We generally agree with Burt's thesis. However, we note that the author did not discuss epigenetics, the study of how the environment can alter gene structure and function. Given epigenetic mechanisms, the utility of polygenic risk scores (PRS) is limited in studies of development and mental illness. Finally, in this commentary we expand upon the risks of reliance upon PRSs.

The aim of this work was to compare experimental investigations on effects of lidocaine, calcium and, BRL 34915 on reentries to simulated data obtained by use of a model of propagation based on the Huygens' constriction method already described in previous works. Calcium and lidocaine effects are investigated on anisotropic conduction conditions. In both cases, reduction in conduction velocities are observed. In lidocaine case, a refractory area is located along the longitudinal axis. In agreement with experimental electrical mapping, the simulations (...) show that the stabilization of reentrant excitation is mainly due to the existence of this refractory area around which the reentrant circuit can develop. The experimental study shows that BRL 34915 has both arrhythmogenic and antiarrhythmic effects. A detailed electrophysiological analysis has shown that drug infusion act on normal cardiac cells by decreasing the relative and absolute refractory period. BRL 34915 action is simulated by a decrease in the refractory period showing that the time frequency of the reentrant activity is increased and that the spatial size where the reentry is developing is becoming smaller. These two effects are arrhythmogenic, the simulated data being so in good agreement with the experimental ones. (shrink)

This work presents a specific stock-effort dynamical model. The stocks correspond to two populations of fish moving and growing between two fishery zones. They are harvested by two different fleets. The effort represents the number of fishing boats of the two fleets that operate in the two fishing zones. The bioeconomical model is a set of four ODE's governing the fishing efforts and the stocks in the two fishing areas. Furthermore, the migration of the fish between the two patches is (...) assumed to be faster than the growth of the harvested stock. The displacement of the fleets is also faster than the variation in the number of fishing boats resulting from the investment of the fishing income. So, there are two time scales: a fast one corresponding to the migration between the two patches, and a slow time scale corresponding to growth. We use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model for the total fishing effort and fish stock of the two fishing zones. The mathematical analysis of the model is shown. Under some conditions, we obtain a stable equilibrium, which is a desired situation, as it leads to a sustainable harvesting equilibrium, keeping the stock at exploitable densities. (shrink)

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how (...) the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production. We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations. (shrink)

The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. This study examines the impact of the creation of marine protected areas, from both economic and biological perspectives. The consequences of reserve establishment on the long-run equilibrium fish biomass and fishery catch levels are evaluated. We include (...) reserve size as control variable to maximize catch at equilibrium. A continuous time model is used to simulate the effects of reserve size on fishing catch. Fish movements between the sites is assumed to take place at a faster time scale than the variation of the stock and the change of the fleet size. We take advantage of these two time scales to derive a reduced model governing the dynamics of the total fish stock and the fishing effort. Simulation results suggest that the establishment of a protected marine reserve will always lead to an increase in total fish biomass, an optimal size of a marine reserve can achieve to maximize the catch at equilibrium. (shrink)

Ventricular Fibrillation is responsible for a majority of sudden cardiac death, but little is known about how ventricular tachycardia (VT) degenerates into ventricular fibrillation. Several clinical studies focused only on preventing VT with a class III antiarrhythmic drug resulted in many deaths. Our simulations investigate the interactions between an antiarrhythmic drug likely to suppress a VT and a Figure 8 reentry. A parameter AAR is introduced to increase the action potential duration and therefore simulate various Class III drugs. Simulations are (...) ran under several conditions (phases of the reentry, values of AAR, durations). They show that a VT can be suppressed whatever the phase of the reentry but it strongly depends on the duration of the effect. It confirms that a drug which can suppress a reentry can also worsen it. It also shows a great variety of activation patterns and thus the complexity of antiarrhythmic drugs effects. Simulations also demonstrate that suppressing VT is an increasing function of AAR. (shrink)

The balance between births and deaths in an age-structured population is strongly influenced by the spatial distribution of sub-populations. Our aim was to describe the demographic process of a fish population in an hierarchical dendritic river network, by taking into account the possible movements of individuals. We tried also to quantify the effect of river network changes (damming or channelling) on the global fish population dynamics. The Salmo trutta life pattern was taken as an example for.We proposed a model which (...) includes the demographic and the migration processes, considering migration fast compared to demography. The population was divided into three age-classes and subdivided into fifteen spatial patches, thus having 45 state variables. Both processes were described by means of constant transfer coefficients, so we were dealing with a linear system of difference equations. The discrete case of the variable aggregation method allowed the study of the system through the dominant elements of a much simpler linear system with only three global variables: the total number of individuals in each age-class. (shrink)

In this work we deal with a general class of spatially distributed periodic SIS epidemic models with two time scales. We let susceptible and infected individuals migrate between patches with periodic time dependent migration rates. The existence of two time scales in the system allows to describe certain features of the asymptotic behavior of its solutions with the help of a less dimensional, aggregated, system. We derive global reproduction numbers governing the general spatially distributed nonautonomous system through the aggregated system. (...) We apply this result when the mass action law and the frequency dependent transmission law are considered. Comparing these global reproductive numbers to their non spatially distributed counterparts yields the following: adequate periodic migration rates allow global persistence or eradication of epidemics where locally, in absence of migrations, the contrary is expected. (shrink)

We used computer simulations to study the possible role of the dispersion of cellular coupling, refractoriness or both, in the mechanisms underlying cardiac arrhythmias. Local ischemia was first assumed to induce cell to cell dispersion of the coupling resistance (Case 1), refractory period (Case 2), or both of them (Case 3). Our numerical experiments based on the van Capelle and Durrer model showed that vortices could not be induced by cell to cell variations. With cellular properties dispersed in a patchy (...) way within the ischemic zone, a single activation wave could give rise to abnormal activities. This demonstrates the stability of the wave front under small inhomogeneities. Probabilities of reentry, estimated for the three cases cited above showed that a severe alteration of the coupling resistance may be an important factor in the genesis of reentry. Moreover, use of isochronal maps revealed that vortices were both stable and sustained with an alteration of the coupling alone or combined with a reduction of the action potential duration. Conversely, simulations with reduction of the refractoriness alone, inducing only transient patterns, could exhibit functionally determined reentries. (shrink)

We consider a two-patch epidemiological system where individuals can move from one patch to another, and local interactions between the individuals within a patch are governed by the classical SIRS model. When the time-scale associated with migration is much smaller than the time-scale associated with infection, aggregation methods can be used to simplify the initial complete model formulated as a system of ordinary differential equations. Analysis of the aggregated model then shows that the two-patch basic reproduction rate is smaller than (...) the 1 patch one. We extend this result to a linear chain of P patches . These results are illustrated by some examples for which numerical integration of the system of ordinary differential equations is performed. Simulations of an individual based model implemented with a multi-agent system are also carried out. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Vetera Novis Augere et Perficere:Thomas Aquinas and Christian-Muslim DialogueJoseph Ellul, O.P.Pope Leo XIII's encyclical letter Aeterni Patris, issued on August 4, 1879, sought to address many issues that were challenging nineteenth-century Catholic scholarship and academic life. In proposing the thought of Thomas Aquinas as a model of Catholic teaching, the Pope intended, in his own words, "to strengthen and complete the old by aid of the new,"1 not only (...) by reviving the study of the works and teachings of the Angelic Doctor, especially in the realm of philosophy, but also to uphold as perennial his method of engaging with his contemporaries within and without the Catholic faith.2 It is within this context that we are called upon to reflect upon this appeal: "vetera novis augere et perficere."The thirteenth century was indeed a time of intellectual upheaval, following the introduction of Aristotle and, later on, the translations into Latin of the Arabic commentaries on Aristotle by Ibn Rušd (Lat. Averröes; d. 1198). This event was met within the ecclesiastical world with apprehension, if not outright fear. Neo-Platonic philosophy and its interpretation by Ibn Sina (Lat. Avicenna; d. 1037) was already perfectly acceptable to Mediaeval Christian scholars. The latter was in fact considered an essential tool for understanding the illuminationist thought of St. Augustine. Étienne Gilson even spoke of Augustinisme avicennisant (Avicennized [End Page 1231] Augustinianism).3 The problem was Aristotle and his renowned commentator Ibn Rušd: a pagan commented on by an infidel.One must also note, however, that mediaeval Western intellectuals and institutions were able to encounter and adapt the Islamic legacy, because they already possessed a sufficient scientific base (with of course the contribution of translations of Greek together with Latin works) with which to understand, assimilate, and build upon this new knowledge that appeared from the East. In sum, mediaeval Christendom created living, vibrant societies, constantly searching, always discovering something new.In dealing with the specific (and delicate) subject of Aquinas's dialogue with Islamic thought, it would be necessary to reflect in particular upon two key works of his: the Liber de Veritate Catholicae Fidei contra Errores Infidelium (A Book on the Truth of the Catholic Faith against the Errors of Unbelievers),4 popularly known as the Summa contra gentiles [SCG], together with his De rationibus fidei contra Saracenos, Gnæcos et Armenos ad Cantorem Antiochenum, better known simply as De rationibus fidei.At this point it would be necessary to articulate the term "Islamic thought." Of itself it should not be identified with Islam as a religion. Rather, it should be considered as embracing classical Greek philosophy as interpreted by the Neo-Platonic movement and disseminated through Oriental Christian and Jewish schools of thought. Islamic civilization absorbed these teachings and built its own proper ediice upon these foundations.A Model for Interreligious Dialogue?Proposing Thomas Aquinas as a model for engagement with Islamic thought may also raise a few eyebrows. Hence, it would be appropriate to pose an essential question: "What type of dialogue existed in mediaeval times?" One should begin with an a priori exclusion of dialogue as it is understood today, given the fact that there existed neither the motive nor the means to implement it.In fact mediaeval society was aware of only three religions: the pagan, which had been replaced by Christianity; the Jewish, founded upon the precepts of the First Covenant which "Christ fulilled by his actions and [End Page 1232] by his teaching"5 and which was also believed to prefigure the everlasting New Covenant sealed by Jesus on the Cross; and finally, the Christian, which believed in Jesus as the final revelation of God to humanity.6 With such a vision in mind it is obvious that any doctrine that is not situated within these parameters, or which proposes some form of belief or conduct which was different from, if not contrary to, the Christian vision of God, the cosmos, and society, would be considered as heretical and its promoter an impostor.7When Islam made its appearance in the Christian world, it carried with it a book that it considered of divine provenance, and... (shrink)

Anthropocentrism was born with Man, and certain primitive tribes or ethnic groups considered themselves the center of the world. Their members assumed the generic name “the Men,” and all the rest, including other, tribes or ethnic groups, were part of a more or less hostile environment (to use the modern term).

"Depuis une quinzaine d'années, les études sur Montesquieu se sont profondément renouvelées. Le corpus lui-même, grâce aux OEuvres complètes en cours, et notamment avec la première publication intégrale du manuscrit de travail de L'Esprit des lois, offre des perspectives inédites. Mais c'est aussi l'approche même qui a changé : la diversité des questions et des thèmes que son oeuvre permet d'aborder élargit le champ de la recherche, de la philosophie morale et politique à l'histoire ou l'anthropologie, ou encore à la (...) pensée du droit et de la société. Ce volume en tire méthodiquement les conséquences. Dans la perspective de l'édition critique des OEuvres complètes de Montesquieu, c'est à une relecture non pas radicale, mais en finesse et en profondeur qu'invite ce volume, en développant le rapport entre l'homme et la société, en redessinant la relation aux grands massifs de la tradition philosophique d'une pensée dont on suit jusqu'à son terme la logique, en suggérant des relations inédites à travers des rapprochements qui s'imposent, mais n'avaient pourtant guère été faits : ce qui restait informe ou informulé s'est éclairé, ce dont on devinait l'importance s'est approfondi. Ensuite, que restera-t-il à (re)lire? L'Esprit des lois."--Page [4] de la couverture. (shrink)

The importance of ethical consumerism to many companies worldwide has increased dramatically in recent years. Ethical consumerism encompasses the importance of non-traditional and social components of a company's products and business process to strategic success - such as environmental protectionism, child labor practices and so on. The present paper utilizes a random utility theoretic experimental design to provide estimates of the relative value selected consumers place on the social features of products.

Nearly all studies of consumers’ willingness to engage in ethical or socially responsible purchasing behavior is based on unconstrained survey response methods. In the present article we ask the question of how well does asking consumers the extent to which they care about a specific social or ethical issue relate to how they would behave in a more constrained environment where there is no socially acceptable response. The results of a comparison between traditional survey questions of “intention to purchase” and (...) estimates of individuals willingness-to-pay for social attributes in products reveal that simple survey questions are too “noisy” to provide operationally meaningful information and overstate intentions to a considerable extent. (shrink)

... The purpose of this paper is to try to clarify the extent to which consumers “value” ethical product features when making purchases by utilizing a distinctive methodology – structured choice experiments ( Louviere et al., 2000) – that What Will Consumers Pay ... Jordan J. Louviere ... \n.

This work presents a mathematical model describing the interactions between the cross-shore structure of small pelagic fish population an their exploitation by coastal and offshore fisheries. The complete model is a system of seven ODE’s governing three stocks of small pelagic fish population moving and growing between three zones. Two types of fishing fleets are inter-acting with the fish population, industrial boats, constrained to offshore area, and artisanal boats, operating from the shore. Two time scales were considered and we use (...) aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model, which is a four dimension one. The analysis of the aggregated model is performed. We discuss the possible equilibriums and their meaning in terms of fishery management. An interesting equilibrium state can be obtained for which we can expect coexistence and a stable equilibrium state between fish stocks and fishing efforts. Some identification parameters are also given in the discussion part of the model. (shrink)

We study the case of two sibling species ofHippolais(Aves). Very little differences can be observed in the morphology of both species. The breeding area of these species are complementary. Roughly, one species breeds North and East of Europe (Hippolais icterina) while the other breeds South and West of Europe (Hippolais polyglotta). There exitst a narrow zone of sympatry passing through Burgundy. Since several years, it has been observed that this area of sympatry was moving in the North-East direction at a (...) European scale. This means that progressivelyH. icterina is declining and is replaced byH. polyglotta. Some assumptions can be made in order to explain this evolution, for instance competition or predation. Series of observations concerning the diets of nestlings of both species have been realized. These observations show some differences in the diet compositions. The breeding success of the two species has been studied. Numerical simulations of a competition model taking into account the observed differences between the food types eaten by the two species are presented. These simulations do not explain the regression ofH. icterina. Then, we present numerical simulations of a predation model with one predator attacking the nestlings of both species. These simulations show that with time one of the two preys must extinct. Predation rather than competition seems to be the right explanation. (shrink)

We present a mathematical model of two competing marine species that are harvested. We consider three models according to different levels of complexity, without and with species refuge and density-independent and density-dependent species movement between fishing area and refuge. We particularly study the effects of the fishing pressure on the outcome of the competition. We focus on conditions that allow an inferior competitor to invade as a result of fishing pressure. The model is discussed in relationship to the case of (...) the thiof and the octopus along the Atlantic West African coast. At the origin, the thiof was abundant and the octopus scarce in that region. Since, the fishing pressure has strongly increased in some fishing areas leading to the depletion of the thiof and the invasion of its competitor, the octopus. (shrink)

Outcomes of interspecific competition, and especially the possibility of coexistence, have been extensively studied in theoretical ecology because of their implications in community assemblages. During the last decades, the influence of different time scales through the local/regional dynamics of animal communities has received an increasing attention. Nevertheless, different time scales involved in interspecific competition can result form other processes than spatial dynamics. Here, we envision and analyze a new theoretical framework that couples a game theory approach for competition with a (...) demographic model. We take advantage of these two time scales to derive a reduced model governing the total densities of the two populations and we study how these two time scales interfere and influence outcomes of species competition. We find that a competition process occurring on a faster time scale than demography yields a “priority effect” where the first species introduced outcompetes the other one. We then confirm previous findings stipulating that species coexistence is favored by large difference in time scales because the extinction/recolonization process. Our results then highlight that an integration of demographic and competition time scales at both local and regional levels is mandatory to explain communities assemblages and should become a research priority. (shrink)

This study uses best–worst scaling experiments to examine differences across six countries in the attitudes of consumers towards social and ethical issues that included both product related issues (such as recycled packaging) and general social factors (such as human rights). The experiments were conducted using over 600 respondents from Germany, Spain, Turkey, USA, India, and Korea. The results show that there is indeed some variation in the attitudes towards social and ethical issues across these six countries. However, what is more (...) telling are the similarities seen and the extent to which individual variation dominates observable demographics and country-based variables. (shrink)

Cet article retrace la manière dont j’ai découvert et surtout identifié et authentifié un manuscrit inédit de Montesquieu, les Notes sur Cicéron (conservé dans le fonds de La Brède de la bibliothèque de Bordeaux). Ce document jette un jour nouveau sur la formation philosophique de Montesquieu et révèle une attitude très critique envers la religion, inspirée en grande partie par la lecture de Bayle.

Cet article retrace la manière dont j’ai découvert et surtout identifié et authentifié un manuscrit inédit de Montesquieu, les Notes sur Cicéron (conservé dans le fonds de La Brède de la bibliothèque de Bordeaux). Ce document jette un jour nouveau sur la formation philosophique de Montesquieu et révèle une attitude très critique envers la religion, inspirée en grande partie par la lecture de Bayle.

La nouvelle édition des œuvres complètes de Montesquieu en vingt et un volumes (huit sont parus depuis 1998), rattachée à l’École normale supérieure Lettre et Sciences humaines (Lyon) depuis 2000 et publiée par la Voltaire Foundation (Oxford), se fonde sur une approche nouvelle du corpus manuscrit comme de la conception même de l’œuvre, saisie dans son devenir ; l’établissement du texte comme l’annotation cherchent à en restituer la force initiale, telle qu’elle a pu apparaître aux contemporains de Montesquieu. Cette entreprise (...) se double d’une réflexion constante sur sa propre pratique, par rapport à l’histoire de l’édition et à la réception (et donc l’interprétation) des œuvres de Montesquieu. (shrink)

This study uses best–worst scaling experiments to examine differences across six countries in the attitudes of consumers towards social and ethical issues that included both product related issues (such as recycled packaging) and general social factors (such as human rights). The experiments were conducted using over 600 respondents from Germany, Spain, Turkey, USA, India, and Korea. The results show that there is indeed some variation in the attitudes towards social and ethical issues across these six countries. However, what is more (...) telling are the similarities seen and the extent to which individual variation dominates observable demographics and country-based variables. (shrink)

The aim of this work is to study complex ecological models exhibiting simple dynamics. We consider large scale systems which can be decomposed into weakly coupled subsystems. Perturbation Theory is used in order to get a reduced set of differential equations governing slow time varying global variables. As examples, we study the influence of the individual behaviour of animals in competition and predator-prey models. The animals are assumed to do many activities all day long such as searching for food of (...) different types. The degree of competition as well as the predation pressure are dependent upon these activities. 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 the effect of a change in the average individual behaviour of the animals on interspecific relationships. Computer simulations of the whole sets of equations are compared to simulations of the reduced sets of equations. (shrink)

The incredible achievements of modern scientific theories lead most of us to embrace scientific realism: the view that our best theories offer us at least roughly accurate descriptions of otherwise inaccessible parts of the world like genes, atoms, and the big bang. In Exceeding Our Grasp, Stanford argues that careful attention to the history of scientific investigation invites a challenge to this view that is not well represented in contemporary debates about the nature of the scientific enterprise. The historical record (...) of scientific inquiry, Stanford suggests, is characterized by what he calls the problem of unconceived alternatives. Past scientists have routinely failed even to conceive of alternatives to their own theories and lines of theoretical investigation, alternatives that were both well-confirmed by the evidence available at the time and sufficiently serious as to be ultimately accepted by later scientific communities. Stanford supports this claim with a detailed investigation of the mid-to-late 19th century theories of inheritance and generation proposed in turn by Charles Darwin, Francis Galton, and August Weismann. He goes on to argue that this historical pattern strongly suggests that there are equally well-confirmed and scientifically serious alternatives to our own best theories that remain currently unconceived. Moreover, this challenge is more serious than those rooted in either the so-called pessimistic induction or the underdetermination of theories by evidence, in part because existing realist responses to these latter challenges offer no relief from the problem of unconceived alternatives itself. Stanford concludes by investigating what positive account of the spectacularly successful edifice of modern theoretical science remains open to us if we accept that our best scientific theories are powerful conceptual tools for accomplishing our practical goals, but abandon the view that the descriptions of the world around us that they offer are therefore even probably or approximately true. (shrink)

The place of the emotions among the passions -- The analytic of the emotions I -- The analytic of the emotions II -- The dialectic of the emotions -- Pride, arrogance, and humility -- Shame, embarrassment, and guilt -- Envy -- Jealousy -- Anger -- Love -- Friendship -- Sympathy and empathy.

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)

In this paper, we present a deterministic time discrete mathematical model based on multiregional periodic matrices to describe the dynamics of Sardina pilchardus in the Central Atlantic area of the Moroccan coast. This model deals with two stages (immature and mature) and three spatial zones where sardines are supposed to migrate from one zone to another. The population dynamics is described by an autonomous recurrence equation N(t + 1) = A.N(t), where A is a positive matrix whose entries are estimated (...) using data collected during biannual acoustic surveys carried out from 2001 to 2003 onboard the Norwegian research vessel “Dr Fridtjof Nansen”. The dominant eigenvalue λ of A that gives the long-term growth rate of fish population is smaller than one. This agrees with the stock decrease observed in the data collected. We show that λ is highly sensitive to the recruitment rate and much less sensitive to the reproduction rate. These results can clearly be used to define an efficient scenario in order to fight for instance against a stock decrease. (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)

The aim of this work is to present aggregation methods of hierarchically organized systems allowing one to replace the initial micro-system by a macro-system described by a few global variables. We also study the relations between the fast micro-dynamics and the slow macro-dynamics which can produce global properties. Emergence corresponds to a bottom-up coupling that is the result effected by a micro-level at a macro-level. As an example, we present prey-predator models with different time scales in an heterogeneous environment. A (...) fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to growth and interactions between the populations. Preys must go on spatial patches where resources are located and where predators can attack them. The efficiency of the predators to catch preys is patch dependent. Perturbation methods allow us to aggregate the initial system of differential equations for the patch sub-populations into a macro-system of two differential equations governing the total population densities. We study the case of density independent and density dependent migrations. In the latter case, we show that different functional responses can emerge in the macro prey-predator model as a result of the coupling between the slow and fast systems. (shrink)

Une trentaine de communications célèbrent le 250e anniversaire de l'édition de ¤¤L'esprit des lois¤¤ chez l'imprimeur genevois Barrilot et fils. Le texte est replacé dans son contexte éditorial, historique, genevois et européen. La culture politique et juridique qui le nourrit est analysée, ainsi que la philosophie de l'histoire de son auteur afin de mieux comprendre la modernité des Lumières.

We present a dynamical model of a multi-site fishery. The fish stock is located on a discrete set of fish habitats where it is catched by the fishing fleet. We assume that fishes remain on fishing habitats while the fishing vessels can move at a fast time scale to visit the different fishing sites. We use the existence of two time scales to reduce the dimension of the model : we build an aggregated model considering the habitat fish densities and (...) the total fishing effort. We explore a regulation procedure, which imposes an average residence time in patches. Several equilibria exist, a Fishery Free Equilibria as well as a Sustainable Fishery Equilibria . We show that the dynamics depends on a threshold which is similar to a basic reproduction ratio for the fishery. When the basic reproduction ratio is less or equal to 1, one of the FFEs is globally asymptotically stable , otherwise one of the SFEs is GAS. (shrink)

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of variables in (...) order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to over-exploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery. (shrink)