Harvesting Effort Research Articles

Theoretical and numerical bifurcation analysis in a prey–predator model with prey harvesting effort

This paper explores the influence of harvest efforts on a discrete-time prey–predator model. We established the stability criteria for fixed points in the proposed model. We investigate codim-1 and codim-2 bifurcations, exploring a range of multiple and generic bifurcations within the discrete model. The model demonstrates fold, flip, and Neimark–Sacker bifurcations, as well as resonances such as 1:2, 1:3, and 1:4 at distinct fixed points. Through the application of the critical normal form theorem and bifurcation theory, we calculate normal form coefficients for each bifurcation. Our results show that an excessive prey harvest rate can actually destabilize the model dynamics. Numerical simulations validate our findings, shedding light on the intricate dynamics of the system.

Spatiotemporal analysis of a modified Leslie–Gower model with cross-diffusion and harvesting

This paper considers a modified Leslie–Gower prey-predator reaction–diffusion model introducing harvesting of both species. Both the temporal and spatiotemporal dynamics of the model have been examined. We have found the stability regions and drawn bifurcation diagrams to determine the harvesting effect on the model, revealing that the harvesting has a stabilizing effect. Local bifurcations, such as transcritical and Hopf bifurcations, appear in the temporal system. For the spatiotemporal model, Turing instability conditions have been determined. The amplitude equation for the critical modes has been derived using multiple time scale analyses by taking the harvesting effort as the bifurcating parameter. Also, we have verified the theoretical results by plotting several kinds of stationary patterns, including stripes, spots, and a mix of stripes and spots. This study’s critical observation is that as harvesting effort rises, the patterns steadily turn into spots, i.e., harvesting influences pattern creation strongly. This fosters a dynamic equilibrium, allowing competitors to maintain distance, optimize resource use and survive.

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. We delve into normal forms associated with different bifurcation types, accompanied by numerical examples, observing multistabilities with intricate basin structures. Bistable, tristable, and quadruple attractors characterize the model’s multistable states. Additionally, we find that enriching prey species negatively affects predator abundance, and increasing carrying capacity can lead to a sudden jump in predator population to the brink of extinction. Examining the two-parameter space of predator and prey harvesting efforts, we identify organized periodic structures: Arnold tongues and shrimp-like structures within quasiperiodic and chaotic regions. Arnold tongues exhibit a sequence of periodic adding. The shrimp structures indicate the existence of period-doubling and period-bubbling phenomena. Discussions on ecological interpretations of predator harvesting, including the paradoxical hydra effect, are provided.

Dynamics of a discrete Rosenzweig–MacArthur predator–prey model with piecewise-constant arguments

This paper investigates the dynamics of a new discrete form of the classical continuous Rosenzweig–MacArthur predator–prey model and the biological implications of the dynamics. The discretization method used here is to modify the continuous model to another with piecewise-constant arguments and then to integrate the modified model, which is quite different from the traditional Euler discretization method. First, the existence and local stability of fixed points have been thoroughly discussed. Then, all codimension-1 bifurcations have been studied, including the transcritical bifurcations at the trivial fixed point and the boundary fixed point, and the Neimark–Sacker bifurcation at the unique positive fixed point. Furthermore, it is proved that there are no codimension-2 bifurcations. Finally, the control of the bifurcations is studied. Regarding the biological significance, we have considered the following four aspects: When no harvesting effort is applied to both predators and prey, it is observed that providing more resources to the prey species leads to predator extinction, causing the ecosystem to lose stability. This implies that the paradox of enrichment occurs. When predators are harvested, the system exhibits the hydra effect, i.e. increasing the harvesting effort on predators will lead to an increase in the mean population density of predators. When the prey is harvested, numerical examples indicate that increasing the harvesting effort initially reduces prey density. Upon reaching the bifurcation point, prey density stabilizes while the predator density continues to decline. When both prey and predators are harvested, the biological significance is similar to the previous case. The outcomes of this paper have significant theoretical meaning in the study of population ecology. By MATLAB, the bifurcation diagrams, maximal Lyapunov exponent diagrams, phase portraits and mean population density curves are plotted. Numerical simulations not only show the correctness of the theoretical findings but also reveal many new and interesting dynamics.

Dynamic Analysis and Optimal Control of a Fractional Order Fishery Model with Refuge and Protected Area

In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The paper aims to analyze predator-prey dynamics in a fishery model through the application of fractional derivatives. It is worth emphasizing that we explicitly examine how fractional derivatives affect the dynamics of the model. The existence of each equilibrium point and the stability of the system at the equilibrium point are proved. The theoretical results are proved by numerical simulation. Alternatively, allocate harvesting efforts within an improved model aimed at maximizing economic benefits and ecologically sustainable development. The ideal solution is obtained by applying Pontryagin’s optimal control principle. A large number of numerical simulations show that the optimal control scheme can realize the sustainable development of the ecosystem.

Dynamics of autonomous and nonautonomous Leslie–Gower model for the impacts of fear and its carry‐over effects including predator harvesting

Recently, certain biological field experiments and research findings have revealed that predators not only reduce prey populations through direct predation (lethal effect) but also indirectly affect the growth rate of prey by inducing fear; these nonlethal effects can be carried over seasons or generations. In this paper, we proposed an autonomous and a nonautonomous Leslie–Gower model incorporating some biological factors such as fear and its carry‐over effects, prey refuge, and nonlinear predator harvesting. In the autonomous model, first, we examined the well‐posedness, positivity solutions, and their boundedness. Also, it is shown that new equilibrium points emerge and disappear with the change in intrinsic growth rate of predator. Further, we compute and analyzed the local and global stability at the interior equilibrium points. Furthermore, Hopf bifurcation and direction and stability of limit cycle at interior equilibrium points are established. Moreover, the sensitivity analysis of the biological parameters is carried out numerically with two statistical methods via Latin hypercube sampling and partial rank correlation coefficients. It was found that at the small values of fear factor, carry‐over effect, and refuge behavior of prey parameters, the autonomous system exhibits oscillatory behavior, whereas for small values of prey birth rate and harvesting effort, the system remains stable. However, when intrinsic growth rate of predator increases from a low value to a higher value, the system shows transition from stability to instability and back to stability. We also explore the effects of seasonal variations in biological parameters in the nonautonomous model. Additionally, we investigate the theoretical existence of positive periodic solutions using the continuation theorem. The influences of seasonal variations in some parameters such as prey's birth rate, fear, and its carry‐over effects; refuge behavior of prey; intrinsic growth rate of predator; and harvesting effort are then numerically investigated. The results reveal the emergence of positive periodic solutions and bursting patterns in the seasonally forced model.

Spatiotemporal flow-induced instability of predator-prey model with Crowley-Martin functional response and prey harvesting.

Ecological systems can generate striking large-scale spatial patterns through local interactions and migration. In the presence of diffusion and advection, this work examines the formation of flow-induced patterns in a predator-prey system with a Crowley-Martin functional response and prey harvesting, where the advection reflects the unidirectional flow of each species migration (or flow). Primarily, the impact of diffusion and advection rates on the stability and the associated Turing and flow-induced patterns are investigated. The theoretical implication of flow-induced instability caused by population migration, mainly the relative migrations between prey and predator, is examined, and it also shows that Turing instability is the particular condition of flow-induced instability. The influence of the relative flow of both species and prey-harvesting effort on the emerging pattern is reported. Advection impacts a wide range of spatiotemporal patterns, including bands, spots, and a mixture of bands and spots in both harvested and unharvested dynamics. We also observe the diagonally bend-type banded patterns and straight-type banded patterns due to positive and negative relative flows, respectively. Here, the increasing relative flow increases the band length. The growing harvesting effort also decreases the band length, producing a thin band and a mixture of spots and bands due to the negative and positive relative flows, respectively. One exciting result observed here is that harvesting effort drives the flow-Turing and flow-Turing-Hopf instability into pure-flow instability.

Direct assessment of tropical tuna abundance from their associative behaviour around floating objects.

Managing populations of wild harvested species requires the ability to regularly provide accurate abundance assessments. For most marine species, changes in abundance can only be monitored indirectly, using methods reliant on harvest-based indices, with significant inherent limitations surrounding the estimation and standardization of harvest effort. Tropical tunas are some of the most exploited marine species in the world and are among several species in critical need of alternative methods for estimating abundance. Addressing this concern, we developed the Associative Behaviour-Based abundance Index (ABBI), designed to provide direct abundance estimates for animals, which exhibit an associative behaviour with aggregation sites. Its implementation in the western Indian Ocean on skipjack tuna (Katsuwonus pelamis), yellowfin tuna (Thunnus albacares) and bigeye tuna (Thunnus obesus), revealed similar trajectories in their relative abundance. The ABBI stands as a potentially promising alternative to enhance traditional tropical tuna stock assessments methods, as well as a new opportunity to assess the abundance of other wild species that display an associative behaviour with physical structures found in their natural environment.

Dynamic Complexity of a Nicholson–Bailey Bioeconomic Model with Holling Type-II Functional Response

In this paper, we propose a host–parasitoid model with a Holling type-II functional response and incorporate harvest effort. The Holling type-II response leads to saturation in parasitized hosts, creating a potential economic harvesting opportunity. To address overexploitation risks, we integrate a harvest effort function, determining an optimal threshold to prevent depletion. We explore model dynamics and bifurcations, including co-dimension one behaviors such as flip and Neimark–Sacker bifurcations, we provide numerical examples for validation. Our suggested difference-algebraic model, compared to continuous-time models, exhibits rich dynamics within the Nicholson–Bailey host–parasitoid framework.

Evolution of dispersal and the analysis of a resource flourished population model with harvesting

This study explores a spatially distributed harvesting model that signifies the outcome of the competition of two species in a heterogeneous environment. The model is controlled by reaction-diffusion equations with resource-based diffusion strategies. Two different situations are maintained by the harvesting effects: when the harvesting rates are independent in space and do not exceed the intrinsic growth rate; and when they are proportional to the time-independent intrinsic growth rate. In particular, the competition between both species differs only by their corresponding migration strategy and harvesting intensity. We have computed the main results for the global existence of solutions that represent either coexistence or competitive exclusion of two competing species depending on the harvesting levels and different imposed diffusion strategies. We also established some estimates on harvesting efforts for which coexistence is apparent. Also, some numerical results are exhibited in one and two spatial dimensions, which shed some light on the ecological implementation of the model.

A novel Adaptive Zone-fusion network for precise waxberry semantic segmentation to improve automated-harvesting in a complex orchard environment

In China, waxberries are a specialty fruit that require large harvesting efforts each season. To ameliorate these issues, automated fruit-picking equipment has been widely developed within the last decade. However, most image analysis research used for waxberry segmentation contains issues such as incomplete datasets, insufficient segmentation accuracy, and susceptibility to interference. Here, we developed the Adaptive Zone-fusion Network (AZNet) that enables automated fruit harvesting and is designed to precisely segmentate waxberries in an orchard environment. Initially, we collected a diverse range of images to train and evaluate a better model, and found that AZNet demonstrated exceptional performance and achieved a mean Accuracy (mAcc) of 99.83%, mean Intersection over Union (mIoU) of 96.57%, and mean Dice coefficient (mDice) of 98.20%. To further validate AZNet’s effectiveness, we compared several state-of-the-art (SOTA) models, including DeepLab V3, SegNet, PSPNet, U-Net, RefineNet, FCN, DANet, and FastSCNN. Along with these comparisons, we also performed an ablation study to substantiate the individual impact of each module within AZNet. Through these experiments, we found that AZNet exhibits the capability to achieve accurate semantic segmentation of waxberries in complex orchard environments, and is suitable for automated fruit harvesting devices. Ultimately, AZNet improves upon previous models by constructing information fusion modules through spatial attention, channel attention, Atrous Spatial Pyramid Pooling (ASPP), and graph convolutional methods, which can be utilized in the future to enhance other fruit-picking software to reduce fruit loss and the investment of human resources.

Tumor growth and population modeling in a toxicant-stressed random environment.

When examining some factors that contribute to the growth or decline of a population or tumor, it is essential to consider a random hypothesis. By analyzing the effects of stress on a population (or volume of tumor growth) in a random environment, we develop stochastic models describing the dynamics of the population (or tumor growth) based on random adjustments to the population's intrinsic growth rate, carrying capacity, and harvesting efforts (or tumor treatments). Apart from the models' ability to capture fluctuations, the availability of a shape parameter in the models gives it the flexibility to describe a variety of population/tumor data with different shapes. The distribution of the stressed population size with or without harvesting (or treatments) is derived and used to calculate the maximum expected amount of harvests that can be taken from the population without depleting resources in the long run (or the minimum amount of chemotherapy needed to cause shrinkage or eradication of a tumor). The work done is applied to analyze tumor growth using published data comprising of the volume of breast tumor obtained by orthotopically implanting LM2-[Formula: see text] cells into the right inguinal mammary fat pads of 6- to 8-week-old female Severe Combined Immuno-Deficient mice.

FILIPPOV TYPE PREY–PREDATOR SYSTEM FOR SELECTIVE HARVESTING OF PREY

In this paper, the dynamics of a Filippov system with logistically growing prey and Holling Type II predation is explored. The selective nonlinear harvesting of prey is carried out when the ratio of prey to predator is above a specified threshold value. In order to prevent the extinction of both the species and sustainable economic gains, no harvesting is allowed when the ratio is below a threshold value. The equilibrium states and their stability for the individual smooth are analyzed. Filippov convex method is applied to determine the dynamics on the boundary. The sliding mode dynamics is scrutinized, and it is observed that there is no escaping region. The existence of boundary points, tangent points and pseudo-equilibrium points are established. The conditions are obtained for the visibility of the tangent points. The complex behavior within the sliding region is studied by experimenting with different initial conditions. The increase in harvesting effort may lead to extinction of both the species through the sliding region of the boundary. The change in the stability behavior of both the interior equilibrium states is investigated with respect to model parameters. Border cross bifurcates with threshold value as the bifurcation parameter is shown for both the interior equilibrium states.

Dynamics analysis of a predator-prey model with Allee effect and harvesting effort

<p>In the paper, a predator-prey model with the Allee effect and harvesting effort was proposed to explore the interaction mechanism between prey and predator. Under the framework of mathematical theory deduction, some conditions for the occurrence of transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations were derived with harvesting effort and the Allee effect as key parameters. Under the framework of bifurcation dynamics numerical simulation, the evolution process of specific bifurcation dynamics behavior was gradually visualized to reveal the influence mechanism of the Allee effect and harvesting effort. The research results indicated that the Allee effect and harvesting effort not only seriously affected the bifurcation dynamics essential characteristics of the model (1.3), but also could promote the formation of constant steady state and periodic oscillation persistent survival mode of prey and predator. Furthermore, it is worth noting that appropriate harvesting effort was beneficial for the formation of a sustainable survival cycle between prey and predator. In summary, we hoped that the research findings could contribute to the comprehensive promotion of bifurcation dynamics studies in the predator-prey model.</p>

Bifurcation and optimal harvesting analysis of a discrete-time predator–prey model with fear and prey refuge effects

<p>In this contribution, the complicated dynamical behaviors and optimal harvesting policy of a discrete-time predator–prey model with fear and refuge effects are formulated. Both the fear and prey refuge effects refer to an interaction between predator and prey. In the first place, the existence and local stability of three fixed points of proposed model are investigated by virtue of our methodology, that is, the eigenvalues of the Jacobian matrix. One step further, it is worth mentioning that the model undergoes flip bifurcation (i.e., period–doubling bifurcation) and Neimark–Sacker bifurcation at the interior fixed point by the utilization of bifurcation theory and center manifold theory. Also, optimal harvesting strategy is investigated, and the expressions of optimal harvesting efforts are determined. Two examples, in the end, are put forward to prove that they are consistent with the previous theoretical results.</p>

Harvesting a population model with Allee effect in a periodically varying environment

<abstract><p>A nonautonomous logistic population model with a feature of an Allee threshold has been investigated in a periodically fluctuating environment. A slow periodicity of the harvesting effort was considered and may arise in response to relatively slow fluctuations of the environment. This assumption permits obtaining the analytical approximate solutions of such model using the perturbation approach based on the slow variation. Thus, the analytical expressions of the population evolution in the situation of subcritical and the supercritical harvesting were obtained and discussed in the framework of the Allee effect. Since the exact solution was not available due to the nonlinearity of the system, the numerical computation was considered to validate our analytical approximation. The comparison between the two methods showed a remarkable agreement as the time progressed, while such agreement fell off when the time was close to the initial density. Moreover, in the absence of the periodicity of the harvesting term, the expressions of the population evolution reduced to the exact solutions but in implicit forms. The finding results were appropriate for a wide range of parameter values, which lead to avoiding extensive recalculations while displaying the population behavior.</p></abstract>

The study on the complex nature of a predator-prey model with fractional-order derivatives incorporating refuge and nonlinear prey harvesting

<abstract> <p>The main objective of our research was to explore and develop a fractional-order derivative within the predator-prey framework. The framework includes prey refuge and selective nonlinear harvesting, where the harvesting progressively approaches a threshold value as the density of the harvested population advances. For memory effect, a non-integer order derivative is better than an integer-order derivative. The solutions to the fractional framework were shown to be existence, uniqueness, non-negativity, and boundedness. Matignon's condition was used for analysing local stability, and a suitable Lyapunov function provided global stability. While discussing the Hopf bifurcation's existence condition, we explored derivative order and refuge as bifurcation parameters. We aimed at redefining the predator-prey framework to incorporate fractional order, refuge, and harvesting. This kind of nonlinear harvesting is more realistic and reasonable than the model with constant yield harvesting and constant effort harvesting. The Adams-Bashforth-Moulton PECE algorithm in MATLAB software was used to simulate the proposed outcomes, investigate the impact on various factors, and analyse harvesting's effect on non-integer order predator-prey interactions.</p> </abstract>

Turing-Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator-Prey Model with Allee Effect and Predator Harvesting.

This paper investigates the complex dynamics of a ratio-dependent predator-prey model incorporating the Allee effect in prey and predator harvesting. To explore the joint effect of the harvesting effort and diffusion on the dynamics of the system, we perform the following analyses: (a) The stability of non-negative constant steady states; (b) The sufficient conditions for the occurrence of a Hopf bifurcation, Turing bifurcation, and Turing-Hopf bifurcation; (c) The derivation of the normal form near the Turing-Hopf singularity. Moreover, we provide numerical simulations to illustrate the theoretical results. The results demonstrate that the small change in harvesting effort and the ratio of the diffusion coefficients will destabilize the constant steady states and lead to the complex spatiotemporal behaviors, including homogeneous and inhomogeneous periodic solutions and nonconstant steady states. Moreover, the numerical simulations coincide with our theoretical results.

Bistability in modified Holling II response model with harvesting and Allee effect: Exploring transitions in a noisy environment

Here, we explore the complex dynamics of a predator–prey system with a modified Holling type II functional response and the Allee effect that accounts for a reduced hunting efficiency due to intra-predator interactions. Besides the growth due to focal prey, the predator population follows a Beverton–Holt-like reproduction due to the alternative food sources. The model also considers the impact of harvesting on the predator population, reflecting economic interests in biological resource exploitation. We systematically investigate key aspects, including solution’s positivity, system’s equilibria, stability analysis, and various type of bifurcation. The model is extended to its stochastic version; conditions for the extinction as well as persistence of species are derived. All the theoretical findings are validated with numerical examples. In the deterministic scenario, the Allee effect, harvesting intensity, and the growth in predators due to external food sources exhibit intricate dynamics, such as Hopf, saddle–node (LP) and transcritical bifurcations; we also observe bistable behavior of the system. Notably, less growth in predators due to the other food sources results in extinction, while low intensity of Allee effect leads to bistability, where initial population size matters. A higher Allee effect reduces the region of stability generated by the harvesting effort and the predators’ growth due to additional foods. The stochastic system uncovers diverse transitions in scenarios with high noise intensity, affecting bistability occurred for lower noise intensity. Overall, this study provides valuable insights into predator–prey dynamics, with practical implications for the ecological conservation and resource management.

Controlling chaotic dynamics of a delayed Hassell–Varley type predator–prey model with non-linear harvesting efforts in prey by using imprecise biological parameters

In this article, we have studied the dynamical behaviors of a delayed predator–prey model with non-linear harvesting effort using imprecise parameters. A method has been proposed for dealing with these imprecise parameters using the parametric form of the interval numbers. The proposed predator–prey model represents the Hassell–Varley predation and Michaelis–Menten prey harvest. We have studied the feasibility of various equilibrium points and their stability. The study reveals that the delay model exhibits stable limit cycle fluctuations due to variation in the delay parameter. Numerical simulations are performed to illustrate all analytical results.