referring to the end-note E in the appendix. This Note E (p. 376-7), in turn, rants against ships being taxed by their length and widest breadth rather than by their tonnage leading to ill designed ships being deep and bulky rather than streamlined.] He ends this elaboration about the representation of the marine's interests by stating that, in the absence of such a direct representation in the parliament, the hopes of Britain rest with its sailor kings:
"The existence of Britain depends upon her Marine, and the king should always be bred a sailor—the heir-apparent and presumptive being always sent to sea. In the case of a female, if she did not take kindly to the sea-service, a dispensation might be allowed, on her marrying a sailor, and the foolish law prohibiting our Royal Family from marrying a Briton be put aside." (p. 137). 
Likewise, the horizontal line at page 294 marks the beginning of an elaboration of another sort. Here, Matthew switches from criticizing Steuart's Planter's Guide to criticizing an author (Loudon) that Steuart has quoted at length in one of his end-notes (see here, here and here).
   Again, the horizontal lines are neither consistently associated with the asides by Matthew quoted above. While some of the horizontal lines occur atop of an aside from Matthew (e.g., at pp. 221, 390), not all of the asides are accompanied thus (e.g., pp. 309, 388). Apparently, the function of these horizontal lines is not one for the reader.

The significance of horizontal lines in Matthew (1831)
Given that Matthew was a re-iterative writer adding passages in proof or even while the book was already in press, the horizontal lines may have been marks for the publishers (Adam Black, Edinburgh & Longman et al., London) or the printers (Neill & Co., Edinburgh) telling them where to insert the late additions of Matthew. If this was true, then the thematic breaks would reveal something about Matthew's thinking and his asides about his discontinuous writing, but the horizontal lines would indicate the cleavage sites, where the publishers or printers inserted Matthew's late additions. Some of them were inserted singly others together as indicated by thematic breaks or asides. Testing this hypothesis about the function of the horizontal lines by reverse engineering yielded the following surprise.
   Apparently, the elaboration on Steuart's long quote of Loudon (starting after the horizontal line at the bottom of p. 294), Matthew's spliced re-quote (see here, here and here) and his criticism of this Loudon re-quote (extending from pp. 295-308) got inserted along with the whole part criticizing Cruickshank's Practical Planter (as indicated by the aside at p. 309). The amazing thing that happens, when the horizontal lines in Matthew (1831, pp. 294 + 358) are taken as the joints for dissecting and splicing out the intron (the Loudon loop + the Cruickshank part) [Best use the Project Gutenberg html-version for this job.], is that the result is a rather well composed neat ending for the book:
"We begin to think, from our disposition to ramble from the Allanton system [meaning Steuart, who lived at Allanton House and had proposed a system of transplanting large trees in whole], that we tire of Sir {294} Henry; and we believe, should he follow us thus far, that he will be tired of us. On looking back on what we have written, we are almost disposed to accuse ourselves of being splenetic; but the truth is, we regard the whole art as very unimportant, if not positively pernicious, at least in the way in which it has been exemplified by Sir Henry, as a throwing away of valuable labour to no purpose, if it ought not indeed to be considered as a mere pander to luxury and caprice. We have no sympathy with the aristocratical object of the book, and as little with the aristocratical tone in which it has been bepraised by Sir Walter Scott. We should also have no greater pleasure in the discovery of a royal road to virtue than we should have to the discovery of one to science,—the four cardinal virtues being, as every body knows, writing books, building houses, and raising trees and children, but we should hope, neither by proxy, nor by the Allanton System. While, however, we thus state our opinions with freedom, we do not hesitate to add, that Sir Henry’s volume has afforded us more information, or, at least, more materials for reflection, than any other of the works which we have brought under the notice of our readers.
{text between horizontal lines at pages 294 and 358 spliced out}
    We have now brought before the reader a pretty fair picture of the Forestry of the present day. Some may wonder that the written science of arboriculture should be so imperfect and inaccurate; but the knowledge of the art, and the power of communicating that knowledge, are of so different a {359} character, it not unfrequently happens, that those write who cannot act, and those who can, are incompetent to write—sometimes unwilling; besides, correct opinions on this subject, as on most others, are only just beginning to be formed. We have endeavoured to assist in disentangling the correct from the erroneous. It is impossible for the most wary always to avoid misconception of facts, but man merits the name of rational only, when he evinces a readiness to break from those misconceptions, to which the narrow-minded, the proud, the vain, and the creature of habit and instinct, cling so obstinately. As a friend, we have stood on no ceremony with our brother arboriculturists. We have laid ourselves open to their criticism, and we hope they will shew as little ceremony with us."
This is a crisp, apt and fluid ending of the main text of the book in place of the distinctive halting flow and discontinuity between sections (ignoring for the moment the equally discontinuous appendix with a list of end-notes followed by the evolutionary addendum, a corrigendum, a colophon and, finally, the errata).

External evidence from other contemporary books

Books with no text-interrupting horizontal lines
The one long argument On the Origin of Species by Darwin (1859) has not one horizontal line interrupting the main text. Only two underline the title of the book and the title of the contents page (see image below). Nor do any such lines crop up in later editions, where Darwin added or edited his earlier versions.

   In order to exclude the possibility that horizontal lines became unpopular after 1831, but cluttered all books up to that date, take a look at Volume I of Erasmus Darwin's Zoonomia, first published in 1794 by J. Johnson and printed in St. Paul's Church-yard in London. The title page has two horizontal lines that separate a stanza from Virgil, which is inserted between the author and publisher information. Another pair of horizontal lines separates an entreaty, that the reader may endure a string of definitions necessary at the very beginning of the book. This is inserted between the summary and the text of that chapter (see image). No text-interrupting horizontal lines occur in the remainder.

   Another book from about 30 years before 1831 is the English translation of George Cuvier's Lectures on Comparative Anatomy (1802, vol. I). Here the translators apparently economized on pages by separating chapters through horizontal lines instead of page breaks. This book comes in parts called lectures and each lecture falls into chapters called articles. When one article ended in about the upper two third of a page, a horizontal line would separate it from the next article continuing on the same page. If, however, an article ended close to a page break, no ink or space would be wasted for a horizontal line and the next article simply start at the next page. Lectures were not separated thus, but a new lecture begins at a new page regardless of the space left empty. Again, horizontal lines do not wantonly occur in the middle of chapters/articles.
   A book cited by Matthew (1831, p. 221) in one of his asides has no text-interrupting horizontal lines either (ignoring one that separate a footnote and others that separate adverts appended after the end of the book as well as the usual underlines of titles and sub-headings). This is Peter Barlow (1826). An Essay on the Strength and Stress of Timber, founded upon experiments performed at the Royal Military Academy, third edition. Printed for J. Taylor at the Architectural Library in London.
   Finally, Matthew's own Emigration Fields (1839) has no text-interrupting horizontal lines and no aside, either, of the form: "Since this work went to press ..." This is despite the fact that the publishers forced Matthew to augment his first draft (see Matthew 1839, p. v), which was exclusively on New Zealand, by similar chapters on North America, Mexico and Australia.
   Adam Black was now joined by his brother Charles as the Edinburgh publishers, and his London publishers had exchanged Rees (in Longman, Rees, Orme, Brown, and Green) by Longmans (in Longman, Orme, Brown, Green and Longmans). The printers were, again, Neill & Co. in Edinburgh. This suggests to take the discontinuous writing style and high frequency of text-interrupting horizontal lines as a special feature of the book On Naval Timber rather than attributing it to the author, the publishers, or the printers. Matthew's publishers and printers had probably gone through a steep learning curve in dealing with him as an author the first time and simply would not move a thumb or cogwheel before the fat lady had sung the second time.

These examples just serve to show that well written books did not need such bric-a-brac, neither before nor after 1831, and that the parties involved in 19th century book production were not in the habit of wantonly sprinkling horizontal lines as decorations all over their texts.

Books with text-interrupting horizontal lines
Like Matthew's book, Cruickshank's Practical Planter(1830) has been printed by Neill & Co., though his publishers were William Blackwood (Edinburgh) and T. Cadell (London). Matthew may even have learned about it from the printers given how he added his critique of Cruickshank while the rest of the book was already in press and given his aside saying that "we received a copy" (Matthew 1831, p. 309). Cruickshank contains but one horizontal line in the main text at page 53, and it marks a paragraph that has definitely been added as an afterthought. The whole chapter before is just an enumeration of different trees with a paragraph or two of superficial observations on its habitus, timber etc. But at the end of that chapter, he bethought himself to say something about the special mode of propagation (not by seed) of some of the trees, in particular: the lime, willows, poplars by layers or cuttings respectively.

   Steuart's Planter's Guide (1828) was, again, published by William Blackwood (Edinburgh) and T. Cadell (London) with no separate printer being speciefied (Blackwood did inhouse printing, pers. comm., Julian Derry). Again, the whole book contains but one text-interrupting horizontal line at page 274, but this one is tricky.

The text following that marker reads like a direct address of the readers breaking the fourth wall. One could conclude, at first glance, that the horizontal line signals this to the reader and has no function in showing the publishers or printers, where to insert a late addition. However, on perusing the book more extensively, one soon realizes that Steuart's style is that of soliloqui. In speaking with himself (or his other self), he points to "those" trees or "those," to "those" readers or "those" and observes their different needs. He does address the readers in this way at various places (e.g., pp. 4, 230, 234), but none of these other direct addresses got marked by horizontal lines. It is therefore likely that this horizontal line at page 274 also marks a late addition by Steuart.

Saturday, 27 May 2017

Spinach-iron data transformations: Boussingault (1872) to Berg (1913)

For an introduction see any other entry under the spinach-iron label of this blog

In 1872, Jean-Baptiste Boussingault ("Du fer contenu dans le sang et dans les aliments." Comptes Rendus de l'Académie des Sciences, Tome 74: 1353-1359) published his results on the iron contents in the blood of various animals and in food products. This publication contains a table at pp. 1355-56 listing the contents of "Fer exprimé à l'état métallique. Dans 100 grammes de matiére." This means that the values are not for iron oxide (Fe2O3), which was the usual state in which iron contents were measured but elemental. The second statement ("Dans 100 grammes de matiére.") was specified in the text above the table: "En ce qui concerne les aliments, les dosages ont éte exécutés à l'état où ils sont consommés, c'est-à-dire avec leur eau constitutionnelle." (In the case of food, the dosages were carried out in the state in which they were consumed, that is to say with their constitutional water.) Hence, Boussingault's table gives the iron content for spinach leaves ("Feuilles d'épinards") as 0.0045g per 100 gram fresh matter.

In 1897, Emil Häusermann ("Die Assimilation des Eisens. Zeitschrift für Physiologische Chemie 23: 555-592) published a table (pages 586-588) listing the iron contents of food products per 100g dry matter. He cited Boussingault for various items, but the values vary.

Boussingault (g per 100g fresh matter)     Häusermann (mg per 100g dry matter)
Riz: 0.0015 Reis: 1.7
Haricots blancs: 0.0074 Weisse Bohnen: 8.3
Lentilles: 0.0083 Linsen: 9.5
Pommes de terre: 0.0016 Kartoffeln: 6.4
Feuilles d'epinards: 0.0045 Spinat: 39.1

Obviously, Häusermann took values for the water contents of the food stuffs from elsewhere, in order to calculate the iron contents in the dry matter from Boussingault's values for fresh matter. Apparently, these values of the water contents of the fresh matter were 11.7% in rice, 10.8% in white beans, 12.6% in lentil, 75.0% in potatoes and 88.5% in spinach leaves. Bunge (1892. "Weitere Untersuchungen über die Aufnahme des Eisens in den Organismus des Säuglings." Zeitschrift für Physiologische Chemie 16:173-186) has done the same with Boussingault's data before and given König (1889. "Chemie der menschlichen Nahrungsmittel.") as his source for water contents (see footnote ****, here). As Bunge took the water content for spinach to be 88.49%, we can conclude that König has also been Häusermann's source.

In a later edition, Josef König (1904. Chemie der menschlichen Nahrungs- und Genussmittel, Band 2, p. 353) cited the value of Häusermann properly, that is, he gave the range of values as 32.7-39.1mg per 100gr dry matter (the first value being from Bunge 1892 and the second from Häusermann 1897).

Ragnar Berg (1913. Die Nahrungs- und Genussmittel. p. 34-35) gave the contents of iron-oxide (Fe2O3) in 100g fresh matter as he explained in the introduction at page 6: "Damit nun jeder leicht umrechnen kann [...], habe ich in den folgenden Tabellen [...] den Gehalt von 100 g frischen Nahrungsmitteln an einzelnen Mineralbestandteilen in Grammen [...] aufgeführt."
     Berg (1913, p. 34-35) cited König (1904) with a value of 0.0596g Fe2O3 in 100g fresh spinach. (Berg indicated the sources by superscripts given above the values in the table. As he explained at page 11 of the introduction, the roman numeral I stands for König 1904.) If we assume that Berg took the average value (35.9mg/100g dry matter) of König's range (32.7-39.1mg/100g dry matter), then König's average iron (Fe) content in dry matter amounts to 60% of the iron-oxide (Fe2O3) content that Berg imputed to König for fresh matter.
    Berg can hardly have assumed that 60% of fresh spinach leaves were dry matter, when Häusermann had earlier taken its water content to amount to 88.5% (see above). Berg's transformation factor lies much closer to the 70% that is suggested as the correction factor needed to calculate the portion of the mass of Fe2O3 that is due to the iron in it according to the atomic weights (Fe: 55.8; O: 16). Nevertheless, a discrepancy of 10% remains. That is still not satisfying to see how Berg got from König's range of iron contents for dry matter to his imputation to König of iron-oxide content for fresh matter.

Anyway, Berg also performed his own analysis and that yielded 0.0437g Fe2O3 per 100g fresh matter. As it happens, this value was just about ten times higher than what Boussingault had started with (0.0045g Fe per 100g fresh matter) despite the fact that no decimal separator had been misplaced in any of the various data transformations.

Carl von Noorden & Hugo Salomon (1920. Handbuch der Ernährungslehre. Erster Band, p. 476) gave a range of 44-60mg Fe2O3 per 100g spinach and cited Berg (1913) as well as Hermann Schall & August Heisler (1917. Nahrungsmitteltabelle. 5. Auflage. Curt Kabitzsch Verlag, Würzburg) as sources.

The publication of Schall & Heisler (1917, not online) in turn has two values for spinach at page 41: 60mg and 44mg per 100g fresh matter. The latter value bears a footnote referring that value to "R. Berg" (sic), who had given 0.0437g/100g fresh mater as the result of his own analysis. As Berg also gave 0.0596g/100g fresh weight and referred that to König (1904), I presme that Schall & Heisler have simply taken that value from Berg as well, rounded it, but did not specifically cite König, because they have gotten it from a secondary source. The introduction of Schall & Heisler 81917) states that they collected data from "König, Rubner, Atwater und Byrant, Schwenkenbecher, Sautier, Strauss, Tischler, Leva, v. Noorden, Nauny, Magnus-Levy, Janney, Walker Hall, Brugsch, Bessau und Schmidt, Hesse, Offer und Rosenquist, Vogel, Berg, Albu-Neuberg, das "Deutsche Bäderbuch", die Angaben der Nahrungsmittelindustrie u. a. mehr." Sic! No sources, journals, publishers, years or anything else to ease retrival. The publication contains no reference list either to look up citations.

Saturday, 29 April 2017

Comparing Matthew's and Darwin's theories

The following analyses and compares the evolutionary schemes of Patrick Matthew and Charles Darwin. 

Tldr? Summary: In Matthew's scheme, competition was the main hindrance to evolutionary change. Therefore, he required catastrophes to clear the field of existence for the remnant species surviving such a catastrophe. Only then, they could radiate into and adapt to empty niches and thereby get transformed to become new species. In a fully stocked environment, however, no species transformation was possible. In Darwin's early theory, environmental conditions, such as prevail under domestication, first needed to affect the reproductive system of organisms in such a way that the variability of a species got boosted to a level, where natural selection could work towards species transmutation in the first place. He then sought to find natural conditions that were analogous to those of domestication (e.g., on islands in allopatric situations). In Darwin's mature theory, however, the environmental conditions were moved out of center stage and replaced by the principle of divergence. Competition thereby became the main driver of evolutionary change and speciation could also be sympatric. 
     All three schemes combined the old ideas of natural selection, variation and adaptation in ways that species transmutation became a possibility, where previous schemes supposed that natural selection keeps species fixed and well adapted to their station. However, the three schemes differ so strongly from each other that they must be considered as three different theories about evolution. That is, Darwin did not independently come up with the same theory as Patrick Matthew has done 29 years earlier, but with two theories that are vastly different from Matthew's and from each other. Plagiarism, therefore, is a rather unlikely explanation for the superficial similarities.

1. Matthew’s propositions
In his book On Naval Timber and Arboriculture, Patrick Matthew explicitly excluded the wider range of circumstances under cultivation as the cause of increased differences in varieties and attributed it instead to man’s interference with natural selection:
Man’s interference, by preventing this natural process of selection among plants, independent of the wider range of circumstances to which he introduces them, has increased the difference in varieties particularly in the more domesticated kinds.1 (Matthew 1831, 308)
Furthermore, he regarded adaptation to be relative in comparison to competitors as illustrated by examples that ecologists would today call cases of competitive exclusion:
The natural soil and climate of a tree, is often very far from being the soil and climate most suited to its growth, and is only the situation where it has greater power of occupancy, than any other plant whose germ is present. The pines do not cover the pine barrens of America, because they prefer such soil, or grow most luxuriant in such soil; they would thrive much better, that is, grow faster, in the natural allotment of the oak and the walnut, and also mature to a better wood in this deeper richer soil. But the oak and the walnut banish them to inferior soil from greater power of occupancy in good soil, as the pines, in their turn, banish other plants from inferior sands —some to still more sterile location, by the same means of greater powers of occupancy in these sands.”2 (Matthew 1831, 302f, his emphases)
While the oak did better than the pine on rich soils, it fared worse on poor soils. They excluded each other on the respective soils. Without competition, the pine would also do better on rich soils. While evolutionists could now call this idea relative fitness or adaptedness and ecologists could call it reciprocal competitive exclusion (pines from rich soils oaks from poor soils), Matthew called it the power of occupancy.
    However, Matthew did not state this observation of relative fitness, in order to develop an evolutionary argument. On the contrary, the problem at hand was the practical question where to plant different tree species in order to get the best timber. In particular, Matthew (1831, 302f) used his observation to refute Steuart’s claim that trees should always be planted in the soils and climates that resemble their natural habitat. Instead, he maintained that pines would yield better timber if planted in soils that were richer than their natural provenience because they were only excluded from these soils by competitors.
    And further down he used the same logic of this argument, in order to confirm Cruickshank’s claim that the oak could grow throughout Scotland although it does not tend to do so naturally:
The highest latitude to which a tree, or any other kind of plant, reproducing by seed, naturally extends, depending on the ripening of the seed, and also on the power of occupancy, is however different from that where it will grow, when ripe seeds are produced from the coldest place where they ripen, and all the competitors removed; and under the system of shelter belts, hardy pine nurses, and seeds from the nearest place where they ripen, we have no doubt that oaks may be extended to a colder situation than Nature herself would have placed them. (Matthew 1831, 356f)
Again, the problem at hand was not evolutionary, but the practical question whether the area for growing the valuable oak timber could be expanded by a system of getting seeds from the coldest places, where they still ripen, putting them into nursery belts sheltered by hardy pines and removing all competitors from the immediate vicinity.3
    Finally, he explicated his evolutionary ideas in an addendum to the appendix and integrated his concept of relative fitness (power of occupancy) into it as follows:
1. Species are fixed for long periods of time:
A particular conformity, each after its own kind, when in a state of nature, termed species, no doubt exists to a considerable degree. This conformity [of species] has existed during the last forty centuries. (Matthew 1831, 381)
2. Geologists discover like conformities of fossil species within each epoch, but also almost complete difference between the fossil species of one epoch from those of all others (Matthew 1831, 381).
3. This discontinuity (punctuation in the fossil record) is initiated by catastrophes.
The destructive liquid currents […] destroying nearly all living things, must have reduced existence so much, that an unoccupied field would be formed for new diverging ramifications of life […], these remnants, in the course of time, moulding and accommodating their being anew to the change of circumstances, and to every possible means of subsistence, and the millions of ages of regularity which appear to have followed between the epochs, probably after this accommodation was completed, affording fossil deposits of regular specific character. (Matthew 1831, 382f)
4. Pondering the question whether the transformation of species after such a catastrophe was due to repeated new creation, admixture of species, or adaptation (“gradual circumstance-suited modification”), Matthew (1831, 384) opts for the latter.
5. He then, partly, attributes this adaptation to natural selection in a paragraph in which the power of occupancy re-occurs:
The self-regulating adaptive disposition of organized life may, in part, be traced to the extreme fecundity of Nature, who, as before stated, has, in all the varieties of her offspring, a prolific power much beyond (in many cases a thousandfold) what is necessary to fill up the vacancies caused by senile decay. As the field of existence is limited and pre-occupied, it is only the hardier, more robust, better suited to circumstance individuals, who are able to struggle forward to maturity, these inhabiting only the situations to which they have superior adaptation and greater power of occupancy than any other kind; the weaker, less circumstance-suited, being prematurely destroyed. This principle is in constant action, […] in such immense waste of primary and youthful life, those only come forward to maturity from the strict ordeal by which Nature tests their adaptation to her standard of perfection and fitness to continue their kind by reproduction. (Matthew 1831, 384f, my highlighting)

6. Finally, he states how this explains both the conformity (fixity) of species in the periods of stasis as well as their transformation after catastrophic changes:

From the unremitting operation of this law […], a considerable uniformity of figure, colour, and character, is induced, constituting species; the breed gradually acquiring the very best possible [not perfect] adaptation of these to its condition which it is susceptible of, and when alterations of circumstance occur, thus changing in character to suit these as far as its nature is susceptible of change. (Matthew 1831, 385)

The remainder of this addendum is made up of considerations of additional causes of adaptation (hence he traced adaptation only “in part” to natural selection) as well as the anomaly of the human species that either modifies other species to its needs or exterminates them.

2. Darwin’s theory development
Eiseley (1959) interpreted Darwin’s statements from 1844 and 1868 as if they were informed by one and the same theory. Since then, Darwin studies have traced Darwin’s long theory development in minute detail (e.g., Ruse 1975; Browne 1980; Kohn 1980; 1986; 2009; Schweber 1980; Beddall 1988; Mayr 1992; Richardson 1981; Ospovat 1995; Hector and Hooper 2002; Costa 2009; Mannouris 2011; Pearce 2010; Richards 2012). Consequently, Darwin’s earlier statements should not be decoded using the same theory as his later ones. Before getting into a detailed comparison of Darwin with Matthew, let me briefly sketch Darwin’s intellectual development in a conveniently simplified way. Between his return from the Beagle voyage and 1844, Darwin developed what will be referred to as his early theory of species transformation through natural selection. Between that time and 1856, he was obsessively occupied with taxonomic work concerning small-scale studies of barnacle variation (van Wyhe 2007; Mannouris 2011) as well as large-scale patterns in botanical systematics (Browne 1980). Thereafter, he began to write down his mature theory, posthumously published as Natural Selection (Stauffer 1975), but this was famously interrupted by a letter from from Alfred Russel Wallace precipitating the events that lead to the publication of the Origin of Species as an abstract of the big Natural Selection book he had planned.

2.1 Darwin’s early theory
Despite embracing the idea of species transformation by 1837, he continued to work by theories that agreed with doctrines of natural theology up to the mid-1850s. For example, Darwin (1909[1844]) thought that species hardly varied under natural conditions, because intermarriage would swamp individual variants. He thought that large scale changes in conditions needed to push organisms out of their natural state first. This would affect their reproductive system to increase fortuitous variation in the offspring. Only after this boost of undirected variation could selection adapt the species to the new conditions (Ospovat 1995). Under normal conditions, natural selection was stabilising (keeping species fixed) as generally believed to be true in doctrines of natural theology. Natural selection could only transform species under exceptional conditions.

2.2 Darwin’s later theory
In the mid-1850s Darwin removed the special conditions of existence from the center stage of his theory and allowed that even slight individual differences could be accumulated by natural selection without being swamped. The keystone in this development was his principle of divergence.4 This did not simply explain the long known pattern of diverging ramifications as a contingent result of variation and selection, speciation and extinction, but took divergence as adaptive in itself.5 The sources motivating Darwin’s search for this principle have been traced to studies on embryology, morphology, taxonomy and to an analogy with economics as well as first ecological experiments by von Baer, Owen, Milne-Edwards, Adam Smith and Sinclair respectively (Browne 1980; Kohn 1981; 1986; 2009; Schweber 1980; Beddall 1988; Mayr 1992; Ospovat 1995, chap. 5-8; Hector and Hooper 2002; Paterson 2005; Pearce 2010; Richards 2012).
    Darwin tried to explain a large-scale pattern of taxonomy that the species within larger genera were also more divergent morphologically than the species in smaller genera. He had invested a lot of research into developing a statistical measure for that pattern and the principle of divergence was his explanation of it (Browne 1980). Starting from an analogy with economic division of labour and from experiments by George Sinclair, Darwin apparently arrived at the conclusion that specialisation is also advantageous for species (Tammone 1995) and construed his principle of divergence as an explanation for the taxonomic pattern from it.
   Darwin (1859, 114, 116, 118, 121), took species to be imperfectly adapted and divergent forms to be improved (better specialised) and therefore to almost necessarily exterminate the intermediate forms, which were usually the own parental forms.
As each species tends by its geometrical ratio of reproduction to increase inordinately in number; and as the modified descendants of each species will be enabled to increase by so much the more as they become more diversified in habits and structure, so as to be enabled to seize on many and widely different places in the economy of nature, there will be a constant tendency in natural selection to preserve the most divergent offspring of any one species. Hence during a long-continued course of modification, the slight differences, characteristic of varieties of the same species, tend to be augmented into the greater differences characteristic of species of the same genus. New and improved varieties will inevitably supplant and exterminate the older, less improved and intermediate varieties; and thus species are rendered to a large extent defined and distinct objects. (Darwin 1859, 470)
In particular, Darwin referred to the division of labour being advantageous to an entrepreneur or economy and to experiments by George Sinclair showing that a plot of ground will support more grass blades if sown with different species and genera than if sown with only one species. However, that is only advantageous to the farmer and not to the single grass blade or species.
    Darwin's conclusion that, therefore, it is advantageous for an individual or a variety to diverge from its parental form was a non-sequitur. It does not cogently follow from economic first principles or from Sinclair's experiments. This means that the principle of divergence was not a valid conclusion from the premises (a conclusion is valid that follows necessarily, if the premises where correct). But that does not mean that the principle of divergence is necessarily false as it would be, if all diverging variants were necessarily and always at a disadvantage in comparison with the parental form.
      That is, the logic was not cogent (the conclusion was not valid) but the place it took Darwin to (competition as the driver behind selection) was new and turned out to be fruitful. It is interesting to note that this is one of the many instances in the history of science, where non-cogent reasoning and an invalid conclusion advanced science more than the logically consistent alternative would have done.
Darwin's principle of divergence, even though he arrived at it by a logical non-sequitur, turned competition into the main drive behind natural selection and species transmutation. Matthew, instead, needed catastrophes to clear away the competitors, because he conceived competition to keep a species fixed to its station.
     To distinguish Darwin's early from Darwin's late theory, one could say that the drive for adaptive change was environmental in his early theory, but competitive in his later theory.

3. Theory comparison
Historians of science often claim that Darwin's early theory or theories of others from before The Origin of Species in 1859 included a conception of perfect adaptedness (e.g., Ospovat 1995; Fleming 2013). To address that claim, the meaning of perfect and relative adaptation needs to be clarified first. Perfect adaptation requires two things: (1) A perfectly adapted species will not do better elsewhere and (2) it can also not be ousted from its niche, neither by other species nor by divergent descendants of its own. Suppose a species that was perfectly adapted for one niche but its actual range beyond this spot was restricted by competitors. That would fulfill conditions 1 and 2 from above. But it cannot be Matthew's conception, because such a species would not do better elsewhere.
    Let's stick with Matthew’s example of pines and oaks. If, for example, pines were perfectly adapted for poor soils and cold climate, they would do best there. Rich soils and warmer climate would have adverse physiological effects (similar to over-manuring or desiccation). Pines could still occur on rich soils in the absence of superior competitors, but they would not do as good there as on poor soils. Matthew, however, thinks that pines would really do better on rich soils, if only the competitors would not exclude them. Matthew's concept of imperfect adaptation breaks condition 1 for perfection, but Darwin later theory breaks both condition 1 and 2. 
    This explains why Darwin, in his early theory, needed environmental change to alter the conditions to which a species was perfectly adapted and thus induce it to vary markedly, as if under domestication. First the environmental factors change and render a species ill adapted, then it varies markedly, then natural selection works to transform it. Geographic isolation is needed in this early theory, in order to get more than one species.
   The relative adaptation of pines and oaks in Matthew’s scheme also explains why he did not merely need environmental change but catastrophes. The catastrophe needs to exterminate the competitors and leave an unoccupied field of existence into which the pines could then spread and thereafter adapt to the new conditions which they meet there. That is, Matthew's scheme would even work if, no environmental change occurred, but the competitors were nevertheless removed somehow. That’s why he advised to remove the competitors if one wanted to grow oaks in Scotland or pines on rich soil. Conversely, if the soil of the pine habitats became rich and the climate mild, somehow, but that of the oaks would stay as it was, the latter would simply exterminate the former. Hence, catastrophes.
   Imagine a miraculous catastrophe that would exterminate the majority of all species, but leave the environmental conditions on earth just as they were. Such a catastrophe would have the same effect in Matthew's scheme as one that altered the environmental conditions along with exterminating competitors. With perfect adaptation, however, the pines would keep sitting in their niche of poor soils and cold climates and their spread to adjacent habitats would be an extremely slow process. The variant occurring could move only tiny bits beyond the conditions perfect for their ancestors. It would not possibly yield the ultra-rapid adaptive change that Matthew needs in his scheme.6
   In comparison, Matthew's scheme is one of stasis punctuated by catastrophes; in the periods of stasis natural selection keeps the species to their niches. This agrees with the doctrine of natural theology in that natural selection has a species fixing effect during stasis. It disagrees with natural theology in that species are not perfectly adapted to their niche, but only kept there by competitors. Therefore, catastrophes have a species transforming effect by removing competitors. Matthew does not need repeated creation, because the remnant species will naturally spread into the empty fields of existence after a catastrophe. The same natural selection that kept the species fixed now transforms them.
    In Darwin's mature theory, after the principle of divergence, the environmental conditions included other species, but the fiercest competitor of a parental species was the divergent daughter species. That is, the oak was not exterminated by a catastrophe and then the pine moved in, but the parental oak was exterminated by divergent daughter species (other oaks) that were more specialised and therefore better adapted.
    In Matthew's scheme relative adaptedness means that the pine could do better on rich soils and would spread there, if the competitors (hardwood) were removed. In Darwin's later scheme relative adaptedness means that a pine species which could do better on rich soils could also be better adapted for poor soils than it actually is. Therefore divergent descendant species (that are more specialised for poor soils) will oust the parental species. That is how the principle of divergence is the inverse of Matthew's idea of relative power of occupancy. Where Darwin saw sharp wedges packed close together and driven inwards by incessant blows, Matthew saw pointed arrows lashing outwards by incessant throws.
   As the conception of perfect and relative adaptedness is useless for describing Matthew's scheme of evolutionary change, it should be replaced by a conception that distinguishes between an environmental and a competitive drive for adaptive change. We then see that Matthew's theory conceived competition as the main hindrance to evolutionary change, where Darwin's mature theory saw it as the main driver behind evolutionary change. Matthew needed catastrophes that clear the field from competitors, in order for evolutionary change (spread, adaptation, transformation and radiation into free niches) of the remnant species to become possible.
   In Darwin's early conception the environmental change does not drive evolutionary change by removing competitors, but by removing the species from its zone of comfort and thereby stimulating its variability. In Darwin's late theory, however, competition has become the main drive for evolution and environmental change a facilitating factor. But competition is never a hindrance to adaptive change in any of Darwin's theories as it is in Matthew's!
    For redundancy, Matthew's concept of relative adaptedness means that the pine is not the species that is best adapted to rich soils and therefore ousted from them, and the oak is not the species best adapted to poor soils and therefore ousted from them. However, although both are only better adapted to their natural place than the competitors—not perfectly adapted—Matthew did not use that, in order to develop an intrinsic evolutionary drive from it (like the principle of divergence). Instead he took on board the external driver of catastrophes.
    For Darwin, the pine is better adapted to poor soils than the oak, okay, but it could also be still better adapted to its natural habitation on poor soils. And Darwin uses that for developing an intrinsic evolutionary drive that needs no recourse to external drives. He used to need the external drive of changed conditions in his early theory, in order to push a species from its comfort zone. But his later theory, while it can accommodate such external factors of evolution, has in in-build drive for adaptive change (the principle of divergence).

4. Conclusion

In conclusion, Matthew’s theory of evolution combined the old doctrine that natural selection (usually) keeps the species fixed with the catastrophism that allowed for rapid transformation and radiation of species by natural selection after a catastrophe. Darwin’s principle of divergence, however, was his final break away from the doctrine that natural selection kept species fixed.
    The principle of divergence differs from Matthew’s ideas in its development (from Darwin’s own studies of systematics and an analogy with economics), its causal structure and its consequences. This constitutes a negative paternity test for Matthew. It exculpates Darwin from claims of plagiarising Matthew for the time after he shifted from his early (1844) to his mature theory (1856-58). His early theory, without the principle of divergence, was equally different from Matthew’s ideas:
Darwin: environmental change renders a species ill adapted → this leads to increased variation → this allows species transformation by natural selection;
Matthew: adaptation is always relative → competition keeps species fixed in their natural place → catastrophe removes competition → species spreads and natural selection transforms it to new conditions. 
This exculpates Darwin for the time from his return from the Beagle voyage till 1844. Hence, the time window left for this particular plagiarism claim is hardly open anymore. 

You may wonder why Matthew did not think of the possibility of a better adapted variant of pine occurring on the same spot as its parental form and squeezing it out of it. However, Matthew's proposals that bear on evolution did not form a complete theory without gaps. From what he wrote, I conclude that he simply did not think this through to the end. He proposed the power of occupancy and ill adaptation of pines to their station. Then he went on to derive practical tips on how tree growers can grow better firs on rich soils by keeping the competitors down. Then he criticised all sorts of other authors and, finally, he appended an addendum proposing catastrophes instead of humans keeping the competitors out of the way of remnant species. It's not a comprehensive theory, really, just a collection of thoughts rather loosely attached to the main topic of the book (naval timber) and rather loosely integrated with each other as well.  

--- Notes ---
1 Note that “difference in varieties” does not necessarily mean individual variability.
2 Prideaux John Selby (1842, 391) cites this passage of Matthew only to refuse it: “Matthew, however, in his able treatise on naval timber seems to think that its indigenous location in such districts arises not so much from preference of soils of the nature above-mentioned, as from its having more power of occupancy in such soils than any other plant of the country; and this opinion he endeavours to support by stating that the Pinus sylvestris, planted in a good or rich soil, attains larger dimensions and its best timber properties, and that it is only driven from this superior soil by the greater power of occupancy, and that it is only driven from this superior soil by the greater power of occupancy possessed by the oak and other deciduous trees, an opinion in which we cannot altogether acquiesce, as we see no reason why the fir, if it grows with such additional vigour in a richer soil, as Mr. Matthew asserts, should, at the same time, be unable to maintain a contest with the oak or other tree.” Apparently, Selby did not comprehend the dynamics of competition and simply assumed that equal size at maturity of pine and oak meant equal competitive powers.
3 Again, he reiterated this logic of relative fitness in his book Emigration Fields Matthew (1839, 38): “The soil of Upper Canada is in many places of fair quality, and generally superior to that of the eastern provinces. The timber consists mostly of large-leafed deciduous trees, while that of the eastern provinces is chiefly pine. This distribution is partly due to soil as well as climate, and has lead to the belief that pines prefer inferior soils. This, however, is not the case. Hard-wood trees have only greater power of occupancy in warmer climates and richer soils and pines in the cold and inferior, especially in the more siliceous.” (see also p. 57)
4 Davies (2013, 727) suggested that Wallace (1856, 214)could have inspired Darwin’s principle of divergence: “It is probable that in very few cases is there a direct affinity between two groups, each being more or less distantly related to some common extinct group, so that we should represent their connexion more accurately by making our central line a blank, for the extinct portion of the group, and placing our families right and left, at different distances from it.”
5 Though anachronistic, the modern distinction between stabilising, directional, and disruptive selection can help understand the principle of divergence. Where, beforehand, the usual circumstances of a species rendered natural selection stabilising, or absent according to Darwin’s early theory, and changed conditions of life were required to render it directional (transforming), disruptive selection for divergence could now also occur under the usual conditions of existence. Transformation, speciation, and extinction were no longer conditional upon large-scale changes of physical circumstances.
6 Matthew (1831) believed that “millions of ages” (p. 383) of stasis, the last one lasting “forty centuries” (p. 381) had been punctuated by an equal number of catastrophes followed by short periods of adaptation and diversification. To cut him some slack, let the average period of stasis be 3000 rather than 4000 years. This will amount to 3 billion years of stasis. Life on earth exists for 3.9 billion years, minus the stasis leaves 900 million years for adaptation. Slotting them in after the catastrophes and before the periods of stasis leaves 900 years, on average, for each period of evolutionary change. And in that time the new fauna and flora had to re-evolve from catastrophes “destroying nearly all living things” (p. 382f). This extremely compressive limitation shows that Matthew’s scheme lacked time for evolutionary change.

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