A tragedy of the commons case study: modeling the fishers king crab system in Southern Chile

Illegal fishing in small-scale fisheries is a contentious issue and resists a straightforward interpretation. Particularly, there is little knowledge regarding cooperative interactions between legal and illegal fishers and the potential effects on fisheries arising from these interactions. Taking the Chilean king crab (Lithodes santolla; common name centolla) fishery as a case study, our goal is twofold: (i) to model the effect of illegal-legal fishers' interactions on the fishery and (ii) analyze how management and social behavior affect fishery's outcomes. We framed the analysis of this problem within game theory combined with network theory to represent the architecture of competitive interactions. The fishers' system was set to include registered (legal) fishers and unregistered (illegal) fishers. In the presence of unregistered fishers, legal fishers may decide to cooperate (ignoring the presence of illegal fishers) or defect, which involves becoming a "super fisher" and whitewashing the captures of illegal fishers for a gain. The utility of both players, standard fisher and super fisher depend on the strategy chosen by each of them, as well as on the presence of illegal fishers. The nodes of the network represent the legal fishers (both standard and super fishers) and the links between nodes indicate that these fishers compete for the resource, assumed to be finite and evenly distributed across space. The decision to change (or not) the adopted strategy is modeled considering that fishers are subjected to variable levels of temptation to whitewash the illegal capture and to social pressure to stop doing so. To represent the vital dynamics of the king crab, we propose a model that includes the Allee effect and a term accounting for the crab extraction. We found that the super fisher strategy leads to the decrease of the king crab population under a critical threshold as postulated in the tragedy of the commons hypothesis when there are: (i) high net extraction rates of the network composed of non-competing standard fishers, (ii) high values of the extent of the fishing season, and (iii) high density of illegal fishers. The results suggest that even in the presence of super fishers and illegal fishers, the choice of properly distributed fishing/closure cycles or setting an extraction limit per vessel can prevent the king crab population from falling below a critical threshold. This finding, although controversial, reflects the reality of this fishery that, for decades, has operated under a dynamic in which whitewashing and super fishers have become well established within the system.

Complexity emerges in measures of the marking dynamics in football games

In this article, we study the dynamics of marking in football matches. To do this, we survey and analyze a database containing the trajectories of players from both teams on the field of play during three professional games. We describe the dynamics through the construction of temporal bipartite networks of proximity. Based on the introduced concept of proximity, the nodes are the players, and the links are defined between opponents that are close enough to each other at a given moment. By studying the evolution of the heterogeneity parameter of the networks during the game, we characterize a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we propose a simple model to simulate the players' motion in the field from where we obtained the evolution of a synthetic proximity network. We show that the model captures with a remarkable agreement the complexity of the empirical case, hence it proves to be helpful to elucidate the underlying mechanisms responsible for the observed phenomena.

Evolutionary game inspired by Cipolla's basic laws of human stupidity

In this work we present an evolutionary game inspired by the work of Carlo Cipolla entitled The Basic Laws of Human Stupidity. The game expands the classical scheme of two archetypical strategies, collaborators and defectors, by including two additional strategies. One of these strategies is associated with a stupid player that, according to Cipolla, is the most dangerous one as it undermines the global wealth of the population. By considering a spatial evolutionary game and imitation dynamics that go beyond the paradigm of a rational player we explore the impact of Cipolla's ideas and analyze the extent of the damage that stupid players inflict on the population.

Waves of seed propagation induced by delayed animal dispersion

We study a model of seed dispersal that considers the inclusion of an animal disperser moving diffusively, feeding on fruits and transporting the seeds, which are later deposited and capable of germination. The dynamics depends on several population parameters of growth, decay, harvesting, transport, digestion and germination. In particular, the deposition of transported seeds at places away from their collection sites produces a delay in the dynamics, whose effects are the focus of this work. Analytical and numerical solutions of different simplified scenarios show the existence of travelling waves. The effect of zoochory is apparent in the increase of the velocity of these waves. The results support the hypothesis of the relevance of animal mediated seed dispersion when trying to understand the origin of the high rates of vegetable invasion observed in real systems.

Statistical fluctuations in pedestrian evacuation times and the effect of social contagion

Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models is now available, their calibration and test against empirical data are generally restricted to global averaged quantities; the statistics compiled from the time series of individual escapes ("microscopic" statistics) measured in recent experiments are thus overlooked. In the same spirit, much research has primarily focused on the average global evacuation time, whereas the whole distribution of evacuation times over some set of realizations should matter. In the present paper we propose and discuss the validity of a simple relation between this distribution and the microscopic statistics, which is theoretically valid in the absence of correlations. To this purpose, we develop a minimal cellular automaton, with features that afford a semiquantitative reproduction of the experimental microscopic statistics. We then introduce a process of social contagion of impatient behavior in the model and show that the simple relation under test may dramatically fail at high contagion strengths, the latter being responsible for the emergence of strong correlations in the system. We conclude with comments on the potential practical relevance for safety science of calculations based on microscopic statistics.

Social Learning in Vespula Germanica Wasps: Do They Use Collective Foraging Strategies?

Vespula germanica is a social wasp that has become established outside its native range in many regions of the world, becoming a major pest in the invaded areas. In the present work we analyze social communication processes used by V. germanica when exploiting un-depleted food sources. For this purpose, we investigated the arrival pattern of wasps at a protein bait and evaluated whether a forager recruited conspecifics in three different situations: foragers were able to return to the nest (full communication), foragers were removed on arrival (communication impeded), or only one forager was allowed to return to the nest (local enhancement restricted). Results demonstrated the existence of recruitment in V. germanica, given that very different patterns of wasp arrivals and a higher frequency of wasp visits to the resource were observed when communication flow between experienced and naive foragers was allowed. Our findings showed that recruitment takes place at a distance from the food source, in addition to local enhancement. When both local enhancement and distant recruitment were occurring simultaneously, the pattern of wasp arrival was exponential. When recruitment occurred only distant from the feeder, the arrival pattern was linear, but the number of wasps arriving was twice as many as when neither communication nor local enhancement was allowed. Moreover, when return to the nest was impeded, wasp arrival at the bait was regular and constant, indicating that naive wasps forage individually and are not spatially aggregated. In conclusion, this is the first study to demonstrate recruitment in V. germanica at a distance from the food source by modelling wasps’ arrival to a protein-based resource. In addition, the existence of correlations when communication was allowed and reflected in tandem arrivals indicates that we were not in the presence of random processes.

Random-walk model to study cycles emerging from the exploration-exploitation trade-off

We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the behavior of the walker each time it reaches an already visited site modulating the probability of repeating previous moves. This probability increases with the time elapsed from the last visit. A biological analog of the walker is a frugivore, with the lattice sites representing plants. The memory effect can be associated with the time needed by plants to recover its fruit load. We propose two different strategies, conservative and explorative, as well as intermediate cases, leading to nonintuitive interesting results, such as the emergence of cycles.

Game theory in models of pedestrian room evacuation

We analyze the pedestrian evacuation of a rectangular room with a single door considering a lattice gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational choices and is affected by conflicts between two or more agents that want to advance to the same position. Such conflicts are solved according to certain rules closely related to the concept of strategies in game theory, cooperation and defection. We consider game rules analogous to those from the Prisoner's Dilemma and Stag Hunt games, with payoffs associated to the probabilities of the individuals to advance to the selected site. We find that, even when defecting is the rational choice for any agent, under certain conditions, cooperators can take advantage from mutual cooperation and leave the room more rapidly than defectors.

Invited review: Epidemics on social networks

Since its first formulations almost a century ago, mathematical models fordisease spreading contributed to understand, evaluate and control the epidemic processes.They promoted a dramatic change in how epidemiologists  thought of the propagation of infectious diseases.In the last decade, when the traditional epidemiological models seemed to be exhausted,  new types of models were developed.These new models incorporated concepts from graph theory to describe and model the underlying social structure.Many of these works  merely produced a more detailed extension of the previous results,  but some otherstriggered a completely new paradigm  in the mathematical study of epidemic processes. In this review, we will introduce the basicconcepts of epidemiology, epidemic  modeling and networks, to finally provide a brief description of the mostrelevant results in the field. Received: 6 April 2013,  Accepted: 3 June 2013; Edited by: G. Mindlin; DOI: http://dx.doi.org/10.4279/PIP.050003Cite as: M N Kuperman, Papers in Physics 5, 050003 (2013) 

Relationship between clustering coefficient and the success of cooperation in networks

In recent years the prisoner's dilemma has become a paradigm for the study of the emergence of cooperation in spatially structured populations. Such a structure is usually assumed to be given by a graph. In general, the success of cooperative strategies is associated with the possibility of forming globular clusters, which in turn depends on a feature of the network that is measured by its clustering coefficient. In this work we study the dependence of the success of cooperation on this coefficient for regular networks. Additionally, for both stochastic and deterministic dynamics we show that there is a strong dependence on the initial composition of the population. This hints at the existence of several different mechanisms that could promote or hinder cluster expansion. We have studied in detail some of these mechanisms by concentrating on completely ordered networks (large clustering coefficient) or completely random networks (vanishing clustering coefficient).

A model for the emergence of geopolitical division

In this work, we present a model based on a competitive dynamics that intends to imitate the processes leading to some characteristics of the geopolitical division. The model departs from very simple principles of geopolitical theory and geometrical considerations, but succeeds in explaining the general features related to the actual process. At the same time, we will propose an evolutionary explanation to the fact that most capitals (in Eurasia) are located far from the borders or coasts and, in many cases, close to the barycentre of the respective countries.

Theory of possible effects of the Allee phenomenon on the population of an epidemic reservoir

We investigate possible effects of high-order nonlinearities on the shapes of infection refugia of the reservoir of an infectious disease. We replace Fisher-type equations that have been recently used to describe, among others, the Hantavirus spread in mouse populations by generalizations capable of describing Allee effects that are a consequence of the high-order nonlinearities. After analyzing the equations to calculate steady-state solutions, we study the stability of those solutions and compare to the earlier Fisher-type case. Finally, we consider the spatial modulation of the environment and find that unexpected results appear, including a bifurcation that has not been studied before.

Cultural propagation on social networks

In this work we present a model for the propagation of culture on networks of different topology and by considering different underlying dynamics. We extend a previous model proposed by Axelrod by letting a majority govern the dynamics of changes. This in turn allows us to define a Lyapunov functional for the system.

Periodically varying externally imposed environmental effects on population dynamics

Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms in a standard equation of evolution. Possible applications of the analysis are on the one hand to bacteria in Petri dishes and on the other to rodents in the context of the spread of the Hantavirus epidemic. The analysis shows that spatiotemporal structures emerge, with interesting features which depend on the interplay of separately controllable aspects of the externally imposed environmental changes.

Nonlocal interaction effects on pattern formation in population dynamics

We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is nonlocal, and show that spatial structures with interesting features emerge. These features depend on the nature of the competitive interaction as well as on its range, specifically on the presence or absence of tails in, and the central curvature of, the influence function of the interaction.

Applicability of the Fisher equation to bacterial population dynamics

The applicability of the Fisher equation, which combines diffusion with logistic nonlinearity, to population dynamics of bacterial colonies is studied with the help of explicit analytic solutions for the spatial distribution of a stationary bacterial population under a static mask. The mask protects bacteria from ultraviolet light. The solution, which is in terms of Jacobian elliptic functions, is used to provide a practical prescription to extract Fisher equation parameters from observations and to decide on the validity of the Fisher equation.

Dynamical effects induced by long range activation in a nonequilibrium reaction-diffusion system

We show both experimentally and numerically that the time scales separation introduced by long range activation can induce oscillations and excitability in nonequilibrium reaction-diffusion systems that would otherwise only exhibit bistability. Namely, we show that in the chlorite-tetrathionate reaction, where the autocatalytic species H+ diffuses faster than the substrates, the spatial bistability domain in the nonequilibrium phase diagram is extended with oscillatory and excitability domains. A simple model and a more realistic model qualitatively account for the observed dynamical behavior. The latter model provides quantitative agreement with the experiments.

Spatial bistability and waves in a reaction with acid autocatalysis

The phenomenon of spatial bistability has recently been proposed for a comprehensive understanding of a number of chemical patterns observed in open spatial reactors consisting of thin films of gel diffusively fed from one side. We study experimentally and numerically this phenomenon in the tetrathionate-chlorite reaction characterized by an acid superautocatalysis. We focus on the similarities and differences with previous studies on the chlorine dioxide-iodide reaction. In addition, we show that this reaction, which is only bistable in a continuous stirred tank reactor, can exhibit oscillatory and traveling waves when diffusion comes into play. Our computations suggest that the nonstationary behaviour originates from differential diffusive transport.

Experimental evidence of stochastic resonance without tuning due to non-Gaussian noises

In order to test theoretical predictions, we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non-Gaussian noise. In agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response (robustness). This implies that even a single resonant unit can reach a marked reduction in the need for noise tuning.

An exact analytical solution of a three-component model for competitive coexistence

A three-component competition system is modeled as a reaction-diffusion process. An exact analytical solution has been found that indicates that in certain situations the classical results on extinction and coexistence of Lotka-Volterra-type equations are no longer valid. Cases with one or both predators diffuse are analyzed, and the stability question is discussed.