A Model for the Effect of Toxicant on a Three Species Food-Chain System with "Food-Limited" Growth of Prey Population

The modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system and the state variables of the models are prey and predator densities, concentration of toxicant in the environment and the concentration of toxicant in the prey population. In the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. The stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the stress of toxicant are obtained. Further, it is also found that the predation rate of the intermediate predator is a bifurcating parameter and Hopf-bifurcation occurs at some critical value of this parameter. Finally, numerical simulation is carried out to support the analytical results.

Non-consumptive effects (NCEs) of predators are known to alter prey behaviour, morphology and physiology, ultimately influencing prey fitness. However, NCEs among multiple predator species and on shared prey in pest control have rarely been experimentally isolated. In systems with intraguild predation, intermediate predators (intraguild prey) may reduce prey consumption in the presence of top-predators; on the other hand, intermediate predators may benefit from non-consumptive effects of top-predators on prey (e.g., escape behaviour). I investigated the effects of perceived risk from a top predator (the presence of predator cues) on the interaction between intermediate predators and their prey. I also investigated how these interactions were affected by intermediate predator identity and initial prey density. My model system comprised the adult ladybird Adalia bipunctata (top predator), ladybird Adalia bipunctata larvae and the green lacewing Chrysoperla carnea (intermediate predators), and the pea aphid Acyrthosiphon pisum (prey). Intermediate predators reduced aphid density more strongly in the presence of the adult ladybird cues. Furthermore, the reduction of prey density depended on both the identity of the intermediate predator and initial prey density. The observed multiple predator facilitation was likely driven by non-consumptive effects on the top-predator on prey that rendered them more vulnerable to capture by the intermediate predator. In conclusion, the presence of predation risk may improve prey control by certain predator species. Further studies are required to test non-consumptive effects of different top predator species on intermediate predators in this system and in different multiple predator systems to better understand the role of non-consumptive effects on prey control.

Purpose This study aims to propose modified functional responses for both middle and top predator species to incorporate the observation of Suraci et al. [Nat. Commun., 2016, 7: 10698] due to antipredator behavior of the middle predator, and study how the fear effect in both prey and middle predator species, and hunting cooperation among top predator population influence the dynamics of a food chain model. Design/methodology/approach This study provides a qualitative investigation of a food chain model with modified Holling Type-II functional responses for middle and top predators. The fear effect in both prey and middle predator species, and the cooperative hunting behavior among top predator population is explored in this work. The modified functional responses are proposed for middle and top predators, and the Berec’s encounter-driven approach is used for cooperative hunting in the top predator. Various mathematical properties are investigated related to the model such as boundedness and persistence, equilibrium analysis, local and global stabilities of equilibrium points and the occurrence of various bifurcations. Extensive numerical simulation is performed for the better visualization of the impact of fear effect in both middle predator and prey, and the cooperative hunting among top predator population. Findings The results indicate that fear effect in both middle predator and prey populations can lead from stability to chaos. Furthermore, a high level of fear in prey and a moderate level of hunting cooperation among top predator is beneficial for the species’ coexistence. It is also obtained that the wasting time by middle predator due to fear of top predator promotes species’ coexistence, when the level of reduced encounter rate between top and middle predators is low or moderate. However, a high level of reduced encounter rate may be responsible for the extinction of top predator population. Originality/value This research proposed a modified functional response by considering realistic assumptions and provides the combined role of fear effect in prey and hunting cooperation among top predators, and the impact of reduced encounter rate between top and middle predators along with the wasting time by middle predator while hunting prey, due to antipredator behavior.

Top-predator interference and gestation delay as determinants of the dynamics of a realistic model food chain

The dynamics of food consumption by higher trophic level is complicated as its availability, choice, and consequently their development. The top predator interference has a strong influence on the dynamic structure of the tritrophic food chain system. The proposed article deals with the characteristic features of a three‐tire modified Leslie–Gower model with a one‐prey two‐predator system with the assumption of multiple gestation delays. The intermediate predator of the food chain is taken as a specialist type, whereas the growth of top predator is assumed by sexual reproduction. Two different response functions named Monod–Haldane (M‐H) and Beddington–DeAngelis (B‐D) are considered for the modeling of system dynamics. The population densities of intermediate and top predators are assumed to be affected by two different gestation delays. The boundedness and positive equilibria and their stability conditions are examined theoretically for the delay‐free system. The local and global stability conditions of the delayed system are also determined. With the help of normal form theory and central manifold arguments, the properties of bifurcating periodic solutions are carried out. The numerical computation is performed to validate our analytical findings that show the different dynamical outcomes such as periodic and chaotic dynamics. The Hopf‐bifurcation scenario for different parameters of the model system is well studied. Further, the stability behavior of multiple delays for the different cases is investigated. The system shows chaotic behavior when the gestation delay of intermediate predators is large enough. It is also observed that the top predator density is highly fluctuating through the creation of chaos by the inclusion of time delay. Finally, the time delay destabilizing effect is noticed for three‐way interactions among prey, intermediate predator, and top predator, highlighting its significance in chaotic dynamics.

Dynamical analysis of a delayed tri-trophic food chain consisting of prey, an intermediate, and a top predator is investigated in this paper. The additive Allee effect is introduced in the prey population, and it is assumed that there is a time lag due to the gestation effect in the intermediate predator. The interference among the prey and the intermediate predator is according to Holling type II, while the interaction between the intermediate and top predators follows the Crowley–Martin functional response. The local stability and bifurcation analysis of the proposed model at the interior equilibrium point are studied. Numerical simulations are provided to ensure the mathematical results.

Top predators often have large home ranges and thus are especially vulnerable to habitat loss and fragmentation. Increasing connectance among habitat patches is therefore a common conservation strategy, based in part on models showing that increased migration between subpopulations can reduce vulnerability arising from population isolation. Although three-dimensional models are appropriate for exploring consequences to top predators, the effects of immigration on tri-trophic interactions have rarely been considered. To explore the effects of immigration on the equilibrium abundances of top predators, we studied the effects of immigration in the three-dimensional Rosenzweig-MacArthur model. To investigate the stability of the top predator equilibrium, we used MATCONT to perform a bifurcation analysis. For some combinations of model parameters with low rates of top predator immigration, population trajectories spiral towards a stable focus. Holding other parameters constant, as immigration rate is increased, a supercritical Hopf bifurcation results in a stable limit cycle and thus top predator populations that cycle between high and low abundances. Furthermore, bistability arises as immigration of the intermediate predator is increased. In this case, top predators may exist at relatively low abundances while prey become extinct, or for other initial conditions, the relatively higher top predator abundance controls intermediate predators allowing for non-zero prey population abundance and increased diversity. Thus, our results reveal one of two outcomes when immigration is added to the model. First, over some range of top predator immigration rates, population abundance cycles between high and low values, making extinction from the trough of such cycles more likely than otherwise. Second, for relatively higher intermediate predator migration rates, top predators may exist at low values in a truncated system with impoverished diversity, again with extinction more likely.

Food-Web Dynamics on Some Small Subtropical Islands: Effects of Top and Intermediate Predators

The influence of vigilance on intraguild predation

The impact of toxins on predator and prey populations has recently gained attention in ecological modeling. In our research, we want to develop and analyse a food chain model that integrates the effects of toxins produced within the ecological system. The model focuses on a three-tier food chain, comprising prey, an intermediate predator, and a top predator, where toxins released by species impact their interactions and survival rates. The growth rates of prey and middle predators are assumed to follow a logistic pattern. By incorporating time delays in growth, toxin accumulation and its effects, we explore how delay and toxin influence together alters the stability of the system. In this model, we have shown that the system exhibits uniform persistence. The necessary and sufficient conditions for stability and Hopf-bifurcation of the coexistence interior equilibrium point have been discussed analytically and numerically both, taking delay as threshold parameter. In addition to that, Lyapunov function has been constructed to study the local asymptotic stability of the coexistence interior equilibrium point. Furthermore, numerical simulations have been carried out with appropriate parameter values to validate the analytical results obtained. Finally, in conclusion, the paper summarizes our findings and highlights potential directions for future research on this topic.

Many food webs exist in the ecosystem, and their survival is directly dependent on the growth rate of primary prey; it balances the entire ecosystem. The spatiotemporal dynamics of three species' food webs was proposed and analyzed in this paper, where the intermediate predator's predation term follows Holling Type IV and the top predator's predation term follows Holling Type II. To begin, we examine the system's stability using linear stability analysis. We first obtained an equilibrium solution set and then used a Jacobian method to investigate the system's stability at a biologically feasible equilibrium point. We investigate random movement in species in the presence of diffusion, establish conditions for system stability, and derive the Turing instability condition. Following that, the Turing instability condition for a spatial food web system is calculated. Finally, numerical simulations are used to validate the findings. We discovered several intriguing spatial patterns (spots, strip, and mixed patterns) that help us understand the dynamics of the real-world food web. As a result, the Turing instability analysis used in the complex food web system is especially relevant experimentally because the associated consequences can be researched and applied to a wide range of mathematical, ecological, and biological models.

This paper investigates the dynamics of a tritrophic food chain model incorporating an Allee effect, sexually reproductive generalist top predators, and Holling type IV and Beddington-DeAngelis functional responses for interactions across different trophic levels. Analytically, we explore the feasible equilibria, their local stability, and various bifurcations, including Hopf, saddle-node, transcritical, and Bogdanov-Takens bifurcations. Numerical findings suggest that higher Allee intensity in prey growth leads to the inability of species coexistence, resulting in a decline in species density. Likewise, a lower reproduction rate and a higher strength of intraspecific competition among top predators also prevent the coexistence of species. Conversely, a rapid increase in the reproduction rate and a decrease in the strength of intraspecific competition among top predators enhance the densities of prey and top predators while decreasing intermediate predator density. We also reveal the presence of bistability and tristability phenomena within the system. Furthermore, we extend our autonomous model to its nonautonomous counterpart by introducing seasonally perturbed parameters. Numerical analysis of the nonautonomous model reveals that higher seasonal strength in the reproduction rate and intraspecific competition of top predators induce chaotic behavior, which is also confirmed by the maximum Lyapunov exponent. Additionally, we observe that seasonality may lead to the extinction of species from the ecosystem. Factors such as the Allee effect and growth rate of prey can cause periodicity in population densities. Understanding these trends is critical for controlling changes in population density within the ecosystem. Ecologists, environmentalists, and policymakers stand to benefit significantly from the invaluable insights garnered from this study. Specifically, our findings offer pivotal guidance for shaping future strategies aimed at safeguarding biodiversity and maintaining ecological stability amidst changing environmental conditions. By contributing to the existing body of knowledge, our study advances the field of ecological science, enhancing the comprehension of predator-prey dynamics across diverse ecological conditions.

Prey are often consumed by multiple predator species. Predation rates on shared prey species measured in isolation often do not combine additively due to interference or facilitation among the predator species. Furthermore, the strength of predator interactions and resulting prey mortality may change with habitat type. We experimentally examined predation on amphipods in rock and algal habitats by two species of intertidal crabs, Hemigrapsus sanguineus (top predators) and Carcinus maenas (intermediate predators). Algae provided a safer habitat for amphipods when they were exposed to only a single predator species. When both predator species were present, mortality of amphipods was less than additive in both habitats. However, amphipod mortality was reduced more in rock than algal habitat because intermediate predators were less protected in rock habitat and were increasingly targeted by omnivorous top predators. We found that prey mortality in general was reduced by (1) altered foraging behavior of intermediate predators in the presence of top predators, (2) top predators switching to foraging on intermediate predators rather than shared prey, and (3) density reduction of intermediate predators. The relative importance of these three mechanisms was the same in both habitats; however, the magnitude of each was greater in rock habitat. Our study demonstrates that the strength of specific mechanisms of interference between top and intermediate predators can be quantified but cautions that these results may be habitat specific.

Effects of toxicants on populations: A qualitative: Approach III. Environmental and food chain pathways

THE INFLUENCE OF INTRAGUILD PREDATION ON PREY SUPPRESSION AND PREY RELEASE: A META-ANALYSIS