Growth Rate Of Prey Research Articles

Complex dynamics in an eco-epidemiological model with the cost of anti-predator behaviors

In this paper, we investigate the complex dynamics of a predator–prey model with disease in the prey, which is characterized by the reduction of prey growth rate due to the anti-predator behavior. The value of this study lies in two aspects: Mathematically, it provides the existence and the stability of the equilibria and gives the existence of Hopf bifurcation. And epidemiologically, we find that the influence of the fear factor is complex: (i) The level of the population density decreases with the increasing of the fear factor; (ii) the cost of fear can destabilize the stability and benefit the emergency of the periodic behavior; and (iii) the high level of fear can induce the extinction of the predator. These results may enrich the dynamics of the eco-epidemiological systems.

Stability and Bifurcation Analysis of a Predator-Prey Model with Michaelis-Menten Type Prey Harvesting

In this paper, we investigated stability and bifurcation behaviors of a predator-prey model with Michaelis-Menten type prey harvesting. Sufficient conditions for local and global asymptotically stability of the interior equilibrium point were established. Some critical threshold conditions for transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation were explored analytically. Furthermore, It should be stressed that the fear factor could not only reduce the predator density, but also affect the prey growth rate. Finally, these theoretical results revealed that nonlinear Michaelis-Menten type prey harvesting has played an important role in the dynamic relationship, which also in turn proved the validity of theoretical derivation.

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.

A delay nonautonomous model for the impacts of fear and refuge in a three species food chain model with hunting cooperation

In this article, we study the dynamics of a three species food chain model for a predator–prey system with hunting cooperation in predators; due to fear of predation risk, prey population shows anti-predator behavior. Fear of middle-predator affects the growth rate of prey and the fear of top-predator reduces the predation of middle-predator on prey species. The prey and middle-predator are assumed to take refuge against predation. Numerical results confirm the stabilizing role of refuge whereas hunting cooperation destroys stability and induces limit cycle oscillations. We find that the fear of middle-predator on prey has tendency to stabilize the system while the fear of top-predator on middle-predator creates instability in the system. Further, time delays are considered in the processes of taking refuges and hunting cooperations. Delay in hunting cooperations creates multiple stability switches in the system. Furthermore, seasonal forcing of parameters related to refuges and hunting cooperations depicts a more realistic scenario. We investigate the behaviors of seasonally forced system in the absence as well as presence of time delays. The seasonally forced system exhibits different types of periodic solutions. Complex bursting patterns are observed due to periodicity in refuge of middle-predator (cooperation of top-predator).

Bifurcations and multistability in a food chain model with nanoparticles

In the present paper, we report the effect of nanoparticles in a three-species aquatic food chain model. It is assumed that due to the unavoidable interactions with nanoparticles, the growth rate of basal prey reduces. Fascinating dynamical scenarios in the model are explored in different bi-parametric spaces. We show that the model exhibits coexisting attractors of different kinds (periodic–periodic/periodic–chaotic) in some regions of the bi-parametric space. We also discover well-organized shrimp-shaped periodic structures in the chaotic regime, indicating the coexistence of order (regular pattern) and chaos. Further, a period-bubbling transition to chaos is found near the inner boundaries of the shrimp-shaped structure. It is also observed that managing the depletion rate of the nanoparticles can be used as a control strategy to prevent population extinction in an aquatic food chain system.

Complex Dynamics of an Eco-Epidemic System with Disease in Prey Species

The objective of this study is to investigate the complex dynamics of an eco-epidemic predator–prey system where disease is transmitted in prey species and predator population is being provided with alternative food. Holling type-II functional response is taken into consideration for interaction of predator and prey species. The half saturation constant for infected prey, the growth rate of susceptible prey and force of infection play a significant role to create complex dynamics in this predator–prey system where alternative food is present. It is seen that healthy disease-free system is possible here. The system shows some important dynamics viz. stable coexistence, Hopf bifurcation, period-doubling bifurcation and chaos. The analytical results obtained from the model are justified numerically.

A NONAUTONOMOUS MODEL FOR THE INTERACTIVE EFFECTS OF FEAR, REFUGE AND ADDITIONAL FOOD IN A PREY–PREDATOR SYSTEM

The importance of fear, refuge and additional food is being increasingly recognized in recent studies, but their combined effects need to be explored. In this paper, we investigate the joint effects of these three ecologically important factors in a prey–predator system with Crowly–Martin type functional response. We find that the fear of predator significantly affects the densities of prey and predator populations whereas the presence of prey refuge and additional food for predator are recognized to have potential impacts to sustain prey and predator in the habitat, respectively. The fear of predator induces limit cycle oscillations while an oscillatory system becomes stable on increasing the refuge. The system first undergoes a supercritical Hopf-bifurcation and then a subcritical Hopf-bifurcation on increasing either the growth rate of prey or growth rate of predator due to additional food. Increasing the quality/quantity of additional food after a certain value causes extinction of prey species and rapid incline in the predator population. An extension is made in the model by considering the seasonal variations in the cost of fear of predator, prey refuge and growth rate of predator due to additional food. The nonautonomous model is shown to exhibit globally attractive positive periodic solution. Moreover, complex dynamics such as higher periodic solutions and bursting patterns are observed due to seasonal variations in the rate parameters.

Influencia del efecto Allee fuerte en las presas y de la competición entre los depredadores en modelos de depredación del tipo Leslie-Gower

It is well known that predator-prey interactions are strongly dependent on the functional response as well as the population growth rates of prey and predators.In this work, the study will be based on a Leslie-Gower type predation model, described by a twodimensional system of ordinary differential equations (ODEs), assuming the prey population is affected by a strong Allee effect and that predators have an alternative food.The functional response will be assumed linear, which is prey-dependent and monotonously increasing. In turn, the equation of growth of predators will also be considered of the logistic type, where the environmental carrying capacity for predators is assumed proportional to the prey population size. Among the most important results obtained is that for a same set of parameters, there are different behaviors of the system solutions, since two attractor equilibrium points can exist. Then, populations can coexist around of fixed population sizes, or the prey population can become extinct. We estimate that the analytical results obtained have an adequate ecological interpretation, under the underlying assumptions in the modeling of the predation interaction with ODEs.

Impact of the Fear Effect on the Stability and Bifurcation of a Leslie–Gower Predator–Prey Model

In this paper, we investigate analytically and numerically the dynamics of a modified Leslie–Gower predator–prey model which is characterized by the reduction of prey growth rate due to the anti-predator behavior. We prove the existence and local/global stability of equilibria of the model, and verify the existence of Hopf bifurcation. In addition, we focus on the influence of the fear effect on the population dynamics of the model and find that the fear effect can not only reduce the population density of both predator and prey, but also destabilize the coexistence equilibrium, which are beneficial to the occurrence of limit-cycle-induced oscillation, or prevent the occurrence of limit cycle oscillation and increase the stability of the system.

Relaxation oscillations of a slow–fast predator–prey model with a piecewise smooth functional response

The paper investigates the relaxation oscillations of a classical predator–prey model, based on the natural ecological assumption that the maximum per capita birth rate of the predator is small in comparison with the intrinsic prey growth rate. Predator’s feeding rate is assumed to be modeled by a piecewise smooth Holling type I functional response including a predator interference, which yields a piecewise smooth slow–fast system. Using geometry singular perturbation theory, we prove that the model has exactly two nested relaxation oscillations surrounding the unique stable node. Additional numerical simulations are provided to verify the analytical results.

Predation potential of hunting and web-building spiders on rice pests of Indian subcontinent

The present study investigated the predation attributes of hunting and web-building spiders of Indian subcontinent against rice-pests, under in-vitro conditions. Field observations revealed that the lynx spider, Oxyopes javanus and the ground-dwelling wolf-spider, Pardosa sumatrana were the most abundant arboreal hunting spiders, while Neoscona theisi and Tetragnatha javana, were the most abundant arboreal web-making spiders, throughout the crop growing season. Laboratory results showed that the prey consumption rates and growth rates of spiders were highest on abundant prey, but the conversion efficiencies were highest on scarce prey. Results identified the highest consumption and growth rates for O. javanus, while conversion efficiencies were highest for N. theisi. The four spider species under study consumed higher number of leafhoppers and lepidopteron adult stage pests in comparison to Leptocorisa bugs and grasshopper nymphs. We, therefore, suggest that the predatory impacts of spiders may be strongly influenced by their species-specific feeding and behavioural attributes, and the anti-predation features of the potential prey.

Native and Invasive Macrophytes Differ in Their Effectiveness as Nurseries for Juvenile Endangered Salmon

For marine biogenic habitats, such as kelp and seagrass, declines and local extinction events cause concern because of the loss of ecosystem services they provide. Many of these habitats function as valuable nurseries, but this function may be eroded when invasive species alter the structure of the habitats. For anadromous salmonids along the northeast Pacific, there is little known about the nursery role of coastal habitats, which presents a challenge for scientists to fully understand their complex life histories necessary for informing resource managers in decision-making processes regarding habitat protection and restoration. To address these issues, we ran a 3-week experiment testing the nursery functions of seagrass (Zostera marina), the invasive alga Sargassum muticum, mixed seagrass-Sargassum, and bare sand plots on the growth, survival, and prey availability for endangered Chinook salmon (Oncorhynchus tshawytscha) smolts. We found mixed effects of each habitat type when compared with each other. Chinook salmon smolts grew less in seagrass when compared with the three other habitats (bare sand, Sargassum, mixed seagrass-Sargassum). However, fish survival was lower in Sargassum habitat compared with seagrass and bare sand. Prey availability was greatest in mixed seagrass-Sargassum habitat compared with bare sand, Sargassum, or seagrass. We used a principal components analysis (PCA) to develop a nursery index using the smolts’ growth rate, percent survival, prey availability, and density of prey in gut contents. The nursery index showed that mixed seagrass-Sargassum habitat had the most positive effects on nursery performance. These results suggest that invasive species can serve positive habitat functions, but only when in the presence of a habitat-forming native species. Our study supports the theory that habitat diversity leads to greater nursery function of coastal ecosystems.

A widespread interaction between generalist and specialist enemies: The role of intraguild predation and Allee effect

A natural food web system involves a diverse community of natural enemies and one of the widespread and common phenomena of such systems is intraguild predation (IGP) (i.e., presence of eating and killing among potential competitors). Here, we investigate the dynamics of a food web system with Allee effect and intraguild predation. In the present study, generalist and specialist natural enemies competing for a shared resource (prey) (intraguild predation) have been introduced. The Allee effect has also been incorporated in the shared prey growth rate. We investigate how parameters defining Allee effect and intraguild predation affect the long-term persistence, extinction and co-existence regions of such species. We outline the conditions under which different types of interior and non-interior equilibria exist and are locally stable. Bi-stable dynamics has also been investigated for the proposed model system for a suitable range of parametric values. A threshold condition on the strength of Allee effect has been obtained assuring the absence of IG predator population along with extinction region of shared prey. To understand the dynamics of the system, a comprehensive study of bifurcation analysis has also been provided taking Allee effect and fertility rate of intraguild predator as bifurcation parameters. These two parameters generate various interesting bifurcations like saddle-node bifurcation and Hopf-bifurcation. We have obtained different parametric regions of Allee parameter for the existence of different boundary and interior equilibria. All the analytical results related with local stability of equilibrium points and all possible successive bifurcations have been supported by different numerical examples, one and two parameter bifurcation diagrams, bi-stability diagram and stability regions of all possible equilibrium points. The impacts of Allee effect on co-existence, stability, extinction of species, their persistence, bistability and bifurcations have been explicitly discussed and the whole dynamics has also been successfully compared with the dynamics of food web without Allee effect. It is observed that the introduction of Allee effect and IG predator induce more rich dynamics and compel the system to be more sensitive to initial population densities.

Spatiotemporal pattern formation in 2D prey-predator system with nonlocal intraspecific competition

There is growing evidence that ecological interactions are often nonlocal. Correspondingly, increasing attention is paid to mathematical models with nonlocal terms as such models may provide a more realistic description of ecological dynamics. Here we consider a nonlocal prey-predator model where the movement of both species is described by the standard Fickian diffusion, and hence is local, but the intra-specific competition of prey is nonlocal and is described by a convolution-type term with the ‘top-hat’ (piecewise-constant) kernel. The prey growth rate also includes the strong Allee effect. The system is studied using a combination of analytical tools and extensive numerical simulations. We obtain that nonlocality makes possible the pattern formation due to the Turing instability, which is not possible in the corresponding local model. We also obtain that the nonlocality creates bistability: it depends on the initial conditions which of the two spatially heterogeneous distributions emerges. Finally, we show that the bifurcation structure of the system is less sensitive to the choice of parametrization than it is in the corresponding nonspatial case, suggesting that nonlocality may decrease the structural sensitivity of the system.

Coexistence in seasonally varying predator–prey systems with Allee effect

A general seasonally-varying predator–prey model with Allee effect in the prey growth is investigated. The analysis is performed only on the basis of some properties determining the shape of the prey growth rate and the functional responses. General conditions for coexistence are determined, both in the case of weak and strong Allee effect. Finally, a modified Leslie–Gower predator–prey model with Allee effect is investigated. Numerical results illustrate the qualitative behaviors of the system, in particular the presence of periodic orbits.

Fear Induced Stabilization in an Intraguild Predation Model

In the present paper, we investigate the impact of fear in an intraguild predation model. We consider that the growth rate of intraguild prey (IG prey) is reduced due to the cost of fear of intraguild predator (IG predator), and the growth rate of basal prey is suppressed due to the cost of fear of both the IG prey and the IG predator. The basic mathematical results such as positively invariant space, boundedness of the solutions, persistence of the system have been investigated. We further analyze the existence and local stability of the biologically feasible equilibrium points, and also study the Hopf-bifurcation analysis of the system with respect to the fear parameter. The direction of Hopf-bifurcation and the stability properties of the periodic solutions have also been investigated. We observe that in the absence of fear, omnivory produces chaos in a three-species food chain system. However, fear can stabilize the chaos thus obtained. We also observe that the system shows bistability behavior between IG prey free equilibrium and IG predator free equilibrium, and bistability between IG prey free equilibrium and interior equilibrium. Furthermore, we observe that for a suitable set of parameter values, the system may exhibit multiple stable limit cycles. We perform extensive numerical simulations to explore the rich dynamics of a simple intraguild predation model with fear effect.

The effects of predation risk on prey stoichiometry: a meta-analysis.

A decade ago, the general stress paradigm (GSP) aimed to develop a predictive framework linking predator effects to ecosystem function. The GSP was based on the notion that animals, across taxa, exhibit similar physiological responses to predation risk that divert resources from growth and reproduction (which require N-rich biomolecules [i.e., protein]) to emergency functions (which require C-rich biomolecules [e.g., carbohydrates]). The GSP predicts that stressed prey should have a greater dietary demand for C-rich resources, a higher body C:N ratio, and elevated N excretion. Now, 10 yr later, we aim to revisit the GSP-using quantitative meta-analysis to test the original predictions of the GSP and how (1) predator hunting mode, (2) multiple stressors, and (3) prey dietary shifts affect prey stoichiometric responses to predation risk. Our data set was consistent with previous work showing that predation risk increases prey glucocorticoid levels and metabolic rates and decreases prey growth rates. We found that predation risk tended to decrease the fat, carbohydrate, and protein content of prey bodies; increased the C:P and N:P of prey bodies; but had no effect on the C, N, P, or C:N content of prey bodies. Additionally, we found no effect of predation risk on the N content of prey excretions. Prey responses to predation risk were unaffected by multiple stressors or the prey's ability to shift their diet, but predator hunting mode did affect the nature of prey stoichiometric responses. Specifically, ambush predators decreased prey macronutrient content and suppressed prey growth, and active predators had no effect on prey macronutrient content and a smaller effect on prey growth than ambush predators. The significant effects of predation risk were supported by robust fail-safe numbers, despite the high between-comparison heterogeneity that was found in all analyses. Our findings highlight the need (1) to test the underlying mechanisms and emerging patterns of the GSP in diverse taxa, (2) to explore the mismatch between prey macronutrient content and elemental stoichiometry, and (3) to expand the conceptual framework to include more inducible defenses (e.g., behavioral and morphological) and predator traits.

Impact of fear effect on the growth of prey in a predator-prey interaction model

Several field data and experiments on a terrestrial vertebrates exhibited that the fear of predators would cause a substantial variability of prey demography. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. Based on the experimental evidence, we proposed and analyzed a prey-predator system introducing the cost of fear into prey reproduction with Holling type-II functional response. We investigate all the biologically feasible equilibrium points, and their stability is analyzed in terms of the model parameters. Our mathematical analysis exhibits that for strong anti-predator responses can stabilize the prey-predator interactions by ignoring the existence of periodic behaviors. Our model system undergoes Hopf bifurcation by considering the birth rate r0 as a bifurcation parameter. For larger prey birth rate, we investigate the transition to a stable coexisting equilibrium state, with oscillatory approach to this equilibrium state, indicating that the greatest characteristic eigenvalues are actually a pair of imaginary eigenvalues with real part negative, which is increasing for r0. We obtained the conditions for the occurrence of Hopf bifurcation and conditions governing the direction of Hopf bifurcation, which imply that the prey birth rate will not only influence the occurrence of Hopf bifurcation but also alter the direction of Hopf bifurcation. We identify the parameter regions associated with the extinct equilibria, predator-free equilibria and coexisting equilibria with respect to prey birth rate, predator mortality rates. Fear can stabilize the predator-prey system at an interior steady state, where all the species can exists together, or it can create the oscillatory coexistence of all the populations. We performed some numerical simulations to investigate the relationship between the effects of fear and other biologically related parameters (including growth/decay rate of prey/predator), which exhibit the impact that fear can have in prey-predator system. Our numerical illustrations also demonstrate that the prey become less sensitive to perceive the risk of predation with increasing prey growth rate or increasing predators decay rate.

Controlling chaos in three species food chain model with fear effect

In this article, we study the impact of fear on the dynamics of a three species food chain model. We propose a model with the assumption that the growth rate of intermediate predator reduces at the cost of fear due to top predator, and the growth rate of prey is suppressed due to the fear of the intermediate predator. We carry out the existence of equilibria, local stability analysis and bifurcation analysis. Our numerical simulation reveals that for a low cost of the fear, system remains chaotic while increase in fear factor leads to stability. Even the large cost of fear causes the population to become extinct. We conclude that the fear effect can stabilize the chaotic dynamics of the system.

Bifurcation analysis and dynamic behavior to a predator-prey model with Beddington-DeAngelis functional response and protection zone

<p style='text-indent:20px;'>In this paper we study the protection zone problem to a predator-prey model subject to Beddington-DeAngelis functional responses and small prey growth rate. This is a successive work to a previous paper of the authors [X. He, S. N. Zheng, Protection zone in a diffusive predator-prey model with Beddington-DeAngelis functional response, J. Math. Biol. 75 (2017) 239-257], where the model with large prey growth rate was considered. At first we establish the existence and multiplicity of positive steady state solutions, and then give the dynamic behavior of the evolution problem. It is proved that there may be no positive steady state, or may have at leat one, two, or even three positive steady states, depending on the parameters involved such as the growth rate, the predation rate, and the food handling time of the predators, the growth rate and the refuge ability of the preys, and the sizes of the habitat with protection zone. In addition, it is shown that the dynamics of the solutions rely on the initial state as well, e.g., though there could be multiple positive steady states, the prey will go to extinction as time tends to infinity if its initial value is small.