A prey-predator fishery model with endogenous switching of harvesting strategy

We propose a dynamic model to describe a fishery where both preys and predators are harvested by a population of fishermen who are allowed to catch only one of the two species at a time. According to the strategy currently employed by each agent, i.e. the harvested variety, at each time period the population of fishermen is partitioned into two groups, and an evolutionary mechanism regulates how agents dynamically switch from one strategy to the other in order to improve their profits. Among the various dynamic models proposed, the most realistic is a hybrid system formed by two ordinary differential equations, describing the dynamics of the interacting species under fishing pressure, and an impulsive variable that evolves in a discrete time scale, in order to describe the changes of the fraction of fishermen that harvest a given stock. The aim of the paper is to analyze the economic consequences of this kind of self-regulating fishery, as well as its biological sustainability, in comparison with other regulatory policies. Our analytic and numerical results give evidence that in some cases this kind of myopic, evolutionary self-regulation might ensure a satisfactory trade-off between profit maximization and resource conservation

Awakened oscillations in coupled consumer-resource pairs

The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables respectively and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted). When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses.Comment: 31 pages, 8 figures 2 tables, 48 reference

Ethics, politics, and Nonsatiation in Consumption: A Synthesis

In contrast with the production of goods and services by firms, where the production costs are minimized under appropriate behavioral assumptions, consumer-producers in neoclassical theory maximize consumption expenditure, i.e., production costs of their outputs. According to Kenneth Boulding, were the impact upon the limited resources available on planet Earth taken into account, consumption expenditure should be minimized. We propose that we keep consumer theory as a reasonable description of reality.However,we should evaluate the long run consequences of such postulated behavior in a larger context,which, as a consequence of larger population with increasing per capita consumption, comprises the overburdening of natural resources. By decomposing the time horizon of cultural evolution into shorter periods of adjustment, we may then distinguish several types of institutional determination of how societies take decisions, as a group and individually. The consumer theory simply reflects the predominant ethical values, of which ideologies, political platforms, and demand patterns are shorter run adjustments.Consumption, Natural Resources, Political Process, Ethics

Pareto-efficient biological pest control enable high efficacy at small costs

Biological pest control is increasingly used in agriculture as a an alternative to traditional chemical pest control. In many cases, this involves a one-off or periodic release of entomopathogens. As the interaction between the entomopathogen and the pest is complex and the production of entomopathogens potentially expensive, it is not surprising that both the efficacy and economic viability of biological pest control are debated. Here, we investigate the performance of very simple control strategies. In particular, we show how Pareto-efficient one-off or periodic release strategies, which optimally trade off between efficacy and economic viability, can be devised and used to enable high efficacy for small economic costs. We demonstrate our method on a pest-pathogen-crop model with a tunable immigration rate of pests. By analyzing this model, we demonstrate that simple Pareto-efficient one-off release strategies are typically efficacious and simultaneously have average profits that are close to the theoretical maximum obtained by less efficacious and complicated profit-optimizing strategies. The only exception occurs for high pest-immigration rates, in which case periodic release is preferable. The methods presented here can be extended to more complex scenarios and thus be used to identify promising biological pest control strategies in many circumstances

Analysis of stability and Hopf bifurcation for an eco-epidemiological model with distributed delay

In this paper, the dynamical behavior of an eco-epidemiological model with distributed delay is studied. Sufficient conditions for the asymptotical stability of all the equilibria are obtained. We prove that there exists a threshold value of the infection rate $b$ beyond which the positive equilibrium bifurcates towards a periodic solution. We further analyze the orbital stability of the periodic orbits arising from bifurcation by applying Poore's condition. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings

Chaos to Permanence-Through Control Theory

Work by Cushing et al. \cite{Cushing} and Kot et al. \cite{Kot} demonstrate that chaotic behavior does occur in biological systems. We demonstrate that chaotic behavior can enable the survival/thriving of the species involved in a system. We adopt the concepts of persistence/permanence as measures of survival/thriving of the species \cite{EVG}. We utilize present chaotic behavior and a control algorithm based on \cite{Vincent97,Vincent2001} to push a non-permanent system into permanence. The algorithm uses the chaotic orbits present in the system to obtain the desired state. We apply the algorithm to a Lotka-Volterra type two-prey, one-predator model from \cite{Harvesting}, a ratio-dependent one-prey, two-predator model from \cite{EVG} and a simple prey-specialist predator-generalist predator (for ex: plant-insect pest-spider) interaction model \cite{Upad} and demonstrate its effectiveness in taking advantage of chaotic behavior to achieve a desirable state for all species involved

Chaos to Permanence - Through Control Theory

Work by Cushing et al. [18] and Kot et al. [60] demonstrate that chaotic behavior does occur in biological systems. We demonstrate that chaotic behavior can enable the survival/thriving of the species involved in a system. We adopt the concepts of persistence/permanence as measures of survival/thriving of the species [35]. We utilize present chaotic behavior and a control algorithm based on [66, 72] to push a non-permanent system into permanence. The algorithm uses the chaotic orbits present in the system to obtain the desired state. We apply the algorithm to a Lotka-Volterra type two-prey, one-predator model from [30], a ratio-dependent one-prey, two-predator model from [35] and a simple prey-specialist predator-generalist predator (for ex: plant-insect pest-spider) interaction model [67] and demonstrate its effectiveness in taking advantage of chaotic behavior to achieve a desirable state for all species involved