The Dynamics of Pasture-Herbivores-Carnivores with Sigmoidal Density Dependent Harvesting

We investigate biomass-herbivore-carnivore (top predator) interactions in terms of a tritrophic dynamical systems model. The harvesting rates of the herbivores and the top predators are described by means of a sigmoidal function of the herbivores density and the top predator density, respectively. The main focus in this study is on the dynamics as a function of the natural mortality and the maximal harvesting rate of the top predators. We identify parameter regimes for which we have non-existence of equilibrium points as well as necessary conditions for the existence of such states of the modelling framework. The system does not possess any finite equilibrium states in the regime of high herbivore mortality. In the regime of a high consumption rate of the herbivores and low mortality rates of the top predator, an asymptotically stable finite equilibrium state exists. For this positive equilibrium to exist the mortality of the top predator should not exceed a certain threshold level. We also detect regimes producing coexistence of equilibrium states and their respective stability properties. In the regime of negligible harvesting of the top predator level, we observe a finite window of the natural top predator mortality rates for which oscillations in the top predator-, the herbivore- and the biomass level take place. The lower and upper bound of this window correspond to two Hopf bifurcation points. We also identify a bifurcation diagram using the top predator harvesting rate as a control variable. Using this diagram we detect several saddle node- and Hopf bifurcation points as well as regimes for which we have coexistence of interior equilibrium states, bistability and relaxation type of oscillations.

An evaluation of the marine environmental resilience to the north of Qeshm Island

There is always an adamant need to comprehend and draw the complex challenges of sustainability in order to help organize studies, due to the increasing human-related pressures on coastal zones. Hence, by formulating such a comprehensive framework, it could be possible to anticipate changes and support managerial decisions, as well as the degree of resilience of the region's environment. One of the approaches utilized in littoral or coastal zones is the conceptual framework of drivers, pressure, status, impact, and responses (DPSIR)..Qeshm Island, the largest island in the Persian Gulf, is accounted for being the most vital and strategic areas of the mentioned region. In recent decades, Qeshm has become one of the major cultural, natural, geological, and tourism hubs of the country due to its unique regional characteristics, along with its biodiversity and environmental sensitivity. Thereby, in the present research, a combined approach shall be followed to explore the resilience of the marine environment on the northern coast of Qeshm Island by taking advantage of the socioeconomic criterion. In this respect, the conceptual framework of the DPSIR model is utilized in combination with the structural equation model (SEM-PLS) (or partial least squares), which is one of the nonexperimental techniques, to quantify the results in the best manner possible. On the basis of the fuzzy cognitive map (FCM), the regional economic index bearing the weights of 0.62, 0.62, and 0.5, along with an institutional-managerial and biological index, respectively, denotes a two-way positive correlation, whereas this factor has a two-way, but adverse correlation, relationship with a weight of 0.65 in terms of the sociocultural index. Similarly, there is also a one-way and negative relationship, as to the economic index, with a weight of 0.69 which is in relevance with the physio-chemical index.

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. Here, partially mixed spatial models are defined in which the dispersal of only one of the communities (prey or predator) is considered. In our study, the spatial heterogeneity is induced by dissimilar (unbalanced) dispersal rates between the patches. A large difference between the predator dispersal rates may stabilize the unstable positive equilibrium of the model. The existence of two ecological phenomena are found under independent harvesting strategy: stability switching and hydra effect. When prey or predator is harvested in a heterogenious environment, a positive stable steady state becomes unstable with increasing the harvesting effort, and a further increase in the effort leads to a stable equilibrium. Thus, a stability switching happens. Furthermore, the predator biomass (at stable state) in both the patches (and hence total predator stock) increases when the patch with a higher predator density is harvested; resulting a hydra effect. These two phenomena do not occur in the non-spatial RM model. Hence, spatial heterogeneity induces stability switching and hydra effect.

The interplay between fishery yield and top predator culling in a multispecies fishery context

In food webs, fishery can play the role of top predator, competing thus with other top predators for valuable food resources. In this view, it has been claimed in fisheries management that culling of top predators can be a means to improve fishery yield. To investigate this hypothesis, we use theoretical population models to assess in a multispecies context how fishery yield from target species harvest responds to top predator cull. Defying crisp summary, the four analysed food web models show that this response may be either positive or negative or both, indicating that in terms of multispecies fishery management the harvest yield may not accrue as a consequence of predator removal. In addition, this multitude of behaviours points also to the fact that the response of fishery yield to top predator cull may be difficult to assess.

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. Thus we may suggest that fishing down the food chain, as suggested by Pauly et al. (1998) is not bound to happen. Our analysis also shows that balancing the harvest between prey, intermediate predator and top predator could give more yield and stabilizing the ecosystem, than the selective harvesting of any one species. This balanced harvesting may not be a win-win situation for yield and resilience, but it could be a most favourable strategy to balance them. This research would help to correlate resilience with yield and determines the desirable selection of two policies, resilience maximizing yield or maximum sustainable yield to safeguard ecological communities.

Meeting Yield and Conservation Objectives by Harvesting Both Juveniles and Adults

Sustainable yields that are at least 80% of the maximum sustainable yield are sometimes referred to as "pretty good yields" (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conservation as a second objective. We show that (1) PGY harvesting strategies can give large conservation benefits and (2) equal harvesting rates of juveniles and adults is often a good strategy. These conclusions are based on trade-off curves between yield and four measures of conservation that form in two established population models, one age-structured model and one stage-structured model, when considering different harvesting rates of juveniles and adults. These conclusions hold for a broad range of parameter settings, although our investigation of robustness also reveals that (3) predictions of the age-structured model are more sensitive to variations in parameter values than those of the stage-structured model. Finally, we find that (4) measures of stability that are often quite difficult to assess in the field (e.g., basic reproduction ratio and resilience) are systematically negatively correlated with impacts on biomass and size structure, so that these later quantities can provide integrative signals to detect possible collapses.

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. It is shown that searching for a general theory to unify the harvesting induced stability must take into account the number of trophic levels and the degree of species enrichment, the outcomes that cannot be obtained from the earlier reports on prey-predator models. We also identify the situation where harvesting induces instability switching: the non-equilibrium state enters into a stable steady-state and then, upon more intensive harvesting, the steady-state again loses its stability. One of the new and important results is also that the MSY may not exist for harvesting the top predator. In general, our results contribute to biological conservation theory, fishery and ecosystem biodiversity management.