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

Ecological thresholds and large carnivores conservation: Implications for the Amur tiger and leopard in China

The ecological threshold concept describes how changes in one or more factors at thresholds can result in a large shift in the state of an ecosystem. This concept focuses attention on limiting factors that affect the tolerance of systems or organisms and changes in them. Accumulating empirical evidence for the existence of ecological thresholds has created favorable conditions for practical application to wildlife conservation. Applying the concept has the potential to enhance conservation of two large carnivores, Amur tiger and leopard, and the knowledge gained could guide the construction of a proposed national park. In this review, ecological thresholds that result from considering a paradigm of bottom-up control were evaluated for their potential to contribute to the conservation of Amur tiger and leopard. Our review highlights that large carnivores, as top predators, are potentially affected by ecological thresholds arising from changes in climate (or weather), habitat, vegetation, prey, competitors, and anthropogenic disturbances. What's more, interactions between factors and context dependence need to be considered in threshold research and conservation practice, because they may amplify the response of ecosystems or organisms to changes in specific drivers. Application of the threshold concept leads to a more thorough evaluation of conservation needs, and could be used to guide future Amur tiger and leopard research and conservation in China. Such application may inform the conservation of other large carnivores worldwide

Spatiotemporal dynamics in a spatial plankton system

In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that, on increasing the value of the fish predation rates, the sequences spots $\rightarrow$ spot-stripe mixtures$\rightarrow$ stripes$\rightarrow$ hole-stripe mixtures holes$\rightarrow$ wave pattern is observed. Our study shows that the spatially extended model system has not only more complex dynamic patterns in the space, but also has spiral waves.Comment: Published Pape

Harvesting and Conversation in a Predator-Prey System

Optimal harvesting of prey in a predator-prey ecosystem is studiedunder the condition that the existence of the predator has value. Predators (birds) and humans (fishers) compete for prey (shellfish). The behavior of the system is studied and conditions for optimal control are deduced. Various optimal harvesting rates are identified for particular ecosystem characteristics, harvesting costs, the discount rate value, and value functions for birds. These optimal harvest rates are constant harvesting, at levels possibly leading to the extinction of birds, or oscillating harvesting, giving rise to oscillating stocks of birds and shellfish. The approach path towards an optimal regime is shown qualitatively and consists of alternating between harvesting maximally and not harvesting at all

Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations

In this paper, the static and dynamic behaviour of a fractional-order predator–prey model are studied, where the nonlinear interactions between the two species lead to multiple stable states. As has been found in many previous systems, the stability of such states can be dependent on the fractional order of the time derivative, which is included as a phenomenological model of memory-effects in the predator and prey species. However, what is less well understood is the transient behaviour and dependence of the observed domains of attraction for each stable state on the order of the fractional time derivative. These dependencies are investigated using analytical (for the stability of equilibria) and numerical (for the observed domains of attraction) techniques. Results reveal far richer dynamics compared to the integer-order model. We conclude that, as well as the species and controllable parameters, the memory effect of the species will play a role in the observed behaviour of the system

On a three-tier ecological food chain model with deterministic and random harvesting: A mathematical study

In the present study, we consider a nutrient-autotroph-herbivore ecosystem model where the herbivore species is assumed to have a commercial value. We use a Holling type-II harvest function to model density dependent herbivore harvesting. Stability criteria of the resulting model is investigated both from analytical and numerical viewpoints. The investigation revealed the existence of a number of threshold values of the harvest rate that have a remarkable influence on the system dynamics. Next we incorporate a noise term in the parameter representing harvest rate to model the phenomenon of poaching as random harvesting. The stochastic model is analyzed for exponential mean square stability and the resulting criteria in terms of harvest related parameters obtained. These parameter thresholds could be utilized to develop effective harvesting strategies and wildlife management policies which take into account the overall survival of the ecological populations

The Impacts of Harvesting Activities on Prey-Predator Fishery Model in the Presence of Toxin

The present paper discusses a prey-predator fishery model where both species are subjected to harvesting effort. Both species release some toxic substances to each other. The prey species obeys the law of logistic growth. The model is a modified version from the classic Lotka-Volterra predator-prey model. The equilibria of the model are obtained and the dynamical behaviors of the proposed system are examined. Simulations of the model are performed and bifurcation diagrams are studied. The effects of harvesting and toxin on the stability of steady states are examined. In the present research, we found that the impact of harvesting activities is more influential on the dynamical behaviors in the fishery model than that of the toxin