(N)ature rises up by connections, little by little and without leaps, as though it proceeds by an unbroken web, it proceeds in a leisurely and placid uninterrupted course. There is no gap, no break, no dispersion of forms: they have, in turn, been connected, ring within ring. That very golden chain is universal in its embrace. - Juan Eusebio Nieremberg, 1635 [ 1 , p.29]

From very early in the Middle Eastern and European religious and intellectual traditions, chains, cords, ladders and stairways served as metaphors for order in the world, or between earth and heaven 2 3 4 5 6 . The image of a tree sometimes served in the same metaphorical sense [ 5 , pp.319-329; 6 , p.22]. A linear order in nature was compatible, for example, with the hierarchical arrangement of creation implied by emanationist cosmology, correspondences between spiritual and earthly bodies, and the literal or figurative ascent of the soul or mind toward God. Even the incipient change, beginning in the Twelfth century, from a God-centric to a man-centric hierarchy provided no cause to question the underlying assumption of a linear arrangement or ordering in nature.

Within this Great Chain of Being, organised matter on earth might constitute a greater or lesser portion. In the Physicorum elementorum of Charles de Bouelles 7 , for example, earth, water, air and fire constituted only four of the 25 hierarchical levels that culminate in the Deity (Figure 1). By contrast, the Liber de ascensu et descensu intellectus of Ramon Llull 8 presents an eight-step stairway of which stones, fire, plants, brute animals and man form the first five steps, and the Deity is reached at step eight (Figure 2). In principle, not only large inclusive groups (animals, plants) but indeed every taxon of being, no matter how minor, might be ordered linearly, in accord with Aristotle's famous description of organized matter as

...proceeding little by little from things lifeless to animal life in such a way that it is impossible to determine the exact line of demarcation, nor on which side thereof an intermediate form should lie. Thus, next after lifeless things in the upward scale comes the plant, and of plants one will differ from another as to its amount of apparent vitality; and, in a word, the whole genus of plants, whilst it is devoid of life as compared with an animal, is endowed with life as compared with other corporeal entities. Indeed, as we have just remarked, there is observed in plants a continuous scale of ascent toward the animal [ 9 , 588b:4).

Beginning in the Sixteenth century, botanical and zoological treatises were sometimes arranged to present organisms as forming a more-or-less ascending (or descending) series 10 11 12 13 . A particularly fine-grained linear arrangement appeared in the 1788 Flore Françoise by Jean-Baptiste Lamarck 14 , although Peter Stevens hints that this arrangement per se may be due more to the Abbé René-Just de Haüy than to Lamarck himself [ 15 , 79f145]. But already by that point in the late Eighteenth century, the Great Chain was widely seen as inadequate in describing biological diversity. This crisis was brought about by four related developments, which I briefly present in turn.

First (chronologically) was Richard Bradley's argument that degree of perfection must not be argued from mere Platonic form or essence, but arrived at instead by analysis of "figure or parts" [ 16 , p.18]. His wonderful Philosophical Account of the Works of Nature (1721) arranges minerals, plants and animals in an ascending, if idiosyncratic, scale of nature, with innumerable descriptions, comparisons and analogies relating to their exterior body parts, internal circulation of fluids, features of reproduction, rates of growth and development, metamorphosis, activity, strength, "spirit" [ 16 , p.89] and "uses". Bradley was comfortable with the idea of perfection (e.g. of body parts), but observed multiple, non-uniform progressions, with individual species being imperfect in some regards and more-perfect in others. Indeed in respect of the linear arrangement of animals, Bradley famously concluded:

"I suppose it may be wonder'd at, that hitherto I have not mentioned Mankind, who is so remarkable a Creature, and Lord of all the rest; I confess, was I to have placed him where the Parts of his Body would most agree with those of the created Bodies mention'd in this Treatise, I must have set him in the middle of this Chapter; but I suppose my Reader will excuse me, if I shew him so much regard, that I rather speak of him in the summing up of my Scale, than let him be encompass'd with wild Beasts." [ 16 , p.117]

Second, the vast expansion in knowledge of animal, plant and microbial diversity in the Seventeenth and Eighteenth centuries 17 18 19 20 21 22 did not yield a more-continuous Chain; critics from Voltaire [ 23 , pp.58-60] to Dr Johnson 24 (and later, Eldridge & Gould 25 ) could point to innumerable discontinuities, not to mention the fundamental paradox of continuity among discrete entities. Churchmen and philosophers had long grappled with the concept of plenitude (complete realisation of possibility) given the obvious imperfection of the world 4 , with Peter Lombard arguing that we cannot deny to God the fullest scope of action in creation, i.e. he could have created a more-complete, more-perfect universe had he so willed 26 . But had the voyages of discovery been set up as an experimental test of morphological continuity across nature, the null hypothesis (discontinuity) would not have been rejected.

Third, and far more seriously, certain high-profile discoveries could not be fit into any reasonable linear arrangement of nature. Debate raged through the first half of the Eighteenth century (and beyond) on whether coral polyps were animal, vegetable, mineral, or some combination thereof 16 27 28 29 30 . Placing the green Hydra 31 among the mosses, for instance, would remove it far from the self-motile worms or insects. Likewise it seemed impossible to decide whether "the little Proteus" Volvox [ 32 , III pp.621-624] should be placed at the base of the plant scale, or at the base of the animals. In his beautifully written Contemplation de la Nature (1764-65), sometimes considered the culmination of the case for a Great Chain of Being, Charles Bonnet felt compelled to ask whether insects and shellfish need to be assigned to "lateral and parallel branches off this great Trunk" [ 33 , III p.xx].

Finally, it was becoming increasingly apparent that the continuity, if any, between plants and animals did not join the most-perfect plants (for Bonnet, "sensitive" plants such as Mimosa) with the least-perfect animals such as jellyfish. According to Linnaeus in aphorism 153 of Philosophia botanica:

Nature herself associates and joins Minerals and Plants and Animals; but in so doing it does not connect the most perfect Plants with Animals that are said to be the most imperfect, but imperfect Animals and imperfect Plants are combined.... [ 34 , §153]

I consider it unlikely that Linnaeus intended to argue that the combining (combinat) of imperfect animals and imperfect plants was more-integral than the associating and joining (sociat et conjugit) of minerals, plants and animals, and not only because sociat is equally well translated unites. Others later did draw this distinction: Flittner 35 , for example, claimed that zoophytes, corals, sponges and seaweeds shared both plant and animal natures; and dual or alternating identities were frequently invoked e.g. in descriptions of coral polyps, alternating life-history stages of algae, and unicellular organisms such as diatoms 36 37 . In aphorism 153 Linnaeus probably did, however, intend to contrast "imperfect" with "maximally imperfect": nature joined the former.

Of course, linking the most-simple plants with the most-simple animals would yield not a linear scale or chain, but rather a dichotomy, as in the letter V; and if plants and animals were contiguous at multiple points (not only the maximally imperfect), order in nature would more resemble the letter Y. The Great Chain was in deep crisis.

Although at first Linnaeus accepted that nature is ordered in a linear scale 38 , by 1750 or 1751 he realized that even the plants could not be arranged in a simple unitary continuum. This casts an interesting light on aphorism 77 of his Philosophia Botanica [ 34 , §77], the three well-known parts of which might not, on initial reading, seem to be closely related:

The fragments of the natural method are to be diligently sought out. This is the first and last desideratum in botanical study. Nature does not make leaps. All plants show affinities on either side, like territories in a geographical map.

In the first two sentences, Linnaeus acknowledges that his own system of nature corresponds to the natural method only in small disjoint parts (fragments). Nature is, however, without gaps (Linnaeus takes this quotation verbatim from Ray 39 ) and among the plants one family can be contiguous to one, two, or more than two others - unlike in a chain, where each family must have exactly two neighbors (even the least-perfect plants would be joined below to the minerals, as the most-perfect plants would be joined above to the animals). His map analogy seems not to have been taken literally at first, as no Map of Plants appears to have been rendered until Paul Giseke did so in 1792, fourteen years after Linnaeus's death 40 ; but thereafter the cartographic enterprise persisted until 1859 and beyond, with Alphonse de Candolle developing rules for distributing plant taxa on a two-dimensional "map" 41 . Sachs [ 42 , p.137], Stevens 43 , O'Hara 44 and Ragan 37 mention other early maps of nature.

The concept affinity bears further comment. In the late Eighteenth and very early Nineteenth centuries, affinities were regularities of resemblance or arrangement among characteristic or functionally important body parts (e.g. those constituting skeletal or organ systems) that indicated an attraction or closeness between the organisms or taxa in which they were found. Some authorities, observing the investigations of Lavoisier on describing the "affinities" that determine how chemical substances attract each other and form compounds of fixed stoichiometry, sought or imagined corresponding affinities in the biological realm that could likewise reveal the true order in nature, or natural laws [ 45 , pp.38-39 and chapter 8; 46 , I pp.535-540]. These affinities could be "morphological, structural, and physiological" [ 47 , IV p.81]. Later, affinity came to be reserved for taxa, whereas the corresponding relation among characters would be called homology [ 44 , p.258]. Innate affinity was properly contrasted with analogy, which was external, superficial or remote.

Keys are hierarchical arrangements intended to aid identification or information retrieval, and are sometimes presented as a branching logical structure, i.e. a tree. An early key of plant genera, by Zaluziansky à Zaluzian (1592), is shown in Figure 3 [ 12 , opp. p.87], and keys were relatively commonplace by the second quarter of the Eighteenth century (e.g. Ray, van Royen, Linnaeus).

Much more interestingly, nearly a century before Darwin's Origin of Species, Peter Simon Pallas proposed in Elenchus Zoophytorum 48 that the gradation among organisms might best be described as a branching tree:

"...various authors desire a certain pleasing scale in nature, of such excellence as will never be found, such as Bradley and Bonnet wish for. The gradation can be expressed no less well, indeed very much better, as various affinities in polyhedric figures, [with] genera of organic bodies distributed close by in numerous small spaces by turns. As Donati has already judiciously observed, the works of Nature are not connected in series in a Scale, but cohere in a Net. On the other hand, the whole system of organic bodies may be well represented by the likeness of a tree that immediately from the root divides both the simplest plants and animals, [but they remain] variously contiguous as they advance up the trunk, Animals and Vegetables; those leading, from Mollusca advancing to Pisces, with great lateral branches of Insects sent out among themselves, from here to Amphibia; and at the extreme top of the tree the Quadrupeds are supported, Aves truly thrust out as an equally great lateral branch below the Quadrupeds. At the same time this image shows the animals to be neither continuous nor neighboring, but standing like a lone tree. Its trunk is the series of the more principal neighboring genera closely appressed; everywhere genera are thrust out like twigs, yet [the principal genera] are never connected to each other by lateral relationships." [ 48 , pp.23-24]

His key points are that (1) animals and vegetables separate from each other immediately at the base of the trunk and proceed upward on their own, forming a dichotomous trunk; (2) the animal and vegetable trunks nonetheless remain contiguous at various points; (3) the animal (and separately, the plant) trunk is formed from series of principal neighboring genera pressed closely against each other; (4) genera are thrust out everywhere "like twigs"; and (5) no lateral relationships connect the principal genera (in the plant trunk or in the animal trunk).

Regarding the third of these points, Pallas wrote Hac figura indicaretur simul Corpora organica, brutis non continua nec affinia esse, sed tantum insistere ceu arbor solo. Truncus e principaliori generum affinium serie confertus. The word principaliori might be translated as more original or even earlier, but we must be careful not to impute a temporal dimension. A 1787 German translation [ 49 , p.48] rendered this passage Der aus der vorzüglichern Reihe anverwandter und dicht für einander stehender Geschlechter zusammengesetzte Stamm..., which in turn may be translated "The trunk, composed of the principal series of genera that are related and stand compact to one another...". Unfortunately Pallas himself is not known ever to have sketched his tree, but the sense conveyed is of a compound trunk - not the solid trunk of the much later interpretation by Thienemann 50 , but instead a bunch of asparagus-shoots as in the "tree of animal life" of Eichwald (Figure 4) 51 . Interestingly, Mikulinskii [ 52 , p.344; 53 , p.315] presents Eichwald's diagram as the first to have depicted Pallas's tree.

Although a prolific author, Carl Edward von Eichwald is little-known today outside Russian-language histories of science (e.g. 52 53 ) in which his name is given as Eduard Ivanovich Eichwald. In his 1821 De regni animalis limitibus 54 , Eichwald states that animalcula (protozoa) "have the rudiments of animal organization, from whence the series of more-perfect animals evolve in ever-elaborating grades and multifarous ramifications". He says repeatedly that animals and plants proceed from a common primordium (for him an organisational concept, not an early point in time), with the simple animals and simple plants proximate in this primordium. Eichwald developed this idea further in Zoologia specialis 51 , proposing that the six primary animal types (Spondylozoa; Podozoa, Taxozoa and Heterozoa; Therozoa; Grammozoa; Cyclozoa; and Phytozoa) had originated in the primaeval shallow ocean; the first type arose from abundant "globules of primitive mucous", followed by the others in temporal succession, each a branch off from, and elevated in relation to, the previous type [ 51 , p.41]. Zoologia specialis is less overtly nature-philosophical than Eichwald's earlier De regni animalis limitibus and clearly presents a branching, transformationist view of the origin of biodiversity. According to Mikulinskii, however, Eichwald was "not particularly a Darwinian in his later writings".

Even earlier in 1801, Augustin Augier 55 represented plants on a multifurcating Arbre botanique, and considered this representation to apply equally to animals and minerals:

"The order that I established among plants is found equally in the three kingdoms of nature, and that seems to me a favorable precedent for it to be regarded as natural. The three kingdoms form three major series which begin with the least perfect beings and end with the most perfect. Under the similarity of their organizations, they are themselves made up of several series or smaller families which are united by beings which, although appearing to take the nature of two or several families, properly belong neither to one nor the other, and by this form transitions; this makes it difficult to find striking characters. Zoophytes unite the three kingdoms; mammals are united to fish by the whales, and birds to quadrupeds by bats, etc." (Augier [ 55 , p.vii] as translated by Stevens [ 43 , p.206])

Stevens 43 finds no evidence that Augier intended this tree to depict an evolution or transformation of species. By contrast, Lamarck made evolutionary change, including the ongoing spontaneous creation of primitive forms and the upward transformation of existing life, the centrepiece of his evolutionary theory. As mentioned above, in Flore Françoise 14 he accepted a unitary scale of (plant) life. Later, in Recherches sur l'organisation des corps vivants 56 he drew back from fine-scaled continuity, although he continued to find continuity across major internal organ systems of animals [ 57 , p.128]. But to explain origins of specific groups of animals - cetaceans, for example - he found it necessary to invoke branches. Lamarck's first tree (Figure 5), presented in an addendum to his 1809 Philosophie zoologique 58 , has few branches, whereas those in Histoire naturelle des animaux sans vertèbres [ 59 , I p.457] showed more (Figure 6). The titles of these trees reveal their evolutionary intent: Tableau servant à montrer l'origine des différens animaux and Ordre présumé de la formation des Animaux, offrant 2 séries séparées, subrameuses respectively. Lamarck's theory of evolution was widely known in his lifetime, but he persisted in linking it to idiosyncratic theories of chemistry and physics, and encountered scientific and political opposition from Cuvier and others 60 61 .

Trees returned a couple of decades later as a depiction of the arrangement of nature (see below), but first we need to introduce the most important alternative: networks.

Remarkably, the network metaphor is older than that of a branching tree. In his 1750 Della storia naturale marina dell'Adriatico 62 , Vitaliano Donati sought to describe the arrangement of aquatic organisms. He argued that regularities in nature allowed one to extrapolate from, or apply analogies based on, the terrestrial (hence more easily observable) Chain to understand the natural history of organisms in the sea, where it may be that transitions from the plant to the animal are most often encountered. But the result was not a single Chain encompassing all life, both terrestrial and aquatic:

When I observe the productions of Nature, I do not see one single and simple progression, or chain of beings, but rather I find a great number of uniform, perpetual and constant progressions. [ 62 , p.xx]

Moreover, these numerous progressions are interconnected:

In each one of those orders, or Classes, nature forms its series and presents its almost imperceptible passages from link to link in its chains. In addition, the links of the chain are joined [uniti] in such a way within the links of another chain, that the natural progressions should have to be compared more to a net [rete] than to a chain, that net being, so to speak, woven with various threads which show, between them, changing communications, connections, and unions. [ 62 , p.xxi]

Where in the second sentence above I translate uniti as joined, the 1758 French translation 63 renders it as entrelacés, interlaced or intertwined.

Giuseppe Olivi [ 64 , I p.68] likewise found the network an appealing metaphor for aquatic nature. Quoting Leibnitz to similar effect, Gottfried Treviranus wrote of nature as being made of "thousands and many thousands of chains, with endless skill entwined down to the smallest knot" [ 65 , I pp.473-475]. As this quotation is from the first book to use the word biology in a modern sense (Biologie, oder Philosophie der lebenden Natur), it can be said that nature-as-network was present at the dawn of modern biology.

We have already encountered the Eighteenth-century concept of affinity (above). Networks of affinities among plants and among animals were depicted in great detail in the late Eighteenth and very early Nineteenth centuries. Notable examples appeared in the Ordines naturales plantarum commentatio botanica of Johann Philipp Rühling (Figure 7) 66 , the Tabula affinitatum animalium of Johann (Jean) Hermann (Figure 8) 67 , and the Tabula affinitatum regni vegetabilis of August Johann Georg Carl Batsch (Figure 9) 68 . In the text Hermann identifies some of these affinities in detail, for example those which, in his opinion, link the rays (genus Raja) individually with Mammalia, Amphibia, Insecta, Aves, Pisces and Vermes [ 67 , p.295].

Treviranus argued [ 65 , I p.474) that whereas a chain allows one to describe only a single facet of organisation, with a network the complete organisation can be taken into account. He did not specify which organisational features might comprise the network of organisms, but the immediately previous section of his treatise discussed gradations in e.g. musculature, circulatory and nervous systems, and the brain. Nor did Treviranus propose that one organisational feature (say, musculature) could be associated with the x-axis of a network diagram, and a second feature (say, nervous-system organisation) with its y-axis; he meant instead that gradations in multiple - indeed all - features could be represented at fine scale, as adjacencies within local neighborhoods of the network. Nor, to my knowledge, did any network (or Linnaean map) proposed in these decades depict affinity on one axis, and analogy on the other.

Georges Cuvier later used the network analogy to emphasize the connectedness of all beings:

...our systematic methods consider only the nearest affinities; they seek to place a being only between two others, and they are unceasingly at fault; the true method sees each being in the midst of all others; it shows all the radiations by which it is connected more or less closely within this immense network which constitutes organised nature [ 69 , I p.569]

Networks appeared in a second, and very different, context shortly after 1750. Buffon held a somewhat idiosyncratic (and occasionally inconsistent) view of nature, believing in the fixity of species while refusing to accept the reality of higher taxa. Like Darwin much later, however, Buffon was interested in animal breeding and in the diversity of forms it could yield. Buffon's well-known diagram of relationships among breeds of dogs (Figure 10) 70 is not only a network but an explicitly genealogical one, albeit in Buffon's view a special case due to the human intervention that is required.

In the passage translated above, Pallas 48 refers to polyhedric representations of order in nature other than series, trees and networks. Here (as elsewhere) the 1787 German translation takes some liberty with the Latin text, elaborating that these polyhedric figures have multiple surfaces and compartments [ 49 , p.47]. I am unaware of pre-1766 representations that could have been so described, apart perhaps from a particularly angular conceptualisation of the Linnaean map. Fifty years later, however, we do encounter a diversity of polyhedric representations of the living world 54 71 72 73 (Figures 11, 12, 13, 14).

Notable among these alternative was the quinarian system, in which groups were arranged as a cycle of cycles. Swainson [ 74 , p.91] credits the modern idea to Fischer de Waldheim [ 75 , p.181], who in 1805 arrayed animals in "a series of contiguous circles around Man as a centre". As developed by Macleay 76 , the animals are constituted as five great natural groups (classes Acrita, Radiata, Annulosa, Vertebrata and Mollusca), each of which is further divisible into five lesser groups; even the imperfectly known Mollusca were unlikely to constitute an exception to this "rule" [ 76 , p.321]. Arranging the five sub-groups in each class into a circle would reveal a series of affinities within that class; and arranging the five class-circles into a larger ring would reveal affinities between sub-groups in different classes, while identifying other similarities as mere analogies [ 76 , p.319]. These analogies moreover might be positioned non-randomly, e.g. forming axes as in Swainson [ 77 , p.200] (Figure 15). Certain otherwise problematic groups, such as Tunicata, could be placed as "osculant" groups at the tangent between adjacent classes. As in the Linnaean map, local affinities did not align head-to-tail into a unitary series or chain: note the order of classes Acrita → Mollusca → Vertebrata → Annulosa → Radiata (→ Acrita) in Macleay's system, with the vertebrate sub-groups Aves and Mammalia as distant as possible from the acritan sub-group Agastria, the point of contact with Vegetabilia [ 76 , p.318] (Figure 16). This allowed Macleay to argue that Lamarck's 1809 tree was really an un-recognised quinarian cycle (Figure 17); perhaps because he considered these regularities to be evidence of a divine design in nature [ 76 , pp.324-325 and elsewhere], he did not ask whether, conversely, his cycles might represent planar sections through Lamarck's trees. Similarly a Venn-like diagram of animal taxa based on embryology 78 might have been (but was not) presented as a planar section through a tree (or a sparse network, if its additional correspondences are to be included).

The quinarian system was adopted by Vigors 79 , Swainson 77 , Lindley [ 80 , p.130; 81 ] (Figure 18), Kaup 82 and others, a seven-cycled system by Newman 83 , and a ten-cycled system by Elias Fries 84 ; however, following criticism by Strickland 85 in 1841 these systems began a terminal slide into disfavour. The quinarian system was nonetheless privileged with a lengthy chapter in the (in)famous Vestiges 86 , and found its way into the popular literature in works such as Hugh Miller's Testimony of the Rocks [ 87 , p.493]. Darwin was thoroughly aware of the quinarian system, and worried that his own theory of natural selection might suffer a similar fate if presented carelessly to the public [ 88 , note 5]. The young Edward Drinker Cope sketched a quinarian classification of amphibia in 1857 [ 89 , p.258], and a variant the theory was taught at the University of Toronto as late as 1870 81 .

O'Hara [ 44 , p.256] characterizes the years 1840-1859 as a "mapmaking" period, in which Strickland and Wallace sought to banish analogy and symmetry (hence quinarian circles and other geometric representations) from systematics. During these two decades at least four investigators published tree diagrams, two depicting stratigraphic series of fossils. From 1840 through at least 1856, in some thirty editions of his popular textbook Elementary Geology, Edward Hitchcock 90 presented a branching diagram representing series of plant and animal fossils in successive strata. These diagrams had been removed by the 1860 edition 91 . Archibald 91 notes that Hitchcock did not accept the transmutation of species, arguing against Lamarck, Chambers (Vestiges) and later Darwin. Louis Agassiz presented a similar tree-like depiction of fossil fish in the first volume of his Recherches sur les poissons fossiles [ 92 , pp.170-171]; like Hitchcock, Agassiz did not accept a transmutation of species.

Alfred Russel Wallace, on the other hand, sought evidence for transmutation of species during explorations in Brazil (1848-1852) and the Malay Archipelago (1854-1862). In 1855 he communicated a paper referring to "branching of the lines of affinity, as intricate as the twigs of a gnarled oak or the vascular system of the human body", and later to "the true Natural System of classification" needing to order "the stem and main branches represented by extinct species" as well as extant diversity, "a vast mass of limbs and boughs and minute twigs and scattered leaves" 93 . In a remarkable paper published the following year, he offered not only branching representations of affinities among two groups of birds (Fissirostres and Scansores), but also an explicit description of his method of tree-building [ 94 , pp. 206-207]. Wallace accepted that there exists a main axis along which many taxa can be arranged in a series of affinities, while affinities of other taxa can be represented as branches and sub-branches to the left and right off this main axis. These affinities [ 94 , p.199] were of structure and "economy" [ 94 , p.195], the latter term connoting features of reproduction, nutrition, physiology and ecology; branch lengths correspond with degree of affinity, and gaps may occur at any point due to extinction of families [ 94 , pp.206,214]. As a consequence, Wallace's trees (Figure 19) were both phylogenies (in the modern sense of showing extant taxa at the branch-tips) and morphoclines. Wallace explicitly stated that his approach followed Lindley and Strickland against the quinarian system of Vigors and Swainson [ 94 , pp.195,206,212].

In 1858 Heinrich Georg Bronn 95 depicted a system of animals, as evidenced by the fossil record, in the form of a branching diagram drawn to resemble an actual tree (Figure 20) and described as a Baum-förmige Bilde des Systems with Äste (branches). His tree depicted a series of species, of increasing organisational perfection, succeeding each other as time progresses; this succession continues on all branches, although at any point in time some new species are necessarily more-perfect than others on lower branches [ 96 , pp.110-116]. Mikulinskii 53 , p.316] notes that Bronn had earlier cited Eichwald's Zoologia specialis 51 , hence presumably had studied Eichwald's (Pallas's) tree. Bronn later made the first translations of Origin of Species into German, adding footnotes and a chapter of his own criticisms; one of these translations was read by Haeckel 97 .

In 1837, in his Notebook B [ 98 , B§21], Darwin famously wrote

organised beings represent a tree. Irregularly branched some branches far more branched. - Hence Genera. - «as many terminal buds dying, as new ones generated»

In successive notes (e.g. [ 98 , B§23,24]) he refers to "the tree of life", and wondered whether "(t)he tree of life should perhaps be called the coral of life" [ 98 , B§25]. Bredekamp 99 argues that the two small branching figures Darwin sketched first in Notebook B [ 98 , B§26] were in fact inspired by specimens he himself had collected and thought to be corals (some later turned out to be calcareous algae); on the other hand, Voss 100 links these sketches to embryological diagrams by the physician Martin Berry. Darwin's more-famous "I think" figure [ 98 , B§36] (Figure 21), while topologically a tree, does not resemble any actual botanical tree, nor does Darwin call it a tree. The mathematical structure today known as a tree (although not the term itself) was introduced a decade later by Kirchhoff 101 and von Staudt [ 102 , pp.20-21], while Arthur Cayley 103 is thought to have been the first to call this structure a tree.

The only illustration in Origin of Species was an abstract tree diagram (Figure 22):

The affinities of all the beings of the same class have sometimes been represented by a great tree. I believe this simile largely speaks the truth. The green and budding twigs may represent existing species; and those produced during each former year may represent the long succession of extinct species. At each period of growth all the growing twigs have tried to branch out on all sides, and to overtop and kill the surrounding twigs and branches, in the same manner as species and groups of species have tried to overmaster other species in the great battle for life. The limbs divided into great branches, and these into lesser and lesser branches, were themselves once, when the tree was small, budding twigs; and this connexion of the former and present buds by ramifying branches may well represent the classification of all extinct and living species in groups subordinate to groups. Of the many twigs which flourished when the tree was a mere bush, only two or three, now grown into great branches, yet survive and bear all the other branches; so with the species which lived during long-past geological periods, very few now have living and modified descendants. ... As buds give rise by growth to fresh buds, and these, if vigorous, branch out and overtop on all sides many a feebler branch, so by generation I believe it has been with the great Tree of Life, which fills with its dead and broken branches the crust of the earth, and covers the surface with its ever branching and beautiful ramifications 104 129 130 .

Darwin's theory of evolution shared points of similarity with certain of the systems described in previous sections of this paper, but was unique in their combination. Like Lamarck and Wallace, he accepted the transmutation of species. Unlike Bonnet, Lamarck, Eichwald, Bronn and Haeckel, he rejected as a "miserable limited view" [ 98 , B§216] the ongoing creation or appearance of new species, instead emphasising the continuity of genealogical lineages from one or a small number of original forms. Darwin did not base his tree on affinity, although successive generations "tend to inherit those advantages which made their common parent (A) more numerous than most of the other inhabitants of the same country" [ 104 , p.118] (in this way, as Darwin put it, affinity will "grow" [ 98 , C§151]). His tree is instead one of genealogical inheritance. He placed extant taxa at the tips of his tree, not at the internal nodes or along the branches. Darwin described the struggle for existence in a Malthusian context, and importantly emphasised the central role of natural selection - his "dangerous idea" [ 105 , p.21] - without recourse to a metaphysical formative force toward perfection or realisation of potential per Bonnet, Lamarck, Eichwald and others.

Darwin attracted strong champions, including Thomas Henry Huxley in the English-speaking world and Ernst Haeckel on the Continent. Haeckel (following Bronn) did not accept every detail of Darwin's argument, but agreed that the natural system is necessarily genealogical, and seized enthusiastically on Darwin's abstract branching diagram as its form. Darwin had argued 104 that the geological record was too incomplete to provide a basis for fleshing-out this tree, so to speak, with actual taxa. Haeckel would instead base his reconstruction method on his so-called biogenetic law: the claim that an individual's ontogeny recapitulated, or re-traced and summarized, its phylogenetic history 106 . In this way he derived Stammbäume (genealogical trees), which he depicted as a proper botanical trees 106 107 to which extant biological taxa were assigned (Figure 23). His initial trees were refined and extended in great detail to numerous taxa. Note that Haeckel did not call his trees phylogenies, reserving this term for a series of morphological stages 108 ; how could ontogeny (a linear process in a single organism) recapitulate phylogeny, unless phylogeny too was linear? The received meaning of phylogeny has since evolved, of course, and is now used to mean genealogical tree, even in contexts where only the branching topology is relevant.

Although it lies outside the scope of this article to review in detail the uptake of Darwin's theories and adoption of the evolutionary tree as an explanation of modern biodiversity, I offer three case studies to illustrate that this uptake and adoption progressed at different rates and to varying extents, if at all, across different fields of biology. Network diagrams 109 and geographical maps persisted in some research communities; and today, as we shall see, network representations are again resurgent in microbial phylogenetics 110 .

Darwin's trees played an integral role in his theory, linking process (genealogical descent-with-modification, plus extinction) with outcome (the diversity of past and present-day species, expressed as hierarchical systems of classification). Trees also provided a common, coherent, and (although this would be discovered only later) mathematically and statistically tractable framework linking much outside his argument per se, from comparative anatomy and development to palaeontology and biogeography, to evolutionary theory, with the result that now "nothing makes sense in biology except in the light of evolution, sub specie evolutionis" [ 176 , p.449]. Darwin's trees are justly considered a landmark not only of biology and of science more broadly, but of modern intellectual and visual culture as well 100 177 .

In this article I have attempted to situate Darwin's trees in historical context, specifically the search for the natural system following the abandonment of the Great Chain of Being. His trees existed, and exist, in other contexts (e.g. sociological, political, religious) which I do not consider here. Darwin was not the first to propose that the system of nature is tree-like, nor that species undergo transmutation along hierarchically branching temporal trajectories. In the decades following 1859, genealogical trees won acceptance in some but certainly not all areas of biology; nor indeed have trees won full acceptance even today, although they remain default hypotheses for most biologists, as indeed more broadly in science and in society. But nature-as-network preceded the branching tree, was never completely supplanted by trees, and seems set to re-emerge as the most-inclusive metaphor for the living world - the "Network of Life" 110 .

As we commemorate Darwin's birth and the Origin of Species, we also look forward to the 375^th anniversary, next year, of Historia naturae, maxime peregrinae and Nieremberg's hint at an unbroken web of nature.

The author declares that they have no competing interests.

MAR planned and wrote this article, and unless otherwise indicated is responsible for the translations from French, Italian, Latin, German and Russian.