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In this note, we examine the proportion of periodic orbits of Anosov flows that lie in an infinite zero density subset of the first homology group. We show that on a logarithmic scale we get convergence to a discrete fractal dimension.
The intersection of development and evolution has always harbored conceptual issues, but many of these are on display in contemporary evolutionary developmental biology (evo-devo). These issues include: (1) the precise constitution of evo-devo, with its focus on both the evolution of development and the developmental basis of evolution, and how it fits within evolutionary theory; (2) the nature of evo-devo model systems that comprise the material of comparative and experimental research; (3) the puzzle of how to understand the widely used notion of 'conserved mechanisms'; (4) the definition of evolutionary novelties and expectations for how to explain them; and (5) the demand of interdisciplinary collaboration that derives from investigating complex phenomena at key moments in the history of life, such as the fin-limb transition. This Element treats these conceptual issues with close attention to both empirical detail and scientific practice to offer new perspectives on evolution and development. This title is also available as Open Access on Cambridge Core.
What happens at the point of interchange between scholarly communities? We examine this question by investigating the case of growing ties between historical sociology and ethnography, two social scientific methods that once seemed to have little in common. Drawing on methodological writings by ethnographers and original interviews with practicing historical sociologists, we argue that these ties have been shaped by structural and methodological homologies between the two disciplines. Structurally, ethnography and historical sociology are similarly positioned in sociology more broadly, as enterprises with sometimes-tense relationships with dominant assumptions of the social sciences. Methodologically, both ethnographers and historical sociologists face the challenges of bounding the research process, navigating access to data, analyzing and retaining data while “in the field,” and overcoming cultural distance between themselves and the worlds they are studying. Taken together, these findings extend work in the sociology of science and knowledge and suggest some key conditions for intellectual efflorescence.
We construct two new classes of topological dynamical systems; one is a factor of a one-sided shift of finite type while the second is a factor of the two-sided shift. The data are a finite graph which presents the shift of finite type, a second finite directed graph and a pair of embeddings of it into the first, satisfying certain conditions. The factor is then obtained from a simple idea based on binary expansion of real numbers. In both cases, we construct natural metrics on the factors and, in the second case, this makes the system a Smale space, in the sense of Ruelle. We compute various algebraic invariants for these systems, including the homology for Smale space developed by the author and the K-theory of various $C^{*}$-algebras associated to them, in terms of the pair of original graphs.
The origin of carbon fixation is a fundamental question in astrobiology. While the Calvin cycle is the most active on the modern Earth, the reductive tricarboxylic acid (TCA) cycle (rTCA) pathway for carbon fixation has been proposed to have played an important role in early evolution. In this study, we examined the evolution of key enzymes in the rTCA, which are rare in extant organisms, occurring in a few groups of Bacteria and Archaea. We investigated one of the least common reactions of this pathway, cleavage of citrate into oxaloacetate and acetyl-CoA, which can be performed by either a two-enzyme system (CCS/CCL) or a single enzyme (ACL) that is assumed to be the result of fusion of the two active sites into a single polypeptide. For broader context, we also studied functionally diverged homologues of these enzymes, succinyl-CoA synthetase (SCS) and citrate synthase. Our phylogenetic analysis of these enzymes in Bacteria and Archaea shows that SCS, a homologue of CCS from distant bacterial taxa capable of citrate cleavage, are monophyletic, suggesting linked horizontal gene transfers of SCS and citrate cleavage enzymes. We also found evidence of the horizontal transfer of SCS from a clade of anaerobic Archaea (Archaeoglobi, Methanomicrobia or Crenarchaeota) to an ancestor of Cyanobacteria/Melainabacteria clade – both of which share a succinate semialdehyde shunt in their oxidative TCA cycles. We identified new bacterial and archaeal taxa for which complete rTCA cycles are theoretically possible, including Syntrophobacter, Desulfofundulus, Beggiatoa, Caldithrix, Ca. Acidulodesulfobacterales and Ca. Micrarchaeota. Finally, we propose a mechanism for syntrophically-regulated fluxes through oxidative and rTCA reactions in microbial communities particularly Haloarchaea-Nanohaloarchaea symbiosis and its implications for carbon fixation during retinal-based phototrophy and the Purple Earth hypothesis. We discuss how the inclusion of an ecological perspective in the studies of evolution of ancient metabolic pathways may be beneficial to understanding the origin of life.
The extraxial-axial theory (EAT) and universal elemental homology (UEH) are often portrayed as mutually exclusive hypotheses of homology within pentaradiate Echinodermata. EAT describes homology upon the echinoderm bauplan, interpreted through early post-metamorphic growth and growth zones, dividing it into axial regions generally associated with elements of the ambulacral system and extraxial regions that are not. UEH describes the detailed construction of the axial skeleton, dividing it into homologous plates and plate series based on symmetry, early growth, and function. These hypotheses are not in conflict; the latter is rooted in refinement of the former. Some interpretive differences arise because many of the morphologies described from eleutherozoan development are difficult to reconcile with Paleozoic forms. Conversely, many elements described for Paleozoic taxa by UEH, such as the peristomial border plates, are absent in eleutherozoans. This Element recommends these two hypotheses be used together to generate a better understanding of homology across Echinodermata.
Let $G$ be a compact connected simple Lie group of type $(n_{1},\,\ldots,\,n_{l})$, where $n_{1}<\cdots < n_{l}$. Let $\mathcal {G}_k$ be the gauge group of the principal $G$-bundle over $S^{4}$ corresponding to $k\in \pi _3(G)\cong \mathbb {Z}$. We calculate the mod-$p$ homology of the classifying space $B\mathcal {G}_k$ provided that $n_{l}< p-1$.
This Introduction provides an overview of the key ways in which literature and economics intersect. It firstly considers how literary texts encode economic knowledge in metaphorical – and more broadly tropic – uses of economic vocabulary, and via styles and forms that stand in a “homological” relation to monetary and financial systems. It then explains how critics have understood the ongoing overlaps between literature and economics as “genres” of writing, which have continued to borrow conventions from one another, even as the discipline of economics has become increasingly technical and mathematical. The Introduction next addresses the ways in which literary texts register the economic pressures to which they are most directly exposed: namely, the pressures of literary consumption and the literary marketplace. It closes by showing how social scientists are increasingly turning to literature and literary studies for economic insights, and by highlighting the emergence of the Economic Humanities as an interdisciplinary research field to which the approaches covered in this Cambridge Companion have made defining contributions.
In recent years, money, finance, and the economy have emerged as central topics in literary studies. The Cambridge Companion to Literature and Economics explains the innovative critical methods that scholars have developed to explore the economic concerns of texts ranging from the medieval period to the present. Across seventeen chapters by field-leading experts, the book highlights how, throughout literary history, economic matters have intersected with crucial topics including race, gender, sexuality, nation, empire, and the environment. It also explores how researchers in other disciplines are turning to literature and literary theory for insights into economic questions. Combining thorough historical coverage with attention to emerging issues and approaches, this Companion will appeal to literary scholars and to historians and social scientists interested in the literary and cultural dimensions of economics.
In this chapter I outline the transformation of systematics into phylogenetics by tracing the emergence of lineage thinking. One of the routes to a realist interpretation of the natural system of systematic relationships was to temporalize it. Lineage thinking emerged when the previously atemporal and symmetrical affinity relationships between contemporaneous taxa were replaced by asymmetrical ancestor-descendant relationships that tracked the arrow of time. This transition was accompanied by a rapid decrease in the diversity of shapes of affinity diagrams published in the systematic literature, and it marked a shift from predominantly reticulating or web-like systems to tree-like figures soon after the publication of Darwin’s On the origin of species in 1859. I argue that this graphic revolution largely records the influence of evolutionary expectations, as biologists redrew their diagrams to fit the theoretical dictates of Darwinian descent with modification. The current swell of enthusiasm for evolutionary networks has driven several recent authors to the peculiar argument that even Darwin disliked the tree of life as an evolutionary metaphor, an argument I will refute. Reconceiving the systematic relationships between taxa as phylogenetic pathways along which body plans evolve had an epistemic corollary. Speculation became a necessary tool for the evolutionary storyteller.
Scarparo has constructed counterexamples to Matui’s HK-conjecture. These counterexamples and other known counterexamples are essentially principal but not principal. In the present paper, a counterexample to the HK-conjecture that is principal is given. Like Scarparo’s original counterexample, our counterexample is the transformation groupoid associated to a particular odometer. However, the relevant group is the fundamental group of a flat manifold (and hence is torsion-free) and the associated odometer action is free. The examples discussed here do satisfy the rational version of the HK-conjecture.
Rapid evolution can be observed happening in nature when selection is unusually strong. We are all familiar, these days, with the evolution of antibiotic resistance in bacteria and the evolution of pesticide resistance in insects. Less familiar, but also very rapid, is the evolution of resistance to heavy metals in populations of plants that have adapted to growing on the spoil-heaps surrounding zinc and lead mines. These cases of unusually strong selection and consequently rapid evolution are all associated with human modification of the environment. The classic case study of evolution happening – industrial melanism in moths – also fits into this category.
Evo-devo has come a long way since its origins a mere four decades ago. Many exciting things have been discovered, and there will be many more discoveries to come in the years ahead. I have tried, in this book, to give you a flavour of this new branch of science. Here, I summarize what I think are its most important conclusions so far and the most important challenges that lie ahead.
In the previous chapter we looked at several different kinds of developmental bias. One of our conclusions was that there are both specific biases, such as the numbers of centipede trunk segments and mammalian neck vertebrae, and general biases, such as the tendency for variant developmental trajectories – and in particular viable ones – to be clustered close to the ancestral trajectory. For example, in the case of snails we noted that the forms of developmental repatterning that were generally available for natural selection to act on were slight quantitative modifications of the pattern of development of the snail that was the ancestor of the clade concerned – an example being developmental trajectories leading to differences in adult shell size. Acknowledging this form of bias entails accepting that evolution of body form does not usually take place via radical-effect macromutations. This is interesting because we saw in Chapter 2 that from the late nineteenth century to the mid-twentieth century, prominent biologists who had a specific interest in the evolution of development, such as William Bateson, D’Arcy Thompson, and Richard Goldschmidt, took a macromutational approach.
Although today we call the scientific study of the relationship between evolution and development ‘evo-devo’, neither that term, nor its longer counterpart ‘evolutionary developmental biology’, existed before about 1980. Yet the study of the relationship between the two great creative processes of the living world has a much longer history – effectively starting in the nineteenth century, the first century in which there was a well-articulated theory of evolution (first Lamarck’s, then Darwin’s). We generally refer to evo-devo’s nineteenth-century antecedent as ‘comparative embryology’. Although in the subsequent period from about 1900 to 1980 there were further studies of the relationship between evolution and development, there is no collective term for this endeavour, because mainstream developmental biology and evolutionary biology were largely separate undertakings during that stretch of time. The few biologists who tried to deal with the two together over this 80-year period might be described as mavericks. Each of them produced interesting bodies of work, but these did not really link up to form a scientific discipline.
Body-plan features that have been discussed so far include symmetry, segmentation, skeletons, and limbs. When these are encountered in different phyla, are they homologous or convergent? There are examples of both of these, plus examples where the answer is not yet clear. Bilateral symmetry of the overall body plan seems to have originated just once. So the fact that vertebrates and arthropods are both bilaterally symmetrical is due to their having inherited that body layout from their last common ancestor; in other words, their bilaterality is homologous. However, although vertebrates and arthropods both have skeletons (whereas animals belonging to many other phyla do not) these represent convergent rather than homologous skeletons – this is clear from the fact that one is ‘endo’, the other ‘exo’. Turning to segments and limbs, the fact that both vertebrates and arthropods have these component parts is hard to interpret with certainty one way or the other. The reason for this is our lack of knowledge of that ancient animal that we call the urbilaterian, or ‘Urby’ for short. Direct evidence of this creature will probably never be forthcoming, since it was almost certainly small and soft-bodied, and has left us with no fossils from which to infer its living form. Instead, we can only make rather indirect inferences based on the point in the animal evolutionary tree at which we think bilaterality arose. However, indirect inference is better than nothing, so here goes.
Here, I list ten important issues where I think that there is a significant risk of misunderstandings among those who are new to the field. After each potential misunderstanding, there is a statement of the correct situation, as I perceive it. Many of these issues are related to the rationale underlying the emergence of evo-devo as a (relatively) new discipline.
Our starting point for discussion of evolutionary pattern is the word ‘clade’. This was introduced by the British biologist Julian Huxley (grandson of Darwin’s bulldog T. H. Huxley) in the 1940s. It means a taxonomic group of a particular kind: one that includes all the descendants of a particular ancestral species, and no others. This kind of group can also be called monophyletic. When the German taxonomist Willi Hennig founded the new approach to taxonomy that we now call cladistics, in the 1950s and 1960s, the idea of a clade was central. For those not familiar with cladistics, Hennig’s main concern was that the evolutionary trees that were used through much of the literature of evolutionary biology confounded two things: closeness of ancestry and similarity in body form.
The two great creative processes of biology are evolution and development. You and I, as adult human beings, are products of both. Evolution took about four billion years to make the first human from a unicellular organism that emerged from the primordial soup. Development, in the form of embryogenesis together with its post-embryonic counterpart, takes less than 20 years to produce an adult human from a different unicellular organism – a fertilized egg or zygote. By this measure, development operates more than 200 million times faster than evolution. However, despite their very different timescales, the two great creative processes of biology are intrinsically interwoven. Evo-devo is the scientific study of this interweaving. Its full name is evolutionary developmental biology, but because this is an unwieldy phrase it is almost universally referred to by its nickname.
It is constructive to approach this issue from a historical perspective. Some aspects of animal relatedness have been known for a long time – centuries – while some have only been established in the last few decades. And others remain to be worked out or confirmed. A useful starting point for this historical approach is the 1817 four-volume work Le Règne Animal (The Animal Kingdom) by the French comparative anatomist Georges Cuvier, who divided the kingdom into four embranchements (branches): vertebrates, molluscs, articulates (outwardly segmented animals), and radiates (radially symmetrical animals). We should note here that Cuvier was an anti-evolutionist; he was opposed to the evolutionary theories of his fellow Frenchmen Jean-Baptiste Lamarck and Étienne Geoffroy Saint-Hilaire, and he did not live to see the publication of Darwin’s Origin of Species. However, many non-evolutionists prior to Darwin (from Aristotle onwards) made good attempts at the classification of animals, even though the fruits of their labours would not be given an evolutionary interpretation until later. Here, I will discuss Cuvier’s suggested groups as being evolutionary ones, even though that is not how he saw them.