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42-443: One way of depicting ascendency is to regard it as "organized power", because the index represents the magnitude of the power that is flowing within the system towards particular ends, as distinct from power that is dissipated naturally. Almost half a century earlier, Alfred J. Lotka (1922) had suggested that a system's capacity to prevail in evolution was related to its ability to capture useful power. Ascendency can thus be regarded as

84-492: A Cartesian grid . The work is widely admired by biologists, anthropologists and architects among others, but is often not read by people who cite it. Peter Medawar explains this as being because it clearly pioneered the use of mathematics in biology , and helped to defeat mystical ideas of vitalism ; but that the book is weakened by Thompson's failure to understand the role of evolution and evolutionary history in shaping living structures. Philip Ball and Michael Ruse , on

126-459: A Man (1930), Length of Life (1936), and Twenty-five Years of Health Progress (1937). On Growth and Form On Growth and Form is a book by the Scottish mathematical biologist D'Arcy Wentworth Thompson (1860–1948). The book is long – 793 pages in the first edition of 1917, 1116 pages in the second edition of 1942. The book covers many topics including the effects of scale on

168-479: A bio-statistician, who sought to apply the principles of the physical sciences to biological sciences as well. His main interest was demography , which possibly influenced his professional choice as a statistician at Metropolitan Life Insurance . One of Lotka's earliest publications, in 1912, proposed a solution to Ronald Ross 's second malaria model. In 1923, he published a thorough five-part analysis and extension of both Ross's malaria models. The fourth part in

210-503: A central guiding feature of his work in ecosystem ecology . Odum called Lotka's law the maximum power principle . Lotka's work in mathematical demography began in 1907 with the publication of articles in the journal Science and American Journal of Science . He published several dozen articles on the subject over more than two decades, culminating with Théorie Analytique des Associations Biologiques (Analytical Theory of Biological Associations). The 45-page Part 1, titled Principes ,

252-485: A classic "for its exploration of natural geometries in the dynamics of growth and physical processes." They note the "extraordinary optimism" in the book, its vision of the world as "a symphony of harmonious forces", and its huge range, including: the laws governing the dimension of organisms and their growth, the statics and dynamics at work in cells and tissues including the phenomena of geometrical packing, membranes under tension, symmetries, and cell division; as well as

294-453: A mass of examples, Thompson pointed out correlations between biological forms and mechanical phenomena. He showed the similarity in the forms of jellyfish and the forms of drops of liquid falling into viscous fluid, and between the internal supporting structures in the hollow bones of birds and well-known engineering truss designs. He described phyllotaxis (numerical relationships between spiral structures in plants) and its relationship to

336-406: A refinement of Lotka's supposition that also takes into account how power is actually being channeled within a system. In mathematical terms, ascendency is the product of the aggregate amount of material or energy being transferred in an ecosystem times the coherency with which the outputs from the members of the system relate to the set of inputs to the same components ( Ulanowicz 1986). Coherence

378-485: A very simple kind, while others are more striking and more unexpected. A comparatively simple case, involving a simple shear, is illustrated by Figs. 373 and 374. Fig. 373 represents, within Cartesian co-ordinates, a certain little oceanic fish known as Argyropelecus olfersi . Fig. 374 represents precisely the same outline, transferred to a system of oblique co-ordinates whose axes are inclined at an angle of 70°; but this

420-586: Is beloved of the circle-squarer, and of all those who seek to find, and then to penetrate, the secrets of the Great Pyramid. It is deep-set in Pythagorean as well as in Euclidean geometry . (1st p. 652 – 2nd p. 934 – Bonner removed) (1st p. 670 – 2nd p. 958 – Bonner p. 221) (1st p. 719 – 2nd p. 1026 – Bonner p. 268) Among the fishes we discover a great variety of deformations, some of them of

462-407: Is a tour de force combining the classical approaches of natural philosophy and geometry with modern biology and mathematics to understand the growth, form, and evolution of plants and animals. Bogin observes that Thompson originated the use of transformational grids to measure growth in two dimensions, but that without modern computers the method was tedious to apply and was not often used. Even so,

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504-569: Is based on an inverse square law where the number of authors writing n papers is 1/ n of the number of authors writing one paper. Each subject area can have associated with it an exponent representing its specific rate of author productivity." Lotka's work sparked additional inquiries, eventually seminally contributing to the field of scientometrics —the scientific study of scientific publications. He teamed up with Louis Israel Dublin , another statistician at Metropolitan Life, to write three books on demography and public health : The Money Value of

546-489: Is best known for his proposal of the predator–prey model , developed simultaneously but independently of Vito Volterra . The Lotka–Volterra model is still the basis of many models used in the analysis of population dynamics in ecology . Lotka was born in Lwów , Austria-Hungary (now Lviv, Ukraine) to Polish-American parents. His parents, Jacques and Marie (Doebely) Lotka, were US nationals. He gained his B.Sc. in 1901 at

588-405: Is gauged by the average mutual information shared between inputs and outputs (Rutledge et al. 1976). Originally, it was thought that ecosystems increase uniformly in ascendency as they developed, but subsequent empirical observation has suggested that all sustainable ecosystems are confined to a narrow "window of vitality" (Ulanowicz 2002). Systems with relative values of ascendency plotting below

630-462: Is limiting the functioning of each component of the ecosystem. It is thought that autocatalytic feedback is the primary route by which systems increase and maintain their ascendencies (Ulanowicz 1997.) Alfred J. Lotka Alfred James Lotka (March 2, 1880 – December 5, 1949) was a Polish-American mathematician , physical chemist , and statistician , famous for his work in population dynamics and energetics . A biophysicist , Lotka

672-535: Is now (as far as can be seen on the scale of the drawing) a very good figure of an allied fish, assigned to a different genus, under the name of Sternoptyx diaphana . Thompson 1917, pages 748–749 (1st p. 778 – 2nd p. 1093 – Bonner p. 326) "J. P. McM[urrich]", reviewing the book in Science in 1917, wrote that "the book is one of the strongest documents in support of the mechanistic view of life that has yet been put forth", contrasting this with "vitalism". The reviewer

714-482: Is the same today as when the first snows fell": adding "so, too, the basic forces acting upon organisms", and comments that we have forgotten other early twentieth century scientists who scorned evolution. In contrast, he argues, Thompson owes his continuing influence to the fact that his alternative doesn't beg questions at every turn. (Also, of course, he wrote beautifully, better than the poets of his day.) The anthropologist Barry Bogin writes that Thompson's book

756-550: The Fibonacci sequence . Perhaps the most famous part of the book is Chapter 17, "The Comparison of Related Forms," where Thompson explored the degree to which differences in the forms of related animals could be described, in work inspired by the German engraver Albrecht Dürer (1471–1528), by mathematical transformations . The book is descriptive rather than experimental science: Thompson did not articulate his insights in

798-509: The Quarterly Review of Biology (of which he was the editor), writes that the book is "a work widely praised, but seldom used. It contains neither original insights that have formed a basis for later advances nor instructive fallacies that have stimulated fruitful attack. This seeming paradox is brilliantly discussed by P. B. Medawar [in] Pluto's Republic ." Williams then attempts a "gross simplification" of Medawar's evaluation: It

840-589: The University of Birmingham , England , he did graduate work in 1901–02 at Leipzig University , received an M.A. in 1909 at Cornell University and a D.Sc. at Birmingham University in 1912. In 1935, he married Romola Beattie. They had no children. He died in Red Bank, New Jersey. Although he is today known mainly for the Lotka–Volterra equations used in ecology , Lotka was a bio-mathematician and

882-443: The "scope of the book and the general approach to the problems dealt with have remained unchanged, but considerable additions have been made and large parts have been recast". He was impressed at the extent to which Thompson had kept up with developments in many sciences, though he thought the mentions of quantum theory and Heisenberg uncertainty unwise. George C. Williams , reviewing the 1942 edition and Bonner's abridged edition for

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924-532: The 1942 edition that he had written "this book in wartime, and its revision has employed me during another war. It gave me solace and occupation, when service was debarred me by my years. Few are left of the friends who helped me write it." An edition of 346 pages was abridged by John Tyler Bonner , and is widely published under the same title. The book, often in the abridged edition, has been reprinted more than 40 times, and has been translated into Chinese, French, German, Greek, Italian, and Spanish. The contents of

966-422: The book "has haunted all discussion of these matters ever since." Shalizi states that Thompson's goal is to show that biology follows inevitably from physics, and to a degree also from chemistry. He argues that when Thompson says "the form of an object is a 'diagram of forces'", Thompson means that we can infer from an object the physical forces that act (or once acted) upon it. Shalizi calls Thompson's account of

1008-479: The book, and notes that Chapter 17 "seems to the reviewer to contain the essence of the long and more or less leisurely thesis... The chapter is devoted to comparison of related forms, largely by the method of co-ordinates. Fundamental differences in these forms are thus revealed", and Buchanan concludes that the large "gaps" indicate that Darwin's endless series of continuous variations is not substantiated. But he does have some criticisms: Thompson should have referenced

1050-400: The bricklayer builds a factory chimney, he lays his bricks in a certain steady, orderly way, with no thought of the spiral patterns to which this orderly sequence inevitably leads, and which spiral patterns are by no means "subjective". The numbers that result from such spiral arrangements are the Fibonacci sequence of ratios 1/2, 2/3, 3.5 ... converging on 0.61803..., the golden ratio which

1092-1019: The chapters in the first edition are summarized below. All but Chapter 11 have the same titles in the second edition, but many are longer, as indicated by the page numbering of the start of each chapter. Bonner's abridgment shortened all the chapters, and removed some completely, again as indicated at the start of each chapter's entry below. (1st edition p. 1 – 2nd edition p. 1 – Bonner p. 1) (1st p. 16 – 2nd p. 22 – Bonner p. 15) (1st p. 50 – 2nd p. 78 – Bonner removed) (1st p. 156 – 2nd p. 286 – Bonner removed) (1st p. 201 – 2nd p. 346 – Bonner p. 49) (1st p. 277 – 2nd p. 444 – Bonner removed) (1st p. 293 – 2nd p. 465 – Bonner p. 88) (1st p. 346 – 2nd p. 566 – Bonner merged with previous chapter) (1st p. 411 – 2nd p. 645 – Bonner p. 132) (1st p. 488 – 2nd p. 741 – Bonner removed) (1st p. 493 – 2nd p. 748 – Bonner p. 172) (1st p. 587 – 2nd p. 850 – Bonner merged with previous chapter) (1st p. 612 – 2nd p. 874 – Bonner p. 202) (1st p. 635 – 2nd p. 912 – Bonner removed) When

1134-498: The effects of hormones on growth; and the relation of molecular configuration and form; genetics is barely mentioned, and experimental embryology and regeneration [despite Thompson's analysis of the latter] are overlooked. The mathematics used consists of statistics and geometry , while thermodynamics is "largely absent". Edmund Mayer, reviewing the second edition in The Anatomical Record in 1943, noted that

1176-400: The engineering and geodesics of skeletons in simple organisms. Beesley and Bonnemaison observe that Thompson saw form "as a product of dynamic forces .. shaped by flows of energy and stages of growth." They praise his "eloquent writing and exquisite illustrations" which have provided inspiration for artists and architects as well as scientists. The statistician Cosma Shalizi writes that

1218-403: The form of hypotheses that can be tested. He was aware of this, saying that "This book of mine has little need of preface, for indeed it is 'all preface' from beginning to end." The first edition appeared in 1917 in a single volume of 793 pages published by Cambridge University Press. A second edition, enlarged to 1116 pages, was published in two volumes in 1942. Thompson wrote in the preface to

1260-434: The form of species, with the smallest hint of vitalism as the unseen driving force. Thompson had previously criticized Darwinism in his paper Some Difficulties of Darwinism . On Growth and Form explained in detail why he believed Darwinism to be an inadequate explanation for the origin of new species . He did not reject natural selection, but regarded it as secondary to physical influences on biological form . Using

1302-473: The other hand, suspect that while Thompson argued for physical mechanisms, his rejection of natural selection bordered on vitalism. D'Arcy Wentworth Thompson was a Scottish biologist and pioneer of mathematical biology. His most famous work, On Growth and Form was written in Dundee, mostly in 1915, but publication was put off until 1917 because of the delays of wartime and Thompson's many late alterations to

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1344-663: The physics of morphogenesis ingenious, extremely elegant, very convincing and, significantly, aimed at very large features of the organism: the architecture of the skeleton, the curve of horns or shells, the outline of the organism as a whole. Shalizi notes Thompson's simplicity, explaining the processes of life "using little that a second-year physics undergrad wouldn't know. (Thompson's anti-reductionist admirers seldom put it this way.)". He notes that Thompson deliberately avoided invoking natural selection as an explanation, and left history, whether of species or of an individual's life, out of his account. He quotes Thompson's "A snow-crystal

1386-653: The series, co-authored by F. R. Sharpe, modeled the time lag for pathogen incubation. Lotka published Elements of Physical Biology in 1925, one of the first books on mathematical biology after D'Arcy Thompson 's On Growth and Form . He is also known for his energetics perspective on evolution . Lotka proposed that natural selection was, at its root, a struggle among organisms for available energy; Lotka's principle states that organisms that survive and prosper are those that capture and use energy more efficiently than their competitors. Lotka extended his energetics framework to human society. In particular, he suggested that

1428-431: The shape of animals and plants, large ones necessarily being relatively thick in shape; the effects of surface tension in shaping soap films and similar structures such as cells; the logarithmic spiral as seen in mollusc shells and ruminant horns; the arrangement of leaves and other plant parts ( phyllotaxis ); and Thompson's own method of transformations, showing the changes in shape of animal skulls and other structures on

1470-414: The shift in reliance from solar energy to nonrenewable energy would pose unique and fundamental challenges to society. These theories made Lotka an important forerunner to the development of biophysical economics and ecological economics , advanced by Frederick Soddy , Howard Odum and others. While at Johns Hopkins, Lotka completed his book Elements of Physical Biology (1925), in which he extended

1512-410: The text. The central theme of the book is that biologists of its author's day overemphasized evolution as the fundamental determinant of the form and structure of living organisms, and underemphasized the roles of physical laws and mechanics . At a time when vitalism was still being considered as a biological theory, he advocated structuralism as an alternative to natural selection in governing

1554-413: The window tend to fall apart due to lack of significant internal constraints, whereas systems above the window tend to be so "brittle" that they become vulnerable to external perturbations. Sensitivity analysis on the components of the ascendency reveals the controlling transfers within the system in the sense of Liebig (Ulanowicz and Baird 1999). That is, ascendency can be used to identify which resource

1596-503: The work of Pierre François Verhulst . His first book summarizes his previous work and organizes his ideas of unity and universality of physical laws, making his works accessible to other scientists. Although the book covered a large number of topics, from energetics of evolution (see below) to the physical nature of consciousness, the author is primarily known today for the Lotka–Volterra equation of population dynamics. His earlier work

1638-543: Was a compelling demonstration of how readily one can use physical and geometric principles in trying to understand biology. This was a major contribution in 1917 when vitalism was still being defended by prominent biologists. The battle was as won as it is ever likely to be by the time of the 1942 edition. The book was deficient because of Thompson's lack of understanding of evolution and antipathy for any concepts of historical causation." The architects Philip Beesley and Sarah Bonnemaison write that Thompson's book at once became

1680-480: Was centered on energetics and applications of thermodynamics in life sciences . Lotka proposed the theory that the Darwinian concept of natural selection could be quantified as a physical law. The law that he proposed was that the selective principle of evolution was one which favoured the maximum useful energy flow transformation. The general systems ecologist Howard T. Odum later applied Lotka's proposal as

1722-631: Was interested in the "discussion of the physical factors determining the size of organisms, especially interesting being the consideration of the conditions which may determine the minimum size". J. W. Buchanan, reviewing the second edition in Physiological Zoology in 1943, described it as "an imposing extension of his earlier attempt to formulate a geometry of Growth and Form" and "beautifully written", but warned that "the reading will not be easy" and that "A vast store of literature has here been assembled and assimilated". Buchanan summarizes

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1764-472: Was published in 1934; the 149-page Part 2, titled Analyse demographique avec application particuliere a l'espece humaine , was published in 1939; both by Hermann & Cie , Paris. Within the field of bibliometrics, particularly that part devoted to studying scientific publications, Lotka is noted for contributing " Lotka's law ". The law, which Lotka discovered, relates to the productivity of scientists. As noted by W. G. Poitier in 1981: "The Lotka distribution

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