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)

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)

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)

The present work is aimed at investigating the effects of myocardial infarction and ischemia on induction of ventricular fibrillation. Electrophysiologic effects of global and local ischemia (variation of the dispersion of refractory periods as well as conduction velocity) on initiation of reentry mechanisms was studied by means of computer simulations based on a cellular automata model of propagation of activation wave through a ventricular surface element. A local area of ischemia where effects of the dispersion of refractory periods are investigated (...) is then simulated. This is made using a Gaussian distribution characterized by its mean and standard deviation. These simulations show that ischemia is capable of initiating reentry phenomena which propagate through the whole ventricle; they are responsible for ventricular fibrillation which causes sudden cardiac death, even when ischemia only involves limited parts of the myocardium. Statistical study of the probability of reentries as a function of both of the size of ischemic zones and the rate of dispersion of refractory periods shows that the latter parameter is of primary importance in triggering cardiac reentries. (shrink)

Limitations of antiarrhythmic drugs on cardiac sudden death prevention appeared since the early 80's. The "Cardiac Arrhythmia Suppression Trial"(CAST) showed more recently that mortality was significantly higher inpatients treated with some particular antiarrhythmic drugs than in non-treated patients. In this field, our group recently demonstrated that a bolus of a Class 1B antiarrhythmic drug was able to trigger a ventricular fibrillation due to transient blocks induction. The aim of the present work was to systematically study, by use of the van (...) Capelle and Durrer (VCD) model which allows to simulate ventricular activation wave propagation, the link between arrhythmogenic effects and the ability of transient blocks to possibly degenerate in severe arrhythmias. A fragment of the ventricular wall is represented by an array of 16384elements electrically coupled. Effects of induction of one or several transient blocks, as the effects of their size and duration on possible induction of reentries have been studied. Results obtained show that various combinations between these different parameters may trigger reentries, ventricular tachycardia and/or more complex patterns assimilable to ventricular fibrillation. These results clearly evidence the fact that possible induction of transient blocks may directly be related to risk factor associated to arrhythmogenic effects of antiarrhythmic drugs. (shrink)

In multicellular organisms, cells are frequently programmed to die. This makes good sense: cells that fail to, or are no longer playing important roles are eliminated. From the cell’s perspective, this also makes sense, since somatic cells in multicellular organisms require the cooperation of clonal relatives. In unicellular organisms, however, programmed cell death poses a difficult and unresolved evolutionary problem. The empirical evidence for PCD in diverse microbial taxa has spurred debates about what precisely PCD means in the case of (...) unicellular organisms. In this article, we survey the concepts of PCD in the literature and the selective pressures associated with its evolution. We show that definitions of PCD have been almost entirely mechanistic and fail to separate questions concerning what PCD fundamentally is from questions about the kinds of mechanisms that realize PCD. We conclude that an evolutionary definition is best able to distinguish PCD from closely related phenomena. Specifically, we define “true” PCD as an adaptation for death triggered by abiotic or biotic environmental stresses. True PCD is thus not only an evolutionary product but must also have been a target of selection. Apparent PCD resulting from pleiotropy, genetic drift, or trade-offs is not true PCD. We call this “ersatz PCD.”. (shrink)

Organismal death is foundational to the evolution of life, and many biological concepts such as natural selection and life history strategy are so fashioned only because individuals are mortal. Organisms, irrespective of their organization, are composed of basic functional units—cells—and it is our understanding of cell death that lies at the heart of most general explanatory frameworks for organismal mortality. Cell death can be exogenous, arising from transmissible diseases, predation, or other misfortunes, but there are also endogenous forms of death (...) that are sometimes the result of adaptive evolution. These endogenous forms of death—often labeled programmed cell death, PCD—originated in the earliest cells and are maintained across the tree of life. Here, we consider two problematic issues related to PCD (and cell mortality generally). First, we trace the original discoveries of cell death from the nineteenth century and place current conceptions of PCD in their historical context. Revisions of our understanding of PCD demand a reassessment of its origin. Our second aim is thus to structure the proposed origin explanations of PCD into coherent arguments. In our analysis we argue for the evolutionary concept of PCD and the viral defense-immunity hypothesis for the origin of PCD. We suggest that this framework offers a plausible account of PCD early in the history of life, and also provides an epistemic basis for the future development of a general evolutionary account of mortality. (shrink)

Research highlights several risk and resilience factors at multiple ecological levels that influence individuals’ mental health and wellbeing in their everyday lives and, more specifically, in disaster or outbreak situations. However, there is limited research on the role of these factors in the early days of the COVID-19 crisis. The present study examined if and how potential risk factors and resilience factors are associated with mental health and well-being outcomes, and whether these resilience factors buffer the associations between risk factors (...) and said outcomes. One to two weeks after the government recommended preventative measures, 1,122 Canadian workers completed an online questionnaire, including multiple wellbeing outcome scales in addition to measures of potential risk and resilience factors. Structural equation models were tested, highlighting that overall, the considered risk factors were associated with poorer wellbeing outcomes, except social distancing which was associated with lower levels of stress. Each of the potential resilience factors was found to have a main effect on one or more of the wellbeing outcomes. Moderation analysis indicated that in general these resilience factors did not, however, buffer the risk factors. The findings confirm that the COVID-19 crisis encompasses several stressors related to the virus as well as to its impact on one’s social, occupational, and financial situation, which put people at risk for lower wellbeing as early as one to two weeks after the crisis began. While several resilience factors emerged as positively related to wellbeing, such factors may not be enough, or sufficiently activated at that time, to buffer the effects of the numerous life changes required by COVID-19. From an ecological perspective, while mental health professionals and public health decision-makers should offer/design services directly focused on mental health and wellbeing, it is important they go beyond celebrating individuals’ inner potential for resilience, and also support individuals in activating their environmental resources during a pandemic. (shrink)

Programmed cell death (PCD) in unicellular organisms is in some instances an altruistic trait. When the beneficiaries are clones or close kin, kin selection theory may be used to explain the evolution of the trait, and when the trait evolves in groups of distantly related individuals, group or multilevel selection theory is invoked. In mixed microbial communities, the benefits are also available to unrelated taxa. But the evolutionary ecology of PCD in communities is poorly understood. Few hypotheses have been offered (...) concerning the community role of PCD despite its far-reaching effects. The hypothesis we consider here is that PCD is a black queen. The Black Queen Hypothesis (BQH) outlines how public goods arising from a leaky function are exploited by other taxa in the community. Black Queen (BQ) traits are essential for community survival, but only some members bear the cost of possessing them, while others lose the trait In addition, BQ traits have been defined in terms of adaptive gene loss, and it is unknown whether this has occurred for PCD. Our conclusion is that PCD fulfils the two most important criteria of a BQ (leakiness and costliness), but that more empirical data are needed for assessing the remaining two criteria. In addition, we hold that for viewing PCD as a BQ, the original BQH needs to include social traits. Thus, despite some empirical and conceptual shortcomings, the BQH provides a helpful avenue for investigating PCD in microbial communities. (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).

The present study investigated whether individual differences between psychologists in thinking styles are associated with accuracy in diagnostic classification. We asked novice and experienced clinicians to classify two clinical cases of clients with two co-occurring psychological disorders. No significant difference in diagnostic accuracy was found between the two groups, but when combining the data from novices and experienced psychologists accuracy was found to be negatively associated with certain decision making strategies and with a higher self-assessed ability and preference for a (...) rational thinking style. Our results underscore the idea that it might be fruitful to look for explanations of differences in the accuracy of diagnostic judgments in individual differences between psychologists (such as in thinking styles or decision making strategies used), rather than in experience level. (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)

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)

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)

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)

... 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.

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)

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)

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)

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)

We assume the existence of a specific G1 protein which is an initiator of DNA replication. This initiator is supposed to be synthesized according to Michaelis-Menten kinetics. In order to start DNA replication, it is assumed that this G1 specific protein must be produced in a required amount. Intra-cellular growth inhibitors and extra-cellular growth factors control the production of the initiator. This model allows to calculate the average G1 phase time as a function of the various chemical concentrations of nutrients, (...) enzymes, growth inhibitors and growth factors. This model is compared to cell kinetics experiments on a leukemic cell line responding to Interleukin 3 deprivation. The curves giving the experimental average G1 phase times with respect to Interleukin-3 concentrations are fitted by the mathematical model with a quite good agreement. (shrink)

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)

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)

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 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)

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)

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)

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)

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 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)

As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very different from (...) each other. Aggregation techniques take advantage of this situation to build a low dimensional reduced system from which behavior we can approximate the dynamics of the complex original system.In this work we extend aggregation techniques to the case of time dependent discrete population models with two time scales where both the fast and the slow processes are allowed to change at their own characteristic time scale, generalizing the results of previous studies. We propose a non-autonomous model with two time scales, construct an aggregated model and give relationship between the variables governing the original and the reduced systems. We also explore how the properties of strong and weak ergodicity, regarding the capacity of the system to forget initial conditions, of the original system can be studied in terms of the reduced system. (shrink)

Aggregation methods allow one to replace a large scale dynamical system (micro-system) by a reduced dynamical system (macro-system) governing a small number of global variables. This aggregation of variables can be performed when two time scales exist, a fast time scale and a slow time scale. Perturbation theory allows to obtain an approximated aggregated dynamical system which describes the behaviour of a few number of slow time varying variables which are constants of motion of the fast part of the micro-system. (...) Aggregation methods are applied to the case of the devastation of the great barrier reef by the starfishes. We recall the Antonelli/Kazarinoff model which implies a stable limit cycle for the corals and starfish populations. This prey-predator model describes the interactions between two species of corals and the starfish. Then, we generalize the Antonelli/Kazarinoff model to the case of two spatial patches with a fast part describing the starfish migration on the patches and the human manipulation of the communities by divers and, a slow part describing the growth and the interactions between the populations. We obtain an aggregated model governing the total coral densities on the patches and the total starfish population. This model can exhibit stable limit cycle oscillations and a Hopf bifurcation. The critical value of the bifurcation parameter is expressed in terms of the proportions of coral species and starfish on the two patches. This implies for example that rather than random killing of starfish by the Australian military, it may be better to send teams of divers to outbreaking reefs when they first occur who will then manipulate the community structure to increase protection. (shrink)