Tritrophic Food Chain Research Articles

A chaotic tri-trophic food chain model supplemented by Allee effect

A chaotic tri-trophic food chain model supplemented by Allee effect

Stability and bifurcation analysis of a tri-trophic food chain model with intraguild predation

The dynamics of a three-component model for food web with intraguild predation is considered. The model is based on the collection of ordinary differential equations that describe the interactions among prey, intermediate predator and top predator. First, the model without self-limitation of the predators is studied. Boundedness of the system and existence of non-negative solutions are established. The local stability analysis of the equilibria is carried out to examine the behavior of the system. The possibility of Hopf bifurcation around non-negative equilibria with consumption rates as bifurcation parameters is studied. Center manifold theorem and the normal form theory are applied to obtain the formulas for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations support the analytical findings, which show that the extinction of one of the predators can occur under certain restrictions on the predation rate of the top predator. Subsequently, numerical analysis of the model with self-limitation of the predators is carried out. Simulations reveal that the system with intraspecific competition in the predator populations can reproduce coexistence between the three species in resource-rich environment.

Trophic transfer and toxicity of silver nanoparticles along a phytoplankton-zooplankton-fish food chain

This study evaluated the bioconcentration metrics, organ-specific distribution, and trophic consequences of silver nanoparticles along a Dunaliella salina-Artemia salina-Poecilia reticulata food chain. To this end, accumulation, tissue-specific distribution, bioconcentration and biomagnification factors, and trophic toxicity of AgNPs were quantitatively investigated along di- and tri-trophic food chains. Overall, silver accumulation increased markedly in intestine and liver tissues, carcass, and embryos of guppy fish with rising exposure concentrations and reducing trophic levels. Following trophic and waterborne exposure, AgNPs illustrated a regular tendency in following order: intestine > liver > embryos > carcass. BCF displayed values of 826, 131, and ≈ 1000 for microalgae, brine shrimp, and guppy fish, respectively. Moreover, BMF showed values <1.00 for 48-h post-hatched nauplii and guppy fish received AgNPs-exposed phytoplankton, yet >1.00 for the liver and whole body of guppy fish treated with AgNPs-exposed nauplii through algae and water, indicating that AgNPs could be biomagnified from the second to third trophic level, but not from the first to second or third levels. Furthermore, the waterborne and trophic exposure of AgNPs considerably induced oxidative stress and reproductive toxicity. Together, this study demonstrated that AgNPs could be biomagnified across trophic chain and consequently cause trophic toxicity.

Untangling the role of tri-trophic food chain model in sustaining quokka population

The introduction of predators like red fox and dingoes in the 1930s took a big toll on the quokka population. This paper is mainly concerned with designing conservation policies for quokka population (an endangered species). For this purpose, we designed a reaction–diffusion tri-tropic food chain model consisting quokka and its two predators, red fox and dingoes. We have shown the global existence, non-negativity and uniform boundedness for the designed spatiotemporal model. Existence and stability analysis of the equilibrium points for the model is done. We applied the prevalent idea of basic reproduction number with its origin from epidemiology to the food chain model, to deduce a condition for extinction and persistence of predator population. Natural systems exhibit an amazing diversity of structures in both living and non-living systems. We found that in the presence of diffusion, the model has the potential of exhibiting Turing instability generating beautiful patterns. Numerical results reveal that quokka tends to avoid places resided by dingoes. Our research aims at finding a solution for the current quokka extinction problem by showing the effect of presence of alternative food for dingoes and prohibiting the external factor causing death of quokka population.

Controlling chaos and pattern formation study in a tritrophic food chain model with cannibalistic intermediate predator

Controlling chaos and pattern formation study in a tritrophic food chain model with cannibalistic intermediate predator

Role of nutritional food value and Allee effect in controlling chaos in a tri-trophic food chain with omnivory nature of top-predator

Role of nutritional food value and Allee effect in controlling chaos in a tri-trophic food chain with omnivory nature of top-predator

Role of nutritional food value and Allee effect in controlling chaos in a tri-trophic food chain with omnivory nature of top-predator

Role of nutritional food value and Allee effect in controlling chaos in a tri-trophic food chain with omnivory nature of top-predator

Deterministic and Stochastic Fractional-Order Hastings-Powell Food Chain Model

In this paper, a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed. The interaction between prey, middle predator and top predator population is investigated. In order to clarify the characteristics of the proposed model, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions of the proposed model are examined. Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained. By using stability analysis of the fractional-order system, it is proved that if the basic reproduction number , the predator free equilibrium point is globally asymptotically stable. The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem. Some numerical examples are given to illustrate the theoretical findings. The impact of harvesting on prey and the middle predator is studied. We conclude that harvesting parameters can control the dynamics of the middle predator. A numerical approximation method is developed for the proposed stochastic fractional-order model.

Explosive tritrophic food chain model with herd behaviour of prey and finite time blow-up of the top predator

Explosive tritrophic food chain model with herd behaviour of prey and finite time blow-up of the top predator

Explosive tritrophic food chain model with herd behaviour of prey and finite time blow-up of the top predator

Explosive tritrophic food chain model with herd behaviour of prey and finite time blow-up of the top predator

Dynamical complexity in a tritrophic food chain model with prey harvesting

The present investigation deals with a tritrophic food web model with Holling-Tanner type II functional response to clarify the dynamical complexity of the eco-systems in the natural environment. The objective of this study is to explore the harvesting mechanism scenario in a three-dimensional interacting species system such as one prey and two specialist predators. Attention has been given to demonstrate the system characteristics near the biologically feasible equilibria. Specifically, stability, Hopf-Andronov bifurcation for the respective system parameters and dissipativeness has been performed in order to scrutinize the system behaviour. Lyapunov exponents are worked out numerically and an unstable scenario for significant parameters of the model system has been executed to characterize the complex dynamics. In addition to, we put forward a detailed numerical simulation to justify the chaotic dynamics of the present system. We conclude that chaotic dynamics can be executed by the prey harvesting parameters.

Fear Effect in a Tri-Trophic Food Chain Model with Holling Type IV Functional Response

Of concern the present study deals with an updated food chain model comprising one prey and two predator species in a natural environment with the inclusion of fear effect in both the prey and the median predator population through Holling type IV functional response. The present model is affluent with intra-specific competition among the hunter species having specific mortality. The model system emphasizes its characteristics in the proximity of the probable equilibrium position in the realm of biological dynamics. The response of the system is explored further for its stability analysis based on prerequisites and Hopf-bifurcation phenomena as well with respect to some significant model parameters. A quantitative analysis based on numerical simulation is also carried out in order to validate the analytical results and thereby the applicability of the model is established.

A “Double” fear effect in a tri-trophic food chain model

A “Double” fear effect in a tri-trophic food chain model

On the sensitivity of food webs to multiple stressors.

Evaluating the effects of multiple stressors on ecosystems is becoming increasingly vital with global changes. The role of species interactions in propagating the effects of stressors, although widely acknowledged, has yet to be formally explored. Here, we conceptualise how stressors propagate through food webs and explore how they affect simulated three-species motifs and food webs of the Canadian St.Lawrence System. We find that overlooking species interactions invariably underestimate the effects of stressors, and that synergistic and antagonistic effects through food webs are prevalent. We also find that interaction type influences a species' susceptibility to stressors; species in omnivory and tri-trophic food chain interactions in particular are sensitive and prone to synergistic and antagonistic effects. Finally, we find that apex predators were negatively affected and mesopredators benefited from the effects of stressors due to their trophic position in the St.Lawrence System, but that species sensitivity is dependent on food web structure. In conceptualising the effects of multiple stressors on food webs, we bring theory closer to practice and show that considering the intricacies of ecological communities is key to assess the net effects of stressors on species.

Bistability in a tri-trophic food chain model: Basin stability perspective.

The most important issue of concern in a food chain is the stability of species and their nature of persistence against system parameter changes. For understanding the stable dynamics and their response against parameter perturbation, the local stability analysis is an insufficient tool. A global stability analysis by the conventional techniques seems to supplement some of the shortcomings, however, it becomes more challenging for multistable ecosystems. Either of the techniques fails to provide a complete description of the complexity in dynamics that may evolve in the system, especially, when there is any transition between the stable states. A tri-trophic resource-consumer-predator food chain model has been revisited here that shows bistability and transition to monostability via a border collision that leads to a state of predator extinction. Although earlier studies have partially revealed the dynamics of such transitions, we would like to present additional and precise information by analyzing the system from the perspective of basin stability. By drawing different bifurcation diagrams against three important parameters, using different initial conditions, we identify the range of parameter values within which the stability of the states persists and changes to various complex dynamics. We emphasize the changes in the geometry of the basins of attraction and get a quantitative estimate of the nature of relative changes in the area of the basins (basin stability) during the transitions. Furthermore, we demonstrate the presence of a down-up control, in addition to the conventional bottom-up and top-down control phenomena in the food chain. The application of basin stability in food networks will go a long way for accurate analysis of their dynamics.

Eco-evolutionary consequences of habitat warming and fragmentation in communities.

Eco-evolutionary dynamics can mediate species and community responses to habitat warming and fragmentation, two of the largest threats to biodiversity and ecosystems. The eco-evolutionary consequences of warming and fragmentation are typically studied independently, hindering our understanding of their simultaneous impacts. Here, we provide a new perspective rooted in trade-offs among traits for understanding their eco-evolutionary consequences. On the one hand, temperature influences traits related to metabolism, such as resource acquisition and activity levels. Such traits are also likely to have trade-offs with other energetically costly traits, like antipredator defences or dispersal. On the other hand, fragmentation can influence a variety of traits (e.g. dispersal) through its effects on the spatial environment experienced by individuals, as well as properties of populations, such as genetic structure. The combined effects of warming and fragmentation on communities should thus reflect their collective impact on traits of individuals and populations, as well as trade-offs at multiple trophic levels, leading to unexpected dynamics when effects are not additive and when evolutionary responses modulate them. Here, we provide a road map to navigate this complexity. First, we review single-species responses to warming and fragmentation. Second, we focus on consumer-resource interactions, considering how eco-evolutionary dynamics can arise in response to warming, fragmentation, and their interaction. Third, we illustrate our perspective with several example scenarios in which trait trade-offs could result in significant eco-evolutionary dynamics. Specifically, we consider the possible eco-evolutionary consequences of (i) evolution in thermal performance of a species involved in a consumer-resource interaction, (ii) ecological or evolutionary changes to encounter and attack rates of consumers, and (iii) changes to top consumer body size in tri-trophic food chains. In these scenarios, we present a number of novel, sometimes counter-intuitive, potential outcomes. Some of these expectations contrast with those solely based on ecological dynamics, for example, evolutionary responses in unexpected directions for resource species or unanticipated population declines in top consumers. Finally, we identify several unanswered questions about the conditions most likely to yield strong eco-evolutionary dynamics, how better to incorporate the role of trade-offs among traits, and the role of eco-evolutionary dynamics in governing responses to warming in fragmented communities.

Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response

In this work, a tritrophic food chain model has been proposed by incorporating Ivlev-like nonmonotonic functional response, where prey is equipped with defense ability. We have performed a detailed dynamical study and pattern formation analysis to obtain complex dynamics of the proposed system. Stability and bifurcation analysis have been performed in the model system. Persistence and permanence are discussed. Bifurcations of codimension-1, in particular, saddle-node, transcritical and Hopf bifurcation are observed. The model system also exhibits bifurcations of codimension-2 such as cusp, Bogdanov-Takens and generalized Hopf bifurcation. Interestingly, it is observed that the middle and top predator population become extinct due to defense ability of prey. Chaotic dynamics is observed via a period-doubling route to chaos with the change in the value of parameter β. The quantification of chaotic dynamics is done, using Lyapunov spectrum and sensitivity analysis. Diffusion induced chaos is studied in the spatiotemporal model system. Hopf bifurcation is seen in the case of a spatially extended system. Further, conditions for Turing instability have been obtained. Pattern formation study is done. In the two-dimensional spatial domain, various non-Turing patterns such as hot-spot, cold-spot, labyrinth patterns are obtained. Ripple and stripe Turing patterns are obtained in case of one-dimensional spatial domain. Also, labyrinth and patchy Turing patterns are obtained in the two-dimensional spatial domain. The spatial distribution of the species shows Turing patterns at the low cost of β, while the increased cost of β changes Turing patterns to non-Turing patterns. Throughout the study, we observe that the parameter β plays an important role in group defense mechanism and is the most sensitive parameter leading to vital change in system dynamics. A wide range of Turing and non-Turing patterns obtained in this work has not been reported so far in literature in any model with group defense.

Study of Stability and Bifurcation of Three Species Food Chain Model with Non-monotone Functional Response

In this research article, we consider a tri-trophic food chain model with one prey and two predators such as- prey, intermediate predator and top predator. In this model, the prey and intermediate predator follows non-monotonic functional response; top predator consumes prey and intermediate predator following Holling type I functional response. The positivity, boundedness of solutions of the proposed model and stability conditions of different equilibrium points are discussed here. Then using Center Manifold theorem, the nature of non-hyperbolic type equilibrium points are discussed. After that, different local bifurcations such as- Saddle-node, Transcritical and Hopf bifurcations are studied theoretically as well as numerically by considering half-saturation constant and death rate of intermediate predator as the bifurcation parameters. Finally, the dynamics of the proposed model has been illustrated with the help of some numerical simulations.

A remark on “ Global dynamics of a tritrophic food chain model subject to the Allee effects in the prey population with sexually reproductive generalized‐type top predator” [Comp and Math Methods. 2019; E1079, pp. 1–23

In Debnath et al. (2019), a tritrophic food chain model subject to a Allee effect on the prey growth and Crowley–Martin senses functional response between intermediate predator and top predator, with a top predator of sexually reproductive type is considered. It is claimed that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, and is dissipative. We show that this is not true. In particular, solutions to the model can blow-up in finite time, even under the restrictions derived in Debnath et al. (2019), for sufficiently chosen initial data. We derive a new extinction boundary for the system. We also conjecture on the effect of the Allee threshold on the blow-up dynamics in the model. All of our results are validated via numerical simulations.

Pattern Formation in Intra-Specific Competition Food Chain System with Bifurcation and Chaos Control

The study is an attempt to explore the competitive effects on the top predators in the tri-trophic food chain model. Holling types II and IV functional responses are used to investigate the complex behavior of the tri-trophic prey–predator system. Reaction–diffusion systems have been used to represent temporal evolution and spatial interaction among the species. Consequently, local and global stabilities, and Hopf-bifurcation have been analyzed. The numerical simulation leads to spontaneous and interesting pattern formation in two dimensions, signifying diffusion interaction between mid- and top-level predators. The effect of diffusion on the chaotic dynamics of the model systems is also investigated. It is found that the chaos mechanism wave-like behavior of the chaotic attractor exists for a long time. The diffusion of this long-term behavior is controlled by using Hybrid Control Strategy.