Prey Model Research Articles

Enchanting dynamics: Juvenile and adult predators with prey model in an intuitionistic fuzzy environment

This study represents an interaction model including juvenile and adult predators along with prey, involving key characteristics like the inability of juvenile predators to reproduce, the impact of adult predators on juvenile growth rates and the transformation of some juveniles to adulthood. Furthermore, it is supposed that adult predators intake prey for sustenance, and the logistic growth of prey is assumed in the non-appearance of adult predators. Intra-species competition among adult predators, together with predation of juveniles and chasing, is conveyed. To tackle the imprecise biological parameters, most parametric values are considered as triangular intuitionistic fuzzy numbers. The model is further processed into an intuitionistic fuzzy model using the Hukuhara derivative and Yager’s ranking method is implemented to make the model crispified. Non-negativity and boundedness of the model are explored, after that, an investigation of possible equilibrium points is discussed. Local and global stability analyses close to these points are supervised. The study accentuates the significant influence of uncertain model parameters on the solution. Especially, uncertain estimates of intra-species competition among adult predators remarkably regulate the model’s stability. Extended uncertainty in intra-species competition for prey, although, is discovered to stabilize the system. In addition, increased consumption of juvenile predators by adult predators is observed to provide the system’s instability.

Dynamical Behavior of a Juvenile Predator, Adult Predator and Prey Model Through Uncertain and Parametric Technique

In this study, an interaction model involving a juvenile predator, an adult predator, and the prey has been developed. It is considered that juvenile predators are unable to reproduce. The adult predator is considered to have an impact on the growth rate of the juvenile predators. It is also assumed that a portion of juvenile predators may become adults. Also, it is considered that adult predators consume prey for food. The logistic growth of prey has been taken into consideration in the absence of an adult predator. The intra-species competition among adult predators is discussed here. It is also assumed that adult predators could chase and eat juvenile predators. Then most of the parametric values are considered interval-valued uncertain numbers. Since it is very hard for us to solve the model when the parametric values are interval-valued. Thus, all of the interval-valued parameters have been simplified into linear parametric form. After that, the nonnegativity and boundedness of the model were discussed. Various possible equilibrium points in the model are analyzed. The model’s local stability and global stability are investigated near these points. It has been noted that the proposed model’s solution is significantly impacted by the uncertain values of the model parameters. Uncertain estimates of intra-species competition among adult predators have been found to have a considerable impact on the stability of the model. It is observed that the increased uncertainty of intra-species competition for prey may stabilize the system. It is reported that the increasing rate of conversion of prey into adult predators can destabilize the ecosystem. It is found that the increasing rate of predation on juvenile predators by adults reduces the number of juveniles that can mature into adults which may create instability in the system.

Two predators, one prey model that integrates the effect of supplementary food resources due to one predator's kleptoparasitism under the possibility of retribution by the other predator

In ecology, foraging requires animals to expend energy in order to obtain resources. The cost of foraging can be reduced through kleptoparasitism, the theft of a resource that another individual has expended effort to acquire. Thus, kleptoparasitism is one of the most significant feeding techniques in ecology. The phenomenon of kleptoparasitism has garnered significant attention from scholars due to its substantial impact on the food chain. However, the proportionate amount of mathematical modelling to facilitate the analysis has made limited progress in the literature. This circumstance motivated us to develop mathematical models that could explain the population dynamics of the prey-predator food chain. This study explores a scenario with two predators and one prey, where one predator is a kleptoparasite and the other is a host. The energy depletion caused by the predator's counterattack subsequent to kleptoparasitism, notwithstanding the nonlethal nature of this antagonism, is an additional component incorporated into this model. It has been suggested that biologically viable equilibria must meet certain parametric conditions in order to exist and to be stable both locally and globally. This article delves deeply into the occurrences of various one-parametric bifurcations, such as saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation, as well as two-parametric bifurcations, such as Bautin bifurcation. A subcritical Hopf bifurcation happens when the growth rate of the first predator is relatively low, while a supercritical Hopf bifurcation occurs when the growth rate of the first predator is quite large, allowing for the coexistence of all three species. Numerical simulations have been conducted to validate our theoretical findings.

Allee Rate Effect in a Prey Model with a Holling Type II Functional Response

In this work, we have built a detailed model of a prey-predator system with mechanical Allee rate and Hollings type II functional response. The model's positive accumulation points' existence, uniqueness, boundaries, and stability analysis are taken into consideration. Numerical simulations are used to discuss Allee's impact on system dynamics.

System of Caputo Fractional Differential Equations with Applications to Predator and Prey Model

In this research article, we provide a methodology to solve the three systems of qth order linear Caputo fractional differential equations, where 0 < q < 1. Since the Caputo derivative is in the convolution form, we can apply the Laplace transform technique. The solution of the two linear system can be used as a tool to study the stability of the equilibrium solution of the Lotka-Volterra predator-prey model. We have referenced three system SIR model in this work. Due to the global nature of the Caputo derivative, the solution obtained is closer to the real data than the integer derivative.

Flowering Coriander (Coriandrum sativum) Strips Do Not Enhance Ecosystem Services in Azorean Orchards.

The effect of flower strips on ecosystem services (ESs) and disservices (EDs) is routinely assessed following changes in service provider densities without measuring the associated levels of ES/EDs. By using the sentinel approach (i.e., exposing a plant, seeds, and prey models in a standardized way), we tested how coriander (Coriandrum sativum) strips planted in mixed orchards on Terceira Island (Azores, Portugal) affected herbivory on lettuce plants, seed predation on wheat and weed seeds, and predation on artificial caterpillars. Vertebrates had more influence than invertebrates on ESs/EDs. Herbivory (ED) after 2 weeks was similar in the coriander and the control plots (mean ± SD; 2.3% ± 3.3% vs. 2.2% ± 2.9%, n = 32 for both). Seed predation was higher in the control than in the coriander plots for both grain (ED; 30.8% ± 38.9% vs. 15.3% ± 10.8%, n = 18 for both) and weed seeds (ES; 2.5% ± 4.1% vs. 0.4% ± 0.5%, n = 18 for both). Vertebrate predation (ES) rates after 48 h were significantly higher in the control (estimate 9%, 95% CI: 4-20%) than in the coriander plots (3%, 1-8%), while no difference was observed for invertebrate predation. Coriander strips did not support increased ES/reduced ED levels in this setting. The tools used can be effective to quantitatively compare multiple ESs/EDs under different farming management strategies.

Stage-Dependent Predation on Prey Species Who Possess Different Life Histories

Two stage-structuredone-population (prey) models together with four prey-predator models are analyzed. Regarding the prey models, where one of them has fecundity elements which depend on the total population while the fecundities of the other depend on the mature part of the population only, we prove that both of them are permanent and moreover that their fixed points undergo supercritical bifurcations, flip, and Neimark-Sacker, respectively, at the various instability thresholds. By use of the models, we also provide a discussion of stability and dynamical properties of species who possess different life histories and extent results obtained elsewhere. Turning to predation, in contrast to what one finds in most papers, we scrutinize cases where both the immature subpopulation of the prey and the mature part are targets for the predator. Among our findings, here is that increased predation may act in both a stabilizing and destabilizing fashion depending on the size of fecundity of prey. Moreover, we present new results about the transition from stability to instability, and we show that whenever predation acts destabilizing, the effect is most profound in cases where the prey possesses a precocious semelparous life history. We also provide several examples where increased predation may turn a stable system chaotic.

Penerapan Model Predator-Prey pada Proses Perkecambahan Biji Kacang Hijau

Mungbean (Vigna radiata L.) is a type of legume plant with high protein and a short life of approximately 2 months. This plant is found in all regions of Indonesia. The morphology of the mungbean plant consists of roots, stems, leaves, flowers, fruits, and seeds. Mungbean seeds have nutritional content but are in an inactive (dormant) form, after being germinated, the nutrient content is activated, thereby increasing digestibility for humans. A germination is a biological event that occurs from a seed in a dormant state until it becomes a growing seed. Sprouts derived from green bean seeds are called bean sprouts. The germination process can increase the nutritional value of mungbeans, thus, in this journal, a study was conducted to determine the growth model of mungbean sprouts in order to determine the best time to consume bean sprouts. In modeling the growth of green bean sprouts, a predator and prey model is used, which is resolved numerically using the fourth order Runge-Kutta method. From the research conducted, it can be concluded that the maximum nutrition of bean sprouts is on the third day since germination begins.

Qualitative analysis and phase of chaos control of the predator-prey model with Holling type-III

In this study, we investigate the dynamics of a discrete-time with predator-prey system with a Holling-III type functional response model. The center manifold theorem and bifurcation theory are used to create existence conditions for flip bifurcations and Neimark-Sacker bifurcations. Bifurcation diagrams, maximum Lyapunov exponents, and phase portraits are examples of numerical simulations that not only show the soundness of theoretical analysis but also show complicated dynamical behaviors and biological processes. From the point of view of biology, this implies that the tiny integral step size can steady the system into locally stable coexistence. Yet, the large integral step size may lead to instability in the system, producing more intricate and richer dynamics. This also means that when the intrinsic death rate of the predator is high, this leads to a chaotic growth rate of the prey. The model has bifurcation features that are similar to those seen in logistic models. In addition, there is a bidirectional Neimark-Sacker bifurcation for both prey and predator, and therefore we obtain a direct correlation in symbiosis. This means that the higher the growth rate of the prey, the greater the growth rate of the predator. Therefore, the operation of predation has increased. The opposite is also true. Finally, the OGY approach is used to control chaos in the predator and prey model. which led to a new concept which we call bifurcation phase of control chaos.

Role of Age-selective Harvesting in a Delayed Predator- prey Model together with Fear and Additional Food

In this paper, we have discussed the dynamical behaviour of a delayed induced harvested predator-prey model incorporating both effects of fear (felt by prey) and additional food (provided to the predator). Hence we have considered selective harvesting terms in both the species that provides some fixed elapsed time to prey and predator population before they are harvested. Ecologically, harvesting of population are restrained below certain age to protect juvenile population. Also the reproduction of prey population can be greatly hindered due to the influence of fear effect. However, to increase the growth rate of predator and to decrease the predatory attack rate on the prey population, it is necessary to incorporate additional food to the predator for maintaining ecological balance. Consideration of age-selective harvesting together with fear effect and additional food compel the proposed system to exhibit Hopf-bifurcation around the coexistence equilibrium point. For better ecological community management, our study reveals the fact that harvesting delay and harvesting intensities should be maintained. Numerical simulations have been performed to validate the analytical findings.

Risk-induced trait response in planktonic larvae is altered under an acidified scenario

Our changing climate is affecting predator-prey interactions in different ways. Increasing atmospheric CO2 is acidifying the ocean and disrupting the chemosensation of several species. Here, we evaluated a risk-induced trait response to a potential predator under an acidified scenario. Using planktonic crab larvae as a prey model, we first analysed their swimming avoidance response to different potential fish predators and conspecific odours. Prey intensified their avoidance response to conspecific and predator odours, but not to all predators, with no maternal effect. Then, larvae were exposed to a responsive predator odour under a predicted acidified scenario. A similar response was observed for both saltwater and predator odour under low pH conditions. Thus, acidification seems to affect the chemosensation of planktonic larvae, leading them to not distinguish between a non-harmful stimulus and a potential predator and potentially bringing a cascade of ecological impairments.

An Approximate Solution to Predator-prey Models Using The Differential Transform Method and Multi-step Differential Transform Method, in Comparison with Results of The Classical Runge-kutta Method

Predator-prey models are the building blocks of the ecosystems as biomasses are grown out of their resource masses. Different relationships exist between these models as different interacting species compete, metamorphosis occurs and migrate strategically aiming for resources to sustain their struggle to exist. To numerically investigate these assumptions, ordinary differential equations are formulated, and a variety of methods are used to obtain and compare approximate solutions against exact solutions, although most numerical methods often require heavy computations that are time-consuming. In this paper, the traditional differential transform (DTM) method is implemented to obtain a numerical approximate solution to prey-predator models. The solution obtained with DTM is convergent locally within a small domain. The multi-step differential transform method (MSDTM) is a technique that improves DTM in the sense that it increases its interval of convergence of the series expansion. One predator-one prey and two-predator-one prey models are considered with a quadratic term which signifies other food sources for its feeding. The result obtained numerically and graphically shows point DTM diverges. The advantage of the new algorithm is that the obtained series solution converges for wide time regions and the solutions obtained from DTM and MSDTM are compared with solutions obtained using the classical Runge-Kutta method of order four. The results demonstrated is that MSDTM computes fast, is reliable and gives good results compared to the solutions obtained using the classical Runge-Kutta method.

Dynamics and pattern formation of a diffusive predator - prey model in the subdiffusive regime in presence of toxicity

Motivated by the fact that the restrictive conditions for a Turing instability are relaxed in subdiffusive regime, we investigate the effects of subdiffusion in the predator - prey model with toxins under the homogeneous Neumann boundary condition. First, the stability analysis of the corresponding ordinary differential equation is carried out. From this analysis, it follows that stability is closely related to the coefficient of toxicity. In addition, the temporal fractional derivative does not systematically widen the range of parameters to maintain a point in the stability domain. Furthermore, we derive the condition which links the Turing instability to the coefficient of toxicity in the subdiffusive regime. System parameters are varied in order to test our mathematical predictions while comparing them to ecological literature. It turns out that the memory effects, linked to the transport process can, depending on the parameters, either stabilize an ecosystem or make a completely different configuration.

A diffusive two predators–one prey model on periodically evolving domains

The paper deals with a diffusive two predators–one prey model with Holling‐type II functional response. We assume that the density of prey and predators is spatially inhomogeneous on a periodically evolving domain and is subject to homogeneous Neumann boundary conditions. We focus on the case in which all populations have periodic logistic growth, if isolated, and no competition occurs between predators. Our main purpose is to study the asymptotic properties of the solutions of this reaction–diffusion model. More specifically, suitable conditions, depending on the domain evolution function and the space dimension, are introduced leading to the extinction of one predator and the stable coexistence of the surviving predator and its prey. Their density, as time tends to infinity, tends to the periodic solution of the corresponding kinetic predator–prey model. Finally, the autonomous model on a fixed domain is treated.

Quantifying shape similarity between prey and uninteresting models to study animal masquerade

Abstract Masquerade occurs when an organism resembles an inedible or uninteresting object (model), such as a leaf, stick, or stone. The shapes of many species are described as similar to those of models in their microhabitats, but these similarities have not been quantified effectively. To describe the shape similarity between an animal and a model, we applied a shape description method in a field study of the four-eyed turtle (Sacalia quadriocellata). Our results showed that shape similarity between turtles and stones in the Hezonggou River was significantly higher midstream than that upstream and downstream. In line with these findings, masquerade efficiency was highest for turtles in the midstream area, with both inexperienced and experienced human ‘predators’. Masquerade efficiency was positively correlated with shape similarity in all stream sections. Shape similarity ranged from 0 to 1, with <0.65 indicating low masquerade efficiency and >0.80 indicating high masquerade efficiency. Our quantitative method was able to provide data that could be used to form an ecologically plausible argument; thus, shape similarity can be used to assess animal’s masquerade efficiency. This method will be of considerable use in future animal masquerade research.

On fractional predator and prey models with mutualistic predation including non-local and nonsingular kernels

In a biological system, discovering the interactions between species is of high importance in the preservation and maintenance of these rare species. In this research work, we have utilized powerful mathematical tools to describe two Lotka–Volterra models with mutualistic predation. The kernel used in the derivative is a non-singular and non-local type that gives us many benefits in practice. Besides, this type of derivative is capable of storing critical system information, which is an essential feature of studying biological models. The equilibrium points of the two dynamical systems are determined. Moreover, the necessary criteria for establishing the stability of points are investigated in terms of the model parameters. These relationships provide significant and applicable results in the maintenance or extinction of systems that are highly valuable in biological and functional aspects. The necessary conditions for the existence and uniqueness of the solutions are provided. To verify the theoretical results, many practical simulations have been performed in various cases. The approximate technique employed is a very efficient and accurate method for solving such biological systems, which can be utilized to solve similar biological problems. Along with approximate numerical solutions, the ”memory effects” on these fractional models are also perused. The results confirm that the use of fractional derivatives is one of the crucial requirements in biological models.

Mechanistically derived Toxicant-mediated predator-prey model under Stoichiometric constraints.

Studies in ecological stoichiometry highlight that grazer dynamics are affected by insufficient food nutrient content (low phosphorus (P)/carbon (C) ratio) as well as excess food nutrient content (high P:C). Contaminant stressors affect all levels of the biological hierarchy, from cells to organs to organisms to populations to entire ecosystems. Eco-toxicological modeling under the framework of ecological stoichiometry predicts the risk of bio-accumulation of a toxicant under stoichiometric constraints. In this paper, we developed and analyzed a Lotka-Volterra type predator- prey model which explicitly tracks the environmental toxicant as well as the toxicant in the populations under stoichiometric constraints. Analytic, numerical, slow-fast steady state and bifurcation theory are employed to predict the risk of toxicant bio-accumulation under varying food conditions. In some cases, our model predicts different population dynamics, including wide amplitude limit cycles where producer densities exhibit very low values and may be in danger of stochastic extinction.

Spatio-temporal patterns in fin whale Balaenoptera physalus habitat use in the northern Gulf of St. Lawrence

Significant ecosystem changes in the Gulf of St. Lawrence (GSL), Canada, have had far-reaching effects at all trophic levels. The abundance of fin whales Balaenoptera physalus has declined significantly in the northern GSL over the past decade. This study aimed to test the hypothesis that the observed decline was correlated to changing environmental conditions. Cetacean sightings data from 292 surveys, resulting in 2986 fin whale encounters from 2007 to 2013, were used to fit 2 separate generalised additive models in terms of (1) bathymetric and oceanographic variables (the proxy model) and (2) modelled krill biomass (the prey model). The concept of ‘handling time’ was introduced to correct for time off search effort, applicable to other studies relying on opportunistically sampled data. While a positive correlation between krill biomass and fin whale numbers was found, the performance of the proxy model (24.2% deviance explained) was overall better than the prey model (11.8%). Annual predictive maps derived from the final proxy model highlighted 2 key areas with recurrently high relative fin whale abundance and a significant overlap with shipping lanes. While both models provided evidence for an annual decline in relative fin whale abundance, static bathymetric features were the most important predictors of habitat use, and no correlation between dynamic variables and the decline was found. High resolution prey data and a better understanding of the feeding ecology of fin whales are proposed to further investigate the predator-prey relationship and decline of fin whales in the GSL.

Dynamical complexities in a predator-prey system involving teams of two prey and one predator

Empirical studies have shown that animals often focus on short-term benefits under conditions of predation risk, which increases the likelihood that they will co-operate with others. With this motivation, we propose and analyze a predator and two prey model with the assumption that during predation the members of both prey make a team to reduce risk of predation. We incorporate Monod–Haldane and Holling type II functional response to model the interaction with predator. Firstly, we discuss conditions which ensure that model system has a unique positive solution. We investigate stability and Hopf bifurcation conditions to explore dynamics of system around positive equilibrium. We also derive Kolmogorov conditions for the parametric restriction of the system. Secondly, we present numerical solution which substantiate our analytical results. In numerical simulation, we observe period doubling and period halving cascade which explore the dynamical complexity of predator-prey system. Finally, we conclude that partial co-operation and low defense may lead to extinction of prey species.

Black swans and canards in two predator – one prey model

In this paper, we show how canards can be easily caught in a class of 3D systems with an exact black swan (a slow invariant manifold of variable stability). We demonstrate this approach to a canard chaseviathe two predator – one prey model. It is shown that the technique described allows us to get various 3D oscillations by changing the shape of the trajectories of two 2D-projections of the original 3D system.