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)

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)

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)

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)

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.

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)

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 ...

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)

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)

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.

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)

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)

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)

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)

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)

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)

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.

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)

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.

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)

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)

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)

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 (...) class='Hi'>Lotka–Volterra type, and show that their quantitative character helps bring into sharper focus the similarities and differences among their respective theoretical contexts. (shrink)

Two populations are subdivided into two categories of individuals (hawks and doves). Individuals fight to have access to a resource which is necessary for their survival. Conflicts occur between individuals belonging to the same population and to different populations. We investigate the long term effects of the conflicts on the stability of the community. The modelis a set of ODE's with four variables corresponding to hawk and dove individuals of the two populations. Two time scales are considered. A fast time (...) scale is used to describe frequent encounters and fightings between individuals trying to monopolize the resource. A slow time scale is used for the demography and the long term effects of encounters. We use aggregation methods in order to reduce this model into a system of two ODE's only for the total densities of the two populations which is found to be a classical Lotka-Volterra competition model. We study different cases of proportions of hawks and doves in both populations on the global coexistence and the mutal exclusion of the two populations. Pure dove tactics in both populations are unstable. In cases of mixed hawk and dove in both populations, there is coexistence. Pure dove or mixed hawk-dove tactics in one population can coexist with pure hawks in the other one when the costs of fightings between hawks are large enough. (shrink)

Volterra's (1926) equations for competition and predator-prey interactions are modified by introduction of root terms. A critical comparison with the original equations shows that the dynamic properties of the systems remain essentially alike, while the modification allows for explicit solution of the differential equations. Detailed solutions and numerical examples are given.

Michael Weisberg and Kenneth Reisman argue that the Volterra Principle can be derived from multiple predator-prey models and that, therefore, the Volterra Principle is a prime example for robustness analysis. In the current article, I give new results regarding the Volterra Principle, extending Weisberg’s and Reisman’s work, and I discuss the consequences of these results for robustness analysis. I argue that we do not end up with multiple, independent models but rather with one general model. (...) I identify the kind of situation in which this generalization approach may occur, and I analyze the generalized Volterra Principle from an explanatory perspective. (shrink)

Theorizing in ecology and evolution often proceeds via the construction of multiple idealized models. To determine whether a theoretical result actually depends on core features of the models and is not an artifact of simplifying assumptions, theorists have developed the technique of robustness analysis, the examination of multiple models looking for common predictions. A striking example of robustness analysis in ecology is the discovery of the Volterra Principle, which describes the effect of general biocides in predator-prey (...) systems. This paper details the discovery of the Volterra Principle and the demonstration of its robustness. It considers the classical ecology literature on robustness and introduces two individual-based models of predation, which are used to further analyze the Volterra Principle. The paper also introduces a distinction between parameter robustness, structural robustness, and representational robustness, and demonstrates that the Volterra Principle exhibits all three kinds of robustness. *Received September 2006; revised May 2007. ‡Earlier versions of this paper were presented at the Australasian Association of Philosophy, the London School of Economics, and the University of Bristol. The authors wish to thank those audiences as well as Patrick Forber, Ken Waters, Deena Skolnick Weisberg, Uri Wilensky, and Bill Wimsatt for many helpful comments. Special thanks to Giacomo Sillari for his assistance in translating Volterra's original paper and his insightful thoughts about Volterra's aims and methods. Some of the research in this paper was supported by NSF grant SES-0620887 to MW. †To contact the authors, please write to: Michael Weisberg, Department of Philosophy, University of Pennsylvania, 433 Logan Hall, Philadelphia, PA 19104; e-mail: [email protected]; Kenneth Reisman, Pluribo, Inc., 100 Park Avenue, Suite 1600, New York, NY 10017; e-mail: [email protected]. (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)

Simulation and Similarity is a novel and comprehensive account of, in first place, models and modeling. The author’s writing is exceptionally clear and intelligible. Simulation is referred to in the book only once, where it is defined as a kind of numerical analysis involving “computing the behavior of the model using a particular set of initial conditions” (82). Modeling, which is defined as “the indirect study of real-world systems via the construction and analysis of models” (4), appears to (...) be the primary focus of this book. This emphasis seems legitimate because the modeling practice precedes any simulation and is the key to its understanding as well.Chapter 2 “Three kinds of models” presents an account of the following kinds of models: concrete models (San Francisco Bay model being an example), mathematical models (Lottka–Volterra model of predation as an example), and computational models (illustrated by Schelling’s segregation model). First model example is a hydraulic one; the .. (shrink)

Why are some models, like the harmonic oscillator, the Ising model, a few Hamiltonian equations in quantum mechanics, the poisson equation, or the Lokta-Volterra equations, repeatedly used within and across scientific domains, whereas theories allow for many more modeling possibilities? Some historians and philosophers of science have already proposed plausible explanations. For example, Kuhn and Cartwright point to a tendency toward conservatism in science, and Humphreys emphasizes the importance of the intractability of what he calls “templates.” This paper (...) investigates more systematically the reasons for this remarkable interdisciplinary recurrence. To this aim, the authors describe in more detail the phenomenon they focus on and review competing potentialexplanations. The authors disentangle the various assumptions underlying these explanations based on sensitivity to a computational constraints and assess its relationships with the other analyzed explanatons. (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)

We review major developmental evidence on the continuity from action to gesture to word and sign in human children, highlighting the important role of caregivers in the development of multimodal communication. In particular, the basic issues considered here and contributing to the current debate on the origins and development of the language-ready brain are: (1) links between early actions, gestures and words and similarities in representational strategies; (2) importance of multimodal communication and the interplay between gestures and spoken words; (3) (...) interconnections between early actions, gestures and signs. The innovation of this report is in connecting these themes together to relevant findings from studies on children between 6 and 36 months of age and highlighting interesting parallels in studies on ape communicative behavior. (shrink)

This memoir consists of two parts, of which the first deals with the foundations of the theory of the struggle for existence, and begins with the introduction of the important concept of quantity of life, besides that of population. The fundamental equations are then established for the case where the individuals of a biological association mutually devour each other, the reasoning being based on the principle of encounters and on the fundamental hypothesis of the existence of equivalents of the individuals (...) constituting the different species which form the association.Having now obtained the equations which determine the rates of change of the numbers of individuals and of the quantities of life of the species, the memoir proceeds to find the equations relating to the stationary state, by establishing theorems which are afterwards applied for the purpose of obtaining the three general laws of the fluctuations. This investigation of the equilibrium state is then followed by the determination of the integrals of the fluctuation equations, and the deduction from these of their most important consequences.The second part of the memoir contains the enumeration and demonstration of the general laws of the struggle for existence, which flow from the discussion of the principles and the integrals obtained in the first part. In this way there is established a new sort of dynamics, demographic dynamics, which, though substantially different from the dynamics of material systems, is developed from an analogous point of view.The second part begins with the principle of the conservation of demographic energy, according to which there are two sorts of energy, one actual and one potential, which transform mutually the one into the other. This principle is the analogue of the principle of conservation of mechanical energy. It is followed by the enunciation of the three laws relating to the biological fluctuations, the experimental verification of which has been investigated by several naturalists. The success which has attended their efforts is well known.Everybody knows the importance ofHamilton's principle in mechanics and in all the domains of physical science. An analogous variation principle can be found in biology, and from it one can deduce the fluctuation equations in the canonical Hamiltonian form and also in the form of a Jacobian partial differential equation. Their integrals in involution from the subject next studied, and in this way are found cases where the integration is reducible to quadratures.Hamilton's principle leads to the principle of least action . There exists also in biology a closely related principle, which may be called the principle of least vital action. Its analytical form is such that it requires the existence of a true minimum, a state of affairs which does not always hold good in the analogous case in mechanics.Die Abhandlung besteht aus zwei Teilen: Der erste ist den Grundlagen der Theorie des Kampfes ums Dasein gewidmet. Man beginnt damit, neben der Bevölkerung die Menge des Lebens einzuführen, welche eine sehr wichtige Rolle spielt. Man geht dann dazu über, die Grundgleichungen für den Fall aufzustellen, in welchem die Individuen einer biologischen Assoziation sich gegenseitig auffressen. Man wendet das Prinzip der Begegnungen an und stützt sich auf die Grundhypothese der Existenz von Individuenäquivalenten der verschiedenen Arten, welche die Assoziation bilden.Wenn man die Gleichungen, welche die Variationen der Individuenzahlen und der Lebensmengen der Arten liefern, gefunden hat, so schreitet man zu den statischen oder Gleichgewichtsgleichungen fort und findet so die Theoreme, die man alsdann benutzt, um die drei allgemeinen Gesetze der Fluktuationen zu erhalten.Nach dem Studium des Gleichgewichtes geht man dazu über, die verschiedenen Integrale der Fluktuationengleichungen zu finden und zieht endlich aus ihnen die wichtigsten Folgerungen.Im zweiten Teile werden die allgemeinen Gesetze des Kampfes ums Dasein, welche aus der Diskussion der Prinzipien und der im ersten Teil gewonnenen Integrale stammen, ausgesprochen und bewiesen. Man baut so eine neue Dynamik auf: die demographische Dynamik, welche, obschon sie wesentlich verschieden von derjenigen der materiellen Systeme ist, sich nach einem analogen Gesichtspunkt entwickelt.Man beginnt in diesem zweiten Teil mit dem Prinzip der Erhaltung der demographischen Energie, nach welchem zwei Energien, die aktuelle und die potentielle, sich ineinander verwandeln. Wir haben hier eine Analogie zum Prinzip der Erhaltung der mechanischen Energie. Dann werden die drei Gesetze der biologischen Fluktuationen formuliert. Für sie haben verschiedene Naturforscher experimentelle Bestätigungen gesucht. Man kennt den Erfolg ihrer Bemühungen.Alle Welt kennt die Bedeutung des Prinzips vonHamilton in der Mechanik und in allen Gebieten der Physik. Man kann ein dem Variationskalkül analoges Prinzip in der Biologie finden. Aus ihm kann man die Fluktuationsgleichungen in der kanonischen Form vonHamilton und in der Gestalt einer Gleichung mit partiellen Differentialquotienten vonJacobi herleiten. Ihre Integrale bilden den Gegenstand der folgenden Studien. Man findet Fälle, in denen die Integration sich auf Quadraturen reduziert.Das Prinzip vonHamilton zieht das Prinzip der kleinsten Wirkung oder das Prinzip vonMaupertuis nach sich. Auch in der Biologie gibt es ein mit dem vorgenannten zusammenhängendes Prinzip, welches man das Prinzip der kleinsten vitalen Wirkung nennen kann. Seine analytische Form ist derart, dass es sich um ein wahres Minimum handelt, das im analogen Fall in der Mechanik nicht immer zutrifft. (shrink)

The present study investigates the types of verb and symbolic representational strategies used by 10 deaf signing adults and 13 deaf signing children who described in Italian Sign Language 45 video clips representing nine action types generally communicated by five general verbs in spoken Italian. General verbs, in which the same sign was produced to refer to several different physical action types, were rarely used by either group of participants. Both signing children and adults usually produced specific depicting predicates by (...) incorporating, through a representational strategy, the object and/or the modality of the action into the sign. As for the different types of representational strategies, the adults used the hand-as-object strategy more frequently than the children, who, in turn, preferred to use the hand-as-hand strategy, suggesting that different degrees of cognitive complexity are involved in these two symbolic strategies. Addressing the symbolic iconic strategies underlying sign formation could provide new insight into the perceptual and cognitive processes of linguistic meaning construction. The findings reported here support two main assumptions of cognitive linguistics applied to sign languages: there is a strong continuity between gestures and language; lexical units and depicting constructions derive from the same iconic core mechanism of sign creation. (shrink)