Power-law city-size distributions are a statistical regularity researched in many countries and urban systems. In this history of science treatise we reconsider Felix Auerbach’s paper published in 1913. We reviewed his analysis and found (i) that a constant absolute concentration, as introduced by him, is equivalent to a power-law distribution with exponent $$\approx 1$$ ≈ 1, (ii) that Auerbach describes this equivalence, and (iii) that Auerbach also pioneered the empirical analysis of city-size distributions across countries, regions, and time periods. We (...) further investigate his legacy as reflected in citations and find that important follow-up work, e.g. by Lotka (Elements of physical biology. Williams & Wilkins Company, Baltimore, 1925) and Zipf (Human behavior and the principle of least effort: an introduction to human ecology, Martino Publishing, Manfield Centre, CT (2012), 1949), does give proper reference to his discovery—but others do not. For example, only approximately 20% of city-related works citing Zipf (1949) also cite Auerbach (Petermanns Geogr Mitteilungen 59(74):74–76, 1913). To our best knowledge, Lotka (1925) was the first to describe the power-law rank-size rule as it is analyzed today. Saibante (Metron Rivista Internazionale di Statistica 7(2):53–99, 1928), building on Auerbach and Lotka, investigated the power-law rank-size rule across countries, regions, and time periods. Zipf’s achievement was to embed these findings in his monumental 1949 book. We suggest that the use of “Auerbach–Lotka–Zipf law” (or “ALZ-law”) is more appropriate than “Zipf’s law for cities”, which also avoids confusion with Zipf’s law for word frequency. We end the treatise with biographical notes on Auerbach. (shrink)

Philosophers of science regard the Lotka–Volterra model as an exemplar of model transfer across disciplines. This article traces three cases of the Lotka–Volterra model transfer to economics during the 1960–70s. Each model represents a different kind of methodological attitude towards model transfer. After detailing the historical case studies where the Lotka–Volterra model was transferred to economics and how the economists actually adopted it into their model constructions, the following philosophical discussions on interpretation and justification suggest that formal (...) template or structure alone does not produce successful transdomain model transfer; rather it is subject to the model builders’ intentions and interpretation. In addition to interdisciplinary transfer, intradisciplinarity is also crucial to how models are constructed in order to be resituated in their economic context. (shrink)

How do philosophers of science make use of historical case studies? Are their accounts of historical cases purpose-built and lacking in evidential strength as a result of putting forth and discussing philosophical positions? We will study these questions through the examination of three different philosophical case studies. All of them focus on modeling and on Vito Volterra, contrasting his work to that of other theoreticians. We argue that the worries concerning the evidential role of historical case studies in philosophy are (...) partially unfounded, and the evidential and hermeneutical roles of case studies need not be played against each other. In philosophy of science, case studies are often tied to conceptual and theoretical analysis and development, rendering their evidential and theoretic/hermeneutic roles intertwined. Moreover, the problems of resituating or generalizing local knowledge are not specific to philosophy of science but commonplace in many scientific practices—which show similarities to the actual use of historical case studies by philosophers of science. (shrink)

The complexity and the variability of parameters occurring in ecological dynamical systems imply a large number of equations.Different methods, more or less successful, have been described to reduce this number of equations. For instance, in the paper of Auger and Roussarie (1993), the authors describe how to obtain a reduction by considering different time-scales. They consider a system which can be sub-divided into sub-systems such that the strengths of the intra-sub-systems interactions are much larger than those of the inter-sub-systems interactions. (...) Using the Central Manifold Theorem, they obtain on the slow-manifold, a perturbation of the external dynamics by the internal dynamics. (shrink)

ABSTRACT Is there something specific about modelling that distinguishes it from many other theoretical endeavours? We consider Michael Weisberg’s thesis that modelling is a form of indirect representation through a close examination of the historical roots of the Lotka–Volterra model. While Weisberg discusses only Volterra’s work, we also study Lotka’s very different design of the Lotka–Volterra model. We will argue that while there are elements of indirect representation in both Volterra’s and Lotka’s modelling approaches, they are (...) largely due to two other features of contemporary model construction processes that Weisberg does not explicitly consider: the methods-drivenness and outcome-orientedness of modelling. 1Introduction 2Modelling as Indirect Representation 3The Design of the Lotka–Volterra Model by Volterra 3.1Volterra’s method of hypothesis 3.2The construction of the Lotka–Volterra model by Volterra 4The Design of the Lotka–Volterra Model by Lotka 4.1Physical biology according to Lotka 4.2Lotka’s systems approach and the Lotka–Volterra model 5Philosophical Discussion: Strategies and Tools of Modelling 5.1Volterra’s path from the method of isolation to the method of hypothesis 5.2The template-based approach of Lotka 5.3Modelling: methods-driven and outcome-oriented 6Conclusion. (shrink)

Social media has become an important way for science communication. Some scholars have examined how to help scientists engage with social media from operational training, policy guidance, and social media services improving. The main contribution of this study is to construct a symbiosis evolution model of science communication ecosystem between scientists and social media platforms based on the symbiosis theory and the Lotka–Volterra model to discuss the evolution of their symbiotic patterns and population size under different symbiosis coefficients. The (...) results indicate that the size of the symbiosis coefficients determines the equilibrium outcome of the symbiosis evolution of scientists and social media platforms; scientists and social media platforms can promote each other’s population size under the mutualism pattern, which can achieve sustainable science communication; “1 + 1 > 2” effect can only be achieved under the symmetric mutualism pattern and the growth of scientists and social media platforms is more stable and sufficient than that of other patterns. The findings will provide additional perspectives for promoting the sustainable development of science communication based on social media. (shrink)

On the basis of the previous publications, a new fractional-order prey-predator model is set up. Firstly, we discuss the existence, uniqueness, and nonnegativity for the involved fractional-order prey-predator model. Secondly, by analyzing the characteristic equation of the considered fractional-order Lotka–Volterra model and regarding the delay as bifurcation variable, we set up a new sufficient criterion to guarantee the stability behavior and the appearance of Hopf bifurcation for the addressed fractional-order Lotka–Volterra system. Thirdly, we perform the computer simulations with (...) Matlab software to substantiate the rationalisation of the analysis conclusions. The obtained results play an important role in maintaining the balance of population in natural world. (shrink)

In spite of having published more than hundred articles and three monographs, the chemist and statistician Alfred James Lotka (1880–1949) is not very well known. Because he had not experienced a conventional academic curriculum, he remained ‚at the margins’ of the scientific community. In 1925 he aimed for a breakthrough with his first monograph Elements of Physical Biology. The basic idea of this study was to understand nature in terms of energy. Lotka’s mathematical approach was highly innovative, although (...) he had borrowed certain notions from his former teacher, the physical chemist Wilhelm Ostwald. This article focuses on the very process of how a new idea developed and spread through the scientific community, and tries to determine to what extent the author—with his personality, his intentions and feelings—was part of this process. This includes looking at the emotional strain that followed the publication of Lotka’s masterpiece. Considering his anxieties, worries and distress during the period of reception, and his efforts to make sure his book was acknowledged by its audience, the article sheds light on often neglected aspects of scientific work such as identification, intention, mimicry, originality, and rivalry. The case study deals with a systematic blindness in the history of science: it takes into account the actors of science, their personality and their strategic moves, in order to come to a better understanding of the close connection between their work and their actions. In addition, the history of Lotka’s worries about the reception of his book might help us challenge the postulate of „publish or perish“ in today’s science. (shrink)

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka-Volterra equations. (...) There are at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, but the other of which yields explanations that are distinctively mathematical in terms of nomological strength. In the first, one first picks out a system or class of systems, finds that the equations hold in a causal -explanatory way; in the second, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non- causal explanations can complement one another. (shrink)

In this paper, I adopt the view that if general forces or processes can be detected in ecology, then the principles or models that represent them should provide predictions that are approximately correct and, when not, should lead to the sorts of intervening factors that usually make trouble. I argue that Lotka–Volterra principles do not meet this standard; in both their simple “strategic” and their complex “tactical” forms they are not approximately correct of the findings of the laboratory experiments (...) and historical studies most likely to confirm them; nor do they instruct ecologists where to look for likely intervening factors. Evidence drawn from long-term case studies and other available data sets suggests that the populations of predators and their prey are not regulated by an interaction between them but are controlled by transient, contingent, and accidental events that affect each animal and each population individualistically. This paper argues that the presence of general forces or processes in ecology should be determined by comparing competing models of these forces not just to each other or to a null model but also to case studies that may challenge theoretical approaches with convincing individualistic causal accounts of the phenomena. (shrink)

The Lotka–Volterra predator-prey-model is a widely known example of model-based science. Here we reexamine Vito Volterra’s and Umberto D’Ancona’s original publications on the model, and in particular their methodological reflections. On this basis we develop several ideas pertaining to the philosophical debate on the scientific practice of modeling. First, we show that Volterra and D’Ancona chose modeling because the problem in hand could not be approached by more direct methods such as causal inference. This suggests a philosophically insightful motivation (...) for choosing the strategy of modeling. Second, we show that the development of the model follows a trajectory from a “how possibly” to a “how actually” model. We discuss how and to what extent Volterra and D’Ancona were able to advance their model along that trajectory. It turns out they were unable to establish that their model was fully applicable to any system. Third, we consider another instance of model-based science: Darwin’s model of the origin and distribution of coral atolls in the Pacific Ocean. Darwin argued more successfully that his model faithfully represents the causal structure of the target system, and hence that it is a “how actually” model. (shrink)

In any academic discipline, published articles in respective journals represent "production units" of scientific knowledge, and bibliometric distributions reflect the patterns in such outputs across authors or "producers." Closely following the analysis approach used for similar studies in the economics and finance literature, we present the first study to examine whether there exists an empirical regularity in the bibliometric patterns of research productivity in the business ethics literature. Our results present strong evidence that there indeed exists a distinct empirical regularity. (...) It is the so-called Generalized Lotka's Law of scientific productivity pattern: the number of authors publishing ç papers is about Í /n c of those publishing one paper. We discuss the likely processes that underlie the productivity pattern postulated by the Generalized Lotka's Law. We find that the value of the exponent is equal to about 2.6 for the comprehensive bibliometric data across the two leading business ethics journals. The observed research productivity pattern in the business ethics area, a relatively young discipline, is interestingly very consistent with those found in much older, related business disciplines like economics, accounting, and finance. We discuss the general implications of our findings. (shrink)

Many biological investigations are organized around a small group of species, often referred to as ‘model organisms’, such as the fruit fly Drosophila melanogaster. The terms ‘model’ and ‘modelling’ also occur in biology in association with mathematical and mechanistic theorizing, as in the Lotka–Volterra model of predator-prey dynamics. What is the relation between theoretical models and model organisms? Are these models in the same sense? We offer an account on which the two practices are shown to have different epistemic (...) characters. Theoretical modelling is grounded in explicit and known analogies between model and target. By contrast, inferences from model organisms are empirical extrapolations. Often such extrapolation is based on shared ancestry, sometimes in conjunction with other empirical information. One implication is that such inferences are unique to biology, whereas theoretical models are common across many disciplines. We close by discussing the diversity of uses to which model organisms are put, suggesting how these relate to our overall account. 1 Introduction2 Volterra and Theoretical Modelling3 Drosophila as a Model Organism4 Generalizing from Work on Model Organisms5 Phylogenetic Inference and Model Organisms6 Further Roles of Model Organisms6.1 Preparative experimentation6.2 Model organisms as paradigms6.3 Model organisms as theoretical models6.4 Inspiration for engineers6.5 Anchoring a research community7 Conclusion. (shrink)

one takes to be the most salient, any pair could be judged more similar to each other than to the third. Goodman uses this second problem to showthat there can be no context-free similarity metric, either in the trivial case or in a scientifically ...

Based on the Lotka–Volterra system, a pest-natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold level depending on the pest density and its change rate. The mortality rate of the pest is a saturation function that strictly depends on their density while the release of natural enemies is also a nonlinear pulse term depending (...) on the density of real-time natural enemies. The exact impulsive and phase sets are given. The definition and properties of the Poincaré map corresponding to the pulse points on the phase set are provided. We investigate the existence and stability of boundary and interior order-1 periodic solution. The theoretical analysis developed in the present paper combined with nonlinear controlling measures as well as nonlinear action threshold methods and techniques laid the foundation for the establishment and analysis of other state-dependent feedback control models. (shrink)

In a (2016) paper in this journal, I defuse allegations that theoretical ecological research is problematic because it relies on teleological metaphysical assumptions. Mark Sagoff offers a formal reply. In it, he concedes that I succeeded in establishing that ecologists abandoned robust teleological views long ago and that they use teleological characterizations as metaphors that aid in developing mechanistic explanations of ecological phenomena. Yet, he contends that I did not give enduring criticisms of theoretical ecology a fair shake in my (...) paper. He says this is because enduring criticisms center on concerns about the nature of ecological networks and forces, the instrumentality of ecological laws and theoretical models, and the relation between theoretical and empirical methods in ecology that that paper does not broach. Below I set apart the distinct criticisms Sagoff presents in his commentary and respond to each in turn. (shrink)

Callender and Cohen argue that there is no need for a special account of the constitution of scientific representation. I argue that scientific representation is communal and therefore deeply tied to the practice in which it is embedded. The communal nature is accounted for by licensing, the activities of scientific practice by which scientists establish a representation. A case study of the Lotka-Volterra model reveals how licensure is a constitutive element of the representational relationship. Thus, any account of the (...) constitution of scientific representation must account for licensing, meaning that there is a special problem of scientific representation. (shrink)

Models occupy a central role in the scientific endeavour. Among the many purposes they serve, representation is of great importance. Many models are representations of something else; they stand for, depict, or imitate a selected part of the external world (often referred to as target system, parent system, original, or prototype). Well-known examples include the model of the solar system, the billiard ball model of a gas, the Bohr model of the atom, the Gaussian-chain model of a polymer, the MIT (...) bag model of quark confinement, the Lorenz model of the atmosphere, the Lotka-Volterra model of the predator-prey interaction, or the hydraulic model of an economy, to mention just a few. All these models represent their target systems (or selected parts of them) in one way or another. (shrink)

Models are of central importance in many scientific contexts. The roles the MIT bag model of the nucleon, the billiard ball model of a gas, the Bohr model of the atom, the Gaussian-chain model of a polymer, the Lorenz model of the atmosphere, the Lotka- Volterra model of predator-prey interaction, agent-based and evolutionary models of social interaction, or general equilibrium models of markets play in their respective domains are cases in point.

In this paper, the Helmholtz equation with quadratic damping themes is used for modeling the dynamics of a simple prey-predator system also called a simple Lotka–Volterra system. From the Helmholtz equation with quadratic damping themes obtained after modeling, the equilibrium points have been found, and their stability has been analyzed. Subsequently, the harmonic oscillations have been studied by the harmonic balance method, and the phenomena of resonance and hysteresis are observed. The primary and secondary resonances have been researched by (...) the multiple-scale method, and the conditions of stability of the amplitudes of oscillations are determined. Chaos is detected analytically by the Melnikov method and numerically using the basin of attraction, the bifurcation diagram, the Lyapunov exponent, the phase portrait, and the Poincaré section. The effects of all the parameters of the system are analyzed in detail, and special emphasis is placed on the new parameters. Through this analysis, the complex phenomena such as hysteresis, bistability, amplitude jump, resonances, and chaos have been obtained. The control of the parameters and the necessary conditions to control the aforementioned phenomena have been found. (shrink)

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non-causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka–Volterra equations. There (...) are at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, and another that yields explanations that are distinctively mathematical in terms of nomological strength. In the first case, one first picks out a system or class of systems, and finds that the equations hold in a causal–explanatory way. In the second case, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non-causal explanations can complement one another. _1_. Introduction _2._ Delineating the Boundaries of Causal Explanation _2.1._ Why construe causal explanation narrowly? The land of explanation versus grain-focusing _2.2._ Reasons to narrow the scope of causal explanation _3._ Broadening the Scope of Mathematical Explanation _4._ Lotka–Volterra: Same Model, Different Explanation Types _4.1._ General biocide in the Lotka–Volterra model _4.2._ Two ways a model can hold, yielding causal versus mathematical explanations _5._ Four Complementary Relationships between Mathematical and Causal Explanation _5.1._ Slight reformulations of explananda _5.2._ Causal distortion of idealized mathematical models _5.3._ Partial explanations requiring supplementation _5.4._ Explanatory dimensionality _6._ Conclusion. (shrink)

Two examples demonstrate the possibility of extremely complicated non-convergent behavior in evolutionary game dynamics. For the Taylor-Jonker flow, the stable orbits for three strategies were investigated by Zeeman. Chaos does not occur with three strategies. This papers presents numerical evidence that chaotic dynamics on a strange attractor does occur with four strategies. Thus phenomenon is closely related to known examples of complicated behavior in Lotka-Volterra ecological models.

These lectures outline the project of a general organology, which is to say an account of life when it is no longer just biological but technical, or when it involves not just organic matter but organized inorganic matter. This organology is also shown to require a modified Simondonian account of the shift from vital individuation to a three-stranded process of psychic, collective and technical individuation. Furthermore, such an approach involves extending the Derridean reading of Socrates's discussion of writing as a (...) pharmakon, so that it becomes a more general account of the pharmacological character of retention and protention. By going back to Leroi-Gourhan, we can recognize that this also means pursuing the history of retentional modifications unfolding in the course of the history of what, with Lotka, can also be called exosomatization. It is thus a question of how exteriorization can, today, in an epoch when it becomes digital, and in an epoch that produces vast amounts of entropy at the thermodynamic, biological and noetic levels, still possibly produce new forms of interiorization, that is, new forms of thought, care and desire, amounting to so many chances to struggle against the planetary-scale pharmacological crisis with which we are currently afflicted. (shrink)

The debates over the future of human population and the earth’s environment, and similar large issues, usually take place without reference to explicit models. Debate would be clarified if such models were employed. We propose that the logistic equation and its extensions like the generalized logistic and the Lotka-Volterra equations, so familiar to ecologists, can easily be modified to model the important "macro" questions that motivated the three thinkers of our title. The long term rate of population growth must (...) normally be controlled by the rate of improvement in K, the carrying capacity of the earth. K will in turn be controlled by the rate of technological progress. The present situation, in which technological improvement (but also perhaps environmental deterioration) are increasing at rates above r, the Malthusian intrinsic rate of natural increase, is probably unique in human history. Can present levels of human prosperity and population growth be sustained? What processes are most likely to determine the answer to this and similar questions? We here sketch a model that endogenizes technological progress and environmental deterioration in the logistic framework. We discuss extensions of the logistic approach to multiple populations, such as other species, and sub-populations, such as human social classes, using the Lotka-Volterra equations. (shrink)

Michael Weisberg has argued that robustness analysis is useful in evaluating both scientific models and their implications and that robustness analysis comes in three types that share their form and aim. We argue for three cautionary claims regarding Weisberg's reconstruction: robustness analysis may be of limited or no value in evaluating models and their implications; the unificatory reconstruction conceals that the three types of robustness differ in form and role; there is no confluence of types of robustness. We illustrate our (...) central first claim with a case study: the application of Lotka-Volterra models to technology diffusion. (shrink)

The dynamics of single populations up to ecosystems, are often described by one or a set of non-linear ordinary differential equations. In this paper we review the use of bifurcation theory to analyse these non-linear dynamical systems. Bifurcation analysis gives regimes in the parameter space with quantitatively different asymptotic dynamic behaviour of the system. In small-scale systems the underlying models for the populations and their interaction are simple Lotka-Volterra models or more elaborated models with more biological detail. The latter (...) ones are more difficult to analyse, especially when the number of populations is large. Therefore for large-scale systems the Lotka-Volterra equations are still popular despite the limited realism. Various approaches are discussed in which the different time-scale of ecological and evolutionary biological processes are considered together. (shrink)

We study the influence of the individual behaviour of animals on predator-prey models. Populations of preys and predators are divided into sub-populations corresponding to different activity classes. The animals are assumed to do many activities all day long such as searching for food of different types. The preys are more vulnerable when doing some activities during which they are very exposed to predators attacks rather than for others during which they are hidden. We study activity sequences of the animals and (...) also the effect of a change in the average individual behaviour of the animals on Lotka-Volterra prey-predator interactions. Numerical simulations are realized for the whole sets of equations (governing the subpopulations) and are compared to the simulations of the reduced sets of equation (governing the populations). We look for the validity of the method with respect to a scaling factor which measures the differences between the two time scales associated to the fast-varying variables and to the slow-time varying global variables. It is shown that when the two time scales differ of about two orders of magnitude, the approximation is satisfying. (shrink)

Observed biological growth curves generally are sigmoid in appearance. It is common practice to fit such data with either a Verhulst logistic or a Gompertz curve. This paper critically considers the conceptual bases underlying these descriptive models.The logistic model was developed by Verhulst to accommodate the common sense observation that populations cannot keep growing indefinitely. A justification for using the same equation to describe the growth of individuals, based on considerations from chemical kinetics (autocatalysis of a monomolecular reaction), was put (...) forward by Richardson, but met with heavy criticism as a result of his erroneous derivation of the basic equation (Snell, 1929). It errs on the side of over-simplicity (Priestley & Pearsall, 1922). Von Bertalanffy (1957) subsequently based a justification on the assumption that, as a first approximation, the rates of catabolism and anabolism may be assumed to be proportional to weight and power (still vacant places, between the maximal possible and the already accumulated population sizes. This point of view was fiercely challenged by Nicholson (1933), Milne (1962), Smith (1954) and Rubinov (1973). And indeed, what is meant by vacant places has never become entirely clear. Finally Lotka (1925) devised a third leading approach by just truncating a Taylor expansion around zero of the differential law for autonomous growth after the second degree term. (shrink)

Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.

Matrix population models provide a natural tool to analyse state-dependent life-history strategies. Reproductive value and the intrinsic rate of natural increase under a strategy, and the optimal life-history strategy can all be easily characterised using projection matrices. The resultant formulae, however, are not directly comparable with the corresponding formulae for age structured populations such as Lotka's equations and Fisher's formula for reproductive value. This is because formulae involving projection matrices lose track of what happens to an individual over its (...) lifetime and are only concerned with expected numbers of descendants one time step in the future. In contrast the usual age-dependent formulae explicitly followed a single individual through from birth to death.In this paper I show how the state-dependent formulae can be rewritten to be directly comparable with the standard age-structured formulae. Although the formulae are intuitively obvious the decomposition into current and future reproductive success differs from that previously given and is, I suggest, a more natural definition. The derivation of appropriate equations for optimal life-histories relies on results from dynamic programming theory; and is much more general and easier than previous derivations. (shrink)

This article presents the results of a systematic literature review on religiosity and spirituality, particularly in the work context. We aimed to verify the state-of-the-art of scientific production related to these themes. To achieve the proposed objective, we identified 312 articles published in journals in the period between 1960 and 2018 using a rigourous method of analysis and sorting, which resulted in 52 appropriate studies. The analyses presented are based on the three bibliometric laws: those of Lotka, Bradford and (...) Zipf. This article brings contributions that encompass four approaches: measurement scales of spirituality and religiosity; behavioural benefits of religiosity in individuals; insertion of religiosity and spirituality in social service practice; and research directions. This research presents technical and managerial implications to provide theoretical support for the creation of programmes and/or practices of spirituality and religion in the workplace as an effective strategy, towards ethical attitudes. Also, this study contributes to the methodological achievement of SLRs in the field of religion in the workplace, highlighting an effective method for thematic mapping, and holistically identifying new research topics and directions, especially because of the several guidelines presented. (shrink)

The notion of template has recently been discussed in relation to cross-disciplinary transfer of modeling efforts and in relation to the representational content of models. We further develop and disambiguate the notion of template and find that, suitably developed, it is useful in distinguishing and analyzing different types of transfer, none of which supports a non-representationalist view of models. We illustrate our main findings with the modeling of technology substitution with Lotka-Volterra Competition equations.

I begin with the definition of power, and find that it is finalistic inasmuch as work directs energy dissipation in the interests of some system. The maximum power principle of Lotka and Odum implies an optimal energy efficiency for any work; optima are also finalities. I advance a statement of the maximum entropy production principle, suggesting that most work of dissipative structures is carried out at rates entailing energy flows faster than those that would associate with maximum power. This (...) is finalistic in the sense that the out-of-equilibrium universe, taken as an isolated system, entrains work in the interest of global thermodynamic equilibration. I posit an evolutionary scenario, with a development on Earth from abiotic times, when promoting convective energy flows could be viewed as the important function of dissipative structures, to biotic times when the preservation of living dissipative structures was added to the teleology. Dissipative structures are required by the equilibrating universe to enhance local energy gradient dissipation. (shrink)

The question is discussed how noise gained a functional meaning in the context of biology. According to the common view, noise is considered a disturbance or perturbation. I analyze how this understanding changed and what kind of developments during the last 10 years contributed to the emergence of a new understanding of noise. Results gained during a field study in a synthetic biology laboratory show that the emergence of this new research discipline—its highly interdisciplinary character, its new technologies and novel (...) modeling strategies—provided essential impulses, which led to the observed change in the concept of noise. The laboratory study is combined with a historical analysis, which explores the general question as to how concepts travel between disciplines and, specifically, how noise was transferred from engineering and physics into biology. In the past, scientists, such as Lotka and Goodwin, tried to introduce a statistical mechanics into biology and discussed the problem of “unfitting” concepts. The change in the meaning of the concept can be interpreted as a way of making it fit to the novel context in which it is applied. (shrink)

Scientific models are important, if not the sole, units of science. This thesis addresses the following question: in virtue of what do scientific models represent their target systems? In Part i I motivate the question, and lay out some important desiderata that any successful answer must meet. This provides a novel conceptual framework in which to think about the question of scientific representation. I then argue against Callender and Cohen’s attempt to diffuse the question. In Part ii I investigate the (...) ideas that scientific models are ‘similar’, or structurally morphic, to their target systems. I argue that these approaches are misguided, and that at best these relationships concern the accuracy of a pre-existing representational relationship. I also pay particular attention to the sense in which target systems can be appropriately taken to exhibit a ‘structure’, and van Fraassen’s recent argument concerning the pragmatic equivalence between representing phenomena and data. My next target is the idea that models should not be seen as objects in their own right, but rather what look like descriptions of them are actually direct descriptions of target systems, albeit not ones that should be understood literally. I argue that these approaches fail to do justice to the practice of scientific modelling. Finally I turn to the idea that how models represent is grounded, in some sense, in their inferential capacity. I compare this approach to anti-representationalism in the philosophy of language and argue that analogous issues arise in the context of scientific representation. Part iii contains my positive proposal. I provide an account of scientific representation based on Goodman and Elgin’s notion of representation-as. The result is a highly conventional account which is the appropriate level of generality to capture all of its instances, whilst remaining informative about the notion. I illustrate it with reference to the Phillips-Newlyn machine, models of proteins, and the Lotka-Volterra model of predator-prey systems. These examples demonstrate how the account must be understood, and how it sheds light on our understanding of how models are used. I finally demonstrate how the account meets the desiderata laid out at the beginning of the thesis, and outline its implications for further questions from the philosophy of science; not limited to issues surrounding the applicability of mathematics, idealisation, and what it takes for a model to be ‘true’. (shrink)

Sagoff (2016) criticizes widely used “theoretical” methods in ecology; arguing that those methods employ models that rely on problematic metaphysical assumptions and are therefore uninformative and useless for practical decision-making. In this paper, I show that Sagoff misconstrues how such model-based methods work in practice, that the main threads of his argument are problematic, and that his substantive conclusions are consequently unfounded. Along the way, I illuminate several ways the model-based inferential methods he criticizes can be, and have been, usefully (...) informative. (shrink)

The ArgumentThe development of modern mathematical biology took place in the 1920s in three main directions: population dynamics, population genetics, and mathematical theory of epidemics. This paper focuses on the first trend which is considered the most significant. Modern mathematical theory of population dynamics is characterized by three aspects (the first two being in a somewhat critical relationship): the emergence of the mathematical modeling approach, the attempt at establishing it in a reductionist-mechanist conceptual framework, and the revival of Darwinism. The (...) first section is devoted to the analysis of the concept of mathematical model and the second one presents an example of a mathematical model (Van der Pol's model of heartbeat) which is a good prototype of that concept. In section 3 the main trends of mathematization of biology and the cultural and scientific contexts in which they found their development are discussed. Sections 4 and 5 are devoted to the contributions of V. Volterra and A. J. Lotka, to the analysis of the differences of their scientific conceptions, and to a discussion of a case study: the priority dispute concerning the discovery of the Volterra-Lotka equations. The historical analysis developed in this paper is also intended to detect the roots of some recent trends of mathematization of biology. (shrink)

The axiom of extensionality of set theory states that any two classes that have identical members are identical. Yet the class of persons age i at time t and the class of persons age i + 1 at t + l, both including same persons, possess different demographic attributes, and thus appear to be two different classes. The contradiction could be resolved by making a clear distinction between age groups and cohorts. Cohort is a multitude of individuals, which is constituted (...) within a time interval, and endures throughout part of the time continuum. Age group, on the other hand, is only a reference term to which empirical measurement relates, as in birth or death rates. Accordingly, the two concepts, age group i at t, and age group i + 1 at t + 1, are different. The standard population growth model of Leslie and Lotka, however, does not support such a distinction in age groups. An alternative model, proposed recently, implies precisely such a distinction. (shrink)

Background and AimPsycho-oncology is a cross-disciplinary and collaborative sub-specialty of oncology that focuses on the psychological, behavioral, ethical, and social aspects of cancer in clinical settings. The aim of this bibliometric study was to analyze and characterize the research productivity and trends in psycho-oncology between 1980 and 2021.MethodologyIn May 2022, the Scopus® database was searched for psycho-oncology-related publications using predetermined search keywords with specific restrictions. Lotka’s law was applied to check the authors’ productivity, while Bradford’s law was used to (...) assess the core journals in this field. The data was analyzed for different bibliometric indicators in the Biblioshiny package, an RStudio tool for bibliometric analysis.ResultsThe initial search resulted in a total of 2,906 publications. Of which, 1,832 publications were included in the final analysis, published between 1980 and 2021. The analyzed publications were written by 7,363 authors from 74 countries and published in 490 journals. There has been a significant increase in psycho-oncology-related publications after 2010. The most productive year was 2021. The annual scientific growth rate was found to be 13.9%. The most relevant leading author in terms of publications was Luigi Grassi from the University of Ferrara, Italy. Lotka’s law found that the number of authors declined as the number of papers written increased. The core journals were Psycho-Oncology, Supportive Care in Cancer, and Journal of Psychosocial Oncology. The most frequently used author’s keywords other than searching keywords were cancer, oncology, quality of life, depression, and anxiety. Recent psycho-oncology-related topics included mental health, COVID-19 infection in humans, people, pandemic, and tumor. The University of Sydney was the top-ranked institution. The leading country in terms of publications, citations, corresponding author country, and international collaboration was the United States of America. The United States had the strongest collaboration with Australia and Canada.ConclusionThe research hotspots include mental health conditions and interventions in cancer patients. We identified international collaboration and research expenditure to be strongly associated with psycho-oncology research productivity. Researchers’ collaboration, which is visible among developed countries, should be extended to low-income countries in order to expand psycho-oncology-related research and understanding. (shrink)

Quantum frameworks for modeling competitive ecological systems and self-organizing structures have been investigated under multiple perspectives yielded by quantum mechanics. These comprise the description of the phase-space prey–predator competition dynamics in the framework of the Weyl–Wigner quantum mechanics. In this case, from the classical dynamics described by the Lotka–Volterra (LV) Hamiltonian, quantum states convoluted by statistical gaussian ensembles can be analytically evaluated. Quantum modifications on the patterns of equilibrium and stability of the prey–predator dynamics can then be identified. These (...) include quantum distortions over the equilibrium point drivers of the LV dynamics which are quantified through the Wigner current fluxes obtained from an onset Hamiltonian background. In addition, for gaussian ensembles highly localized around the equilibrium point, stability properties are shown to be affected by emergent topological quantum domains which, in some cases, could lead either to extinction and revival scenarios or to the perpetual coexistence of both prey and predator agents identified as quantum observables in microscopic systems. Conclusively, quantum and gaussian statistical driving parameters are shown to affect the stability criteria and the time evolution pattern for such microbiological-like communities. (shrink)

BackgroundDiagnostic ultrasound has long been a part of a physician’s armamentarium, but transcranial focused ultrasound (FUS) is an emerging treatment of neurological disorders. Consequently, the literature in this field is increasing at a rapid pace.ObjectiveThis analysis was aimed to identify the top-cited articles on FUS to discern their origin, spread, current trends highlighting future impact of this novel neurosurgical intervention.MethodsWe searched the Web of Science database on 28th May 2021 and identified the top 100 cited articles. These articles were analyzed (...) with various scientometric parameters like the authors, corresponding authors, country of corresponding author, journal of publication, year of publication. Citation based parameters including total citations, mean citations per article and mean citations, citation count, and the citation per year, citations per year and co-authors per document were studied as well in addition to Hirsch h-index, g-index, m-index, Bradford’s Law, Lotka’s law and Collaboration index.ResultsThe 100 top-cited articles were published between 1998 and 2019 in 45 different journals. The average citations per document and citations per document per year were 97.78 and 12.47, respectively. The most prolific authors were Hynynen K (Medical Biophysics—Toronto), Elias WJ (Neurosurgery—Virginia), Zadicario (InSightec). The Journal of Neurosurgery published the most top-cited articles (n = 11), and most articles originated from the United States, followed by Canada. Among individual institutions, the University of Toronto was the most productive.ConclusionFUS is an emerging treatment of neurological disorders. With its increasing application, the FUS literature is increasing rapidly. Eleven countries contributed to the top 100 cited articles, with the top 2 countries (the United States and Canada) contributing to more than half of these articles. (shrink)

This paper argues that fitness is most usefully understood as those properties of organisms that are explanatory of survival in the broadest sense, not merely descriptive of reproductive success. Borrowing from Rosenberg and Bouchard , fitness in this sense is ecological in that it is defined by the interactions between organisms and environments. There are three sorts of ecological fitness: the well-documented ability to compete, the ability to cooperate , and a third sense of fitness that has received insufficient attention (...) in evolutionary theory, the ability to construct. Following Lotka, it can be understood thermodynamically as the ability to maintain or enlarge the energy-circulating capacity of an ecosystem. An organism that does this could end with its gene frequency unchanged but its probability of survival enhanced since it would sustain or increase the total carrying capacity of its ecosystem. Photosynthesizers and other autotrophs are obvious candidates for organisms that are fit in the constructive sense, but any organisms, including heterotrophs, can exhibit constructive fitness if they have some mechanism for channeling external flows of free energy into their ecosystems. I will briefly examine the prospects for the human species in the light of these considerations. (shrink)

The evolutionary implications of environmental change due to organismic action remain a controversial issue, after a decades—long debate on the subject. Much of this debate has been conducted in qualitative fashion, despite the availability of mathematical models for organism–environment interactions, and for gene frequencies when allele fitness can be related to exploitation of a particular environmental resource. In this article we focus on representative models dealing with niche construction, ecosystem engineering, the Gaia Hypothesis and community interactions of Lotka–Volterra type, (...) and show that their quantitative character helps bring into sharper focus the similarities and differences among their respective theoretical contexts. (shrink)

Le but de cet article est une analyse épistémologique des modèles du mutualisme. À partir de l’analyse Lotka-Volterra, nous chercherons les caractéristiques et les insuffisances épistémologiques de cette famille de modèles. Le travail mathématique de Vito Volterra était une réponse à une situation écologique, la rupture de l’équilibre d’espèces en compétition, considérées comme des espèces « associées ». À partir des équations décrivant les variations de ces populations en compétition, un simple changement de signe suffit pour obtenir les équations (...) décrivant les variations d’effectifs des populations mutualistes. En termes de modélisation, le mutualisme resta longtemps ignoré face au développement des modèles de compétition. Les modèles Lotka-Volterra appliqués au mutualisme aboutissent à un point d’équilibre lorsque les croissances relatives des deux populations sont les mêmes. Des modèles cherchent à distinguer les formes obligatoires et facultatives de mutualisme ; l’existence d’un point d’équilibre et le caractère dominant du mutualisme biologique (obligatoire ou facultatif) sont requis pour la validité de ces modèles. C est ce qui fait leur limite. Depuis la fin des années 1990, divers chercheurs ont mis au point des modèles plus réalistes en termes biologiques, c est-à-dire admettant un passage possible du parasitisme au mutualisme, dans un continuum et selon les densités des deux partenaires. D’un point de vue épistémologique, ces modèles demeurent relatifs au niveau populationnel, donc à l’étude des populations biologiques, ils demandent à être complétés par une analyse du même phénomène biologique au niveau individuel. (shrink)