Dispersal induced catastrophic bifurcations, Arnold tongues, shrimp structures, and stock patterns in an ecological system.

This paper presents a comprehensive analysis of a discrete-time predator-prey model within a homogeneous two-patch environment, incorporating both prey and predator dispersal. We consider a logistic growth for both prey and predator species, and the predation process is based on the Holling type-II functional response in the isolated patches. We explore the existence of multiple coexisting equilibria and establish their stability conditions.

Arnold tongues, shrimp structures, multistability, and ecological paradoxes in a discrete-time predator-prey system.

This paper explores a discrete-time system derived from the well-known continuous-time Rosenzweig-MacArthur model using the piecewise constant argument. Examining the impact of increasing carrying capacity and harvesting efforts, we uncover intricate phenomena, such as periodicity, quasiperiodicity, period-doubling, period-bubbling, and chaos. Our analysis reveals that increasing the carrying capacity of prey species can lead to both system stabilization and destabilization.

Bifurcations and hydra effects in Bazykin's predator-prey model.

We consider Bazykin's model to address harvesting induced stability exchanges through bifurcation analysis. We examine the existence of hydra effects and analyze the stock pattern under predator harvesting. Prey harvesting cannot produce hydra effects in our model, whereas predator harvesting may cause multiple hydra effects.

Stability switching and hydra effect in a predator-prey metapopulation model.

A metapopulation model is investigated to explore how the spatial heterogeneity affects predator-prey interactions. A Rosenzweig-MacArthur (RM) predator-prey model with dispersal of both the prey and predator is formulated. We propose such a system as a well mixed spatial model.

Balancing maximum sustainable yield and ecological resilience in an exploited two-predator one-prey system.

In this paper, we consider a two-predator one-prey system to determine the feedback of exploitation in individual as well as joint population levels. As balancing yield with resilience is highly essential for the conservation of species in the marine ecosystem, here we measure both the maximum sustainable yield (MSY) and resilience simultaneously. Then we investigate both the trade-offs and synergies among maximum yield, conservation, and resilience that emerge from different harvesting plans.

Hydra effects in stable food chain models.

In this paper, we explore the occurrence of the hydra effect in food chains, a popular research theme in the current decade. The hydra effect, one of the paradoxical results in theoretical and applied ecology refers to the fact where increasing mortality rate on a population enhances its own stock. The main focus is to propose a dynamical system model of food chain showing a stable steady state and estimate the variation of stock of targeted species with increasing mortality.

Managing yield and resilience in a harvested tri-trophic food chain model.

In this article, we compare the two ecological services known as yield and resilience, for a tri-trophic food chain model consisting of a prey, an intermediate predator and a top predator. For this comparison process, we use both analytical and numerical techniques. It is shown that a variety of patterns are possible based on the intensity of efforts distributed among different trophic levels.

Harvesting induced stability and instability in a tri-trophic food chain.

Non-equilibrium dynamics in the form of oscillations or chaos is often found to be a natural phenomenon in complex ecological systems. In this paper, we first analyze a tri-trophic food chain, which is an extension of the Rosenzweig-MacArthur di-trophic food chain. We then explore the impact of harvesting individual trophic levels to answer the following questions : a) when a non-equilibrium dynamics persists, b) whether it can locally be stabilized to a steady state, c) when the system switches from a stable steady state to a non-equilibrium dynamics and d) whether the Maximum Sustainable Yield (MSY) always exists when the top predator is harvested.

Biological conservation through marine protected areas in the presence of alternative stable states.

This article addresses how depleted stock can be restored by creation of marine reserve and species mobility when alternative stable states persist in a marine ecosystem. To understand the role of a marine protected area, we develop a two-patch version of an originally single-patch model. In the two-patch model, we prove that some of the locally stable equilibria are not stable equilibria from an ecological viewpoint.

Relationship between exploitation, oscillation, MSY and extinction.

We give answers to two important problems arising in current fisheries: (i) how maximum sustainable yield (MSY) policy is influenced by the initial population level, and (ii) how harvesting, oscillation and MSY are related to each other in prey-predator systems. To examine the impact of initial population on exploitation, we analyze a single species model with strong Allee effect. It is found that even when the MSY exists, the dynamic solution may not converge to the equilibrium stock if the initial population level is higher but near the critical threshold level.

Maximum sustainable yield and species extinction in a prey-predator system: some new results.

Though the maximum sustainable yield (MSY) approach has been legally adopted for the management of world fisheries, it does not provide any guarantee against from species extinction in multispecies communities. In the present article, we describe the appropriateness of the MSY policy in a Holling-Tanner prey-predator system with different types of functional responses. It is observed that for both type I and type II functional responses, harvesting of either prey or predator species at the MSY level is a sustainable fishing policy.

Possible ecosystem impacts of applying maximum sustainable yield policy in food chain models.

This paper describes the possible impacts of maximum sustainable yield (MSY) and maximum sustainable total yield (MSTY) policy in ecosystems. In general it is observed that exploitation at MSY (of single species) or MSTY (of multispecies) level may cause the extinction of several species. In particular, for traditional prey-predator system, fishing under combined harvesting effort at MSTY (if it exists) level may be a sustainable policy, but if MSTY does not exist then it is due to the extinction of the predator species only.

Sustainability and economic consequences of creating marine protected areas in multispecies multiactivity context.

The present study deals with harvesting of prey species in the presence of predator in a multispecies marine fishery. The total habitat is divided into two patches: one is reserve area where fishing is completely banned and other zone is called fishing area where only prey is exploited. We assume that the prey fish possesses heterogeneous intrinsic growth rate with uniform carrying capacity where as predator has constant intrinsic growth rate with prey dependent carrying capacity.

Sustainability and optimal control of an exploited prey predator system through provision of alternative food to predator.

In the present paper, we develop a simple two species prey-predator model in which the predator is partially coupled with alternative prey. The aim is to study the consequences of providing additional food to the predator as well as the effects of harvesting efforts applied to both the species. It is observed that the provision of alternative food to predator is not always beneficial to the system.