Food Web System Research Articles

Complex dynamics of a four-species food-web model: An analysis through Beddington-DeAngelis functional response in the presence of additional food

Abstract The four-dimensional food-web system consisting of two prey species for a generalist middle predator and a top predator is proposed and investigated. The middle predator is predating over both the prey species with a modified Holling type-II functional response. The food-web model is effectively formulated, exhibits bounded behavior, and displays dissipative dynamics. The proposed model’s essential dynamical features are studied regarding local stability. We investigated the four species’ survival and established their persistence criteria. In the proposed model, a transcritical bifurcation occurs at the axial equilibrium point. The numerical simulations reveal the persistence of a chaotic attractor or stable focus. The conclusion is that increasing the food available to the middle predator may make it possible to manage and mitigate the chaos within the food chain.

Investigating food web structure and system function of an artificial reef ecosystem based on carbon and nitrogen stable isotope analysis: implications for reef management

IntroductionFood web is an important basis for identifying trophodynamic processes, and evaluating the structural and functional characteristics of ecosystems. The trophodynamics and system function of artificial reef (AR) ecosystems have rarely been examined.MethodsStable isotope analysis was used to investigate the food web structure and functions of an artificial reef (AR) ecosystem in this study.Results and DiscussionThe δ13C and δ15N values of particulate organic matter (POM) in AR showed noticeable seasonal changes, and the δ13C value of POM in autumn was significantly higher than that in other seasons (p<0.05). There were no significant seasonal variations in the δ13C values of solid organic matter (SOM), and no significant difference between SOM and POM was observed except in autumn. Moreover, macroalgae did not significantly affect the δ13C values of SOM. Phytoplankton may be the primary nutrient source in the AR ecosystem. The δ13C values of most crustaceans in the AR were approximately between (-17.03 ± 0.22) ‰ – (-17.74 ± 0.07) ‰, higher than those of most fish, indicating that they may have different basal nutrient sources. The trophic level (TL) of invertebrates was between 2.00 and 3.09, and that of fish was between 2.98 and 3.66. The distribution of δ13C and TLs of crustaceans and fish showed that, except for crustaceans, bivalve shellfish and zooplankton might also be important food sources for fish in the AR ecosystem.ConclusionThe δ13C and δ15N values of most species in the AR showed good continuity, indicating that they may be mainly produced from the AR ecosystem. Migratory species such as Lateolabrax japonicus and Sepiella maindroni showed higher δ13C values, indicating that they may have migrated from other sea areas. To maintain the stability of the ecosystem structure and function of the AR ecosystem, fishing activities should be carried out following the maximum sustainable yield theory. Future research needs to identify the nutritional relationship between AR and its adjacent sea areas, to depict the food web structure of the AR with higher accuracy.

Contaminant-induced oxidative stress underlies biochemical, molecular and fatty acid profile changes, in gilthead seabream (Sparus aurata L.)

Chemical contaminants such as heavy metals, polybrominated diphenyl ethers (PBDEs) and drugs, are constantly found in the marine environment determining the interest of the scientific community for their side effects on animal welfare, food safety and security. Few studies have analyzed the effects of mix of contaminants in fish, in terms of molecular and nutritional composition response, beside it is indispensable to think more and more on effect of contaminants along the food web system. In this study, Sparus aurata specimens were exposed for 15 days, by diet, to a mixture of carbamazepine (Cbz), polybrominated diphenyl ether-47 (PBDE-47) and cadmium chloride (CdCl2), at two doses (0.375 μg g-1 D1; 37.5 μg g-1 D2) (T15). After, fish were fed with a control diet, without contaminants mix, for other 15 days (T30). The study explored the effect on oxidative stress in the liver, analyzing specific molecular markers and effects on quality, by fatty acid profile and lipid peroxidation. Molecular markers involved in ROS scavenging, such as superoxide dismutase (sod), catalase (cat) and glutathione peroxidase (gpx) were evaluated by gene expression; as markers of quality and lipid peroxidation, the fatty acids (FAs) profile and the level of malondyaldeide (MDA) were assessed. Sod and cat genes underwent to up-regulation after 15 days of diet containing contaminants and showed down-regulation after the next 2 weeks of detoxification (T30). At T15, the FAs profile showed an increase of the saturated fatty acids (SFA), and a decrease of the polyunsatured fatty acids (PUFA). The MDA levels increased over time, indicating an ongoing radical damage. These results suggest that the effects of the contaminants can be perceived not only at molecular but also at nutritional level and that the molecular and biochemical markers adopted could be differently used to monitor the health of aquatic organisms in the marine environment.

Phenology of the black bean aphid, Aphis fabae, on organic crops and effect of parasitoid communities

The data that support the findings of this study is available in the Mendeley Data repository: https://DOI: 10.17632/wnvt4grz9d.1.

Qualitative Analysis of Food-Web Model through Diffusion-Driven Instability

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.

Modeling and Analysis of the Influence of Fear on a Harvested Food Web System

The food web is a crucial conceptual tool for understanding the dynamics of energy transfer in an ecosystem, as well as the feeding relationships among species within a community. It also reveals species interactions and community structure. As a result, an ecological food web system with two predators competing for prey while experiencing fear was developed and studied. The properties of the solution of the system were determined, and all potential equilibrium points were identified. The dynamic behavior in their immediate surroundings was examined both locally and globally. The system’s persistence demands were calculated, and all conceivable forms of local bifurcations were investigated. With the aid of MATLAB, a numerical simulation was used to clarify the control set of parameters and comprehend the overall dynamics. For the system to continue, it was determined that extremely high levels of either fear or harvesting lead to the extinction of one of the predator species. Moreover, in contrast to the ecological assumption that if two species are vying for the same resources, population values cannot be constant, this study showed that it is possible for two competing species to subsist on the same resources.

Temporal Dynamics in Energy Fluxes and Trophic Structure of a Portunus trituberculatus Polyculture Ecosystem During Different Culture Periods

Swimming crab (Portunus trituberculatus) are an important aquaculture species in eastern coastal areas of China. To improve the understanding of P. trituberculatus culture ecosystem functioning, the dynamics of energy flow and trophic structure of a P. trituberculatus polyculture system (co-culture with white shrimp Litopenaeus vannamei and short-necked clam Ruditapes philippinarum) were investigated in this study. Three Ecopath models representing the early, middle, and late culture periods of a P. trituberculatus polyculture ecosystem, respectively, were constructed to compare ecosystem traits at different culture periods. The results demonstrated that detritus was the main energy source in this polyculture ecosystem, and most of the total system throughput occurred at trophic levels I and II. Artificial food input and consumption by the culture organisms increased from early to middle and late periods, which produced marked impacts on biomass structure and primary production. R. philippinarum was considered to have a dominant influence on phytoplankton community dynamics which changed from nano- to pico-phytoplankton predominance, from the middle to the late period. Considering the low utilization efficiency of pico-phytoplankton production, large amounts of detritus accumulated in the sediment in the late period, which may constitute a potential risk for the ecosystem. Ecological network analyses indicated that the total energy flow and level of system organization increased from the early to the middle and late periods, whereas food web complexity and system resilience decreased from early to middle and late periods, which may indicate a trend of decreasing ecosystem stability. The system may be further optimized by increased stocking density of R. philippinarum and by introducing macro-algae at a suitable biomass to increase ecosystem stability, energy utilization efficiency, and aquaculture production.

Hopf-Bifurcation and Pattern Selections in a Three Trophic Level Food Web System

The ecosystem comprises many food webs, and their existence is directly dependent upon the growth rate of primary prey; it balances the whole ecosystem. This paper studies the temporal and spatiotemporal dynamics of three trophic levels of food web system, consisting of two preys and two predators. We first obtained an equilibrium solution set and studied the system’s stability at a biological feasible equilibrium point using a Jacobian method. We show the occurrence of Hopf-bifurcation by considering the growth rate of prey as the bifurcation parameter for the temporal model. In the presence of diffusion, we study random movement in species, establish conditions for the system’s stability, and derive the Turing instability condition. A multiple-scale analysis is used to determine the amplitude equations in the neighborhood of the Turing bifurcation point. After applying amplitude equations, the system has a rich dynamical behavior. The stability analysis of these amplitude equations leads to the development of various Turing patterns. Finally, with numerical simulations, the analytical results are verified. Within this framework, our study through the dynamical behavior of the complex system and bifurcation point based on the prey growth rate can serve as a baseline for numerous researchers working on ecological models from diverse perspectives. As a result, the Hopf-bifurcation and multiple-scale analysis used in the complex food web system is particularly relevant experimentally because the linked consequences may be researched and applied to many mathematical, ecological, and biological models.

Analysing ecological carrying capacity of bivalve aquaculture within the Yellow River Estuary ecoregion through mass-balance modelling

As the largest aquaculture producer in the world, China is facing the challenge of maintaining sustainability while continuing to develop the aquaculture industry to meet socio-economic needs. Models of trophic structure and energy flow can be used to analyse ecological carrying capacity in order to determine whether a large and rapidly increasing aquaculture industry potentially puts sustainable development at risk. The Yellow River Estuary ecoregion in Shandong Province, China, is an ecologically important region, with extensive bivalve aquaculture that is increasing rapidly at an overall growth rate of 4% annually during recent decades. A trophic mass-balance model was used to analyse the ecological carrying capacity of bivalve aquaculture in this ecoregion. The biomass of cultured bivalves is currently 13.3 t km-2 and could be increased to 62.0 t km-2 without exceeding the ecological carrying capacity. Zooplankton are a key factor limiting the ecological carrying capacity and represent a sensitive functional group within the food web system in this ecoregion. At the ecological carrying capacity of cultured bivalves in the Yellow River Estuary ecoregion, harvests would amount to 353.2 t km-2 yr-1 or a total of 4.2 million t yr-1 in this region. If the current average rate of growth in aquaculture in China is maintained, under cautious development, the biomass of cultured bivalves would reach half of the estimated ecological carrying capacity (31.0 t km-2) after 20 yr. This implies that there is capacity for sustainable development of bivalve aquaculture under current environmental conditions.

Biological control for predation invasion based on pair approximation.

Biological invasions have been paid more attention since invasive species may cause certain threats to local ecosystems. When biological control is adopted, selecting control species for effect better becomes the focus of latest studies. A food web system, with one native species, one invasive species as predator, and one introduced control species preying on both native and invasive species, is established based on pair approximation, in which the spatial landscape of biological invasion and control is concerned, and the local and global dispersal strategies of invasive species, in addition to the predation preferences of control species for native and invasive species, are considered. The influence of the initial density and initial spatial structures of the control species is investigated and the effects of control species releasing time are analyzed. Generally, the earlier the species introduction, the better the control effect, especially for invasive species dispersing globally. Interestingly, too low control species predation preference for native species can lead to unsuccessful introduction, while too much predation preference will have a weak control effect. The larger the control species predatory preference for invasive species is, the more conducive it is to biological control. The extinction of the invasive species is closely related to the initial density and concentration of the control species. This study gives some insights on selecting control species, its appropriate releasing time, and the density and spatial aggregation of it. Some real-life examples are elaborated on, which provides references for biological invasion control.

Stability analysis of a complex four species food-web model

This paper aims to study the dynamical behaviours of a four dimensional food web system consisting of a bottom prey, two middle predators and a superpredator(top predator) with Holling Type I and Type II functional responses. A system of four differential equations has been proposed and analyzed. Positivity, boundedness and extinction criteria of the system are studied. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. We also explore the system undergoes a Hopf-bifurcation around interior equilibrium point for a parametric values which has very significant ecological impacts in this work. Computer simulation are carried out to validate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.

Stochastic adaptive fixed-time stabilization of chaotic systems with applications in PMSM and FWS

This investigation addresses the problem of fixed-time stabilization of the chaotic systems influenced by environmental noise. An adaptive control scheme is employed so that it is not necessary to set the related control gains in advance. Specifically, the adaptive control is integrated with fixed-time control protocol successfully for guaranteeing the stability of chaotic systems. In the light of stochastic fixed-time stability theory, the criteria are deduced to ensure the (fixed-time) stabilization of chaotic systems, and the upper bound time is estimated, which is irrelevant to the initial states of the systems. For validating the correctness and effectiveness of theoretical analysis, two representative application cases of permanent magnet synchronous motor (PMSM) and food web system (FWS) are selected at last.

Study on asymptotic behavior of stochastic Lotka\u2013Volterra system in a polluted environment

A three-species non-autonomous stochastic Lotka–Volterra food web system in a polluted environment is proposed, and the existence of positive periodic solutions of this system is established by constructing a proper Lyapunov function. Then the extinction property and its threshold between persistence and extinction are discussed by using Itô’s formula and the strong law of large numbers of martingale, and the sufficient condition of a.s. exponential stability of equilibrium point is obtained. Finally, the conclusions are tested by several numerical simulations.

The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear

The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels. It is assumed that the generalist predator grows logistically using the Leslie-Gower type of growth function. All the solution properties of the model are studied. Local dynamics behaviors are investigated. The basin of attraction for each equilibrium is determined using the Lyapunov function. The conditions of persistence of the model are specified. The study of local bifurcation in the model is done. Numerical simulations are implemented to show the obtained results. It is watched that the system is wealthy in its dynamics including chaos. The fear factor works as a stabilizing factor in the system up to a specific level; otherwise, it leads to the extinction of the predator. However, increasing the prey’s group defense leads to extinction in predator species.

The effect of prey refuge on the dynamics of three species food web system

In this paper, a mathematical model is proposed to study the effect of prey refuge on the dynamics of three species food web system. The food web comprises of a single prey and two competing predators. The two predators predate their prey following Holling type II functional response. In this work we discussed boundedness of the system, existence condition of the equilibrium points and the Jacobean matrix is obtained by linearization techniques. The local stability of the equilibrium points was discussed by using Routh-Hurwitz criteria and the global stability of the equilibrium points by constructing suitable Lyapunov function. Numerical simulation is conducted to support the analytical result. Finally, the effect of prey refuge on the dynamics of one prey two predator was discussed based on the analytical and numerical simulation results. From the numerical simulations, it is found that the dynamical system is persistent for a small value of the refuge constant. However, an increase in the refuge constant leads to the extinction of one of the predator species.

Impacts of environmental factors on the food web structure, energy flows, and system attributes along a subtropical urban river in southern China

Tropical and subtropical rivers are being subjected to multiple stressors from human disturbance (e.g., water pollution and habitat degradation). Understanding the relationship between environmental conditions and the river ecosystem is important for improving river management. We built 14 Ecopath models composed of 28 functional groups (trophic levels [TLs] of 1.0–3.8) along a subtropical urban river to explore the influence of environmental changes on system attributes. From headwaters to downstream, the model outputs showed that the transfer efficiency (TE), energy flow parameters, and ecosystem theory indices exhibited significant (P < 0.05) differences across a longitudinal gradient of disturbance, indicating heterogeneous attributes of local river segments. The high TE values of TLs I, II, and III separated the upper, middle, and lower reaches, respectively, which could be attributed to the shift in dominant consumption flows from upstream ‘periphyton – aquatic insects – insectivorous fish’ to midstream ‘detritus – shrimp – crustaceavorous fish’ and to downstream ‘phytoplankton – filter-feeding invertebrates/fish’. Structural equation modelling was used to test the causal relationships among environmental variables and demonstrated that abiotic factors directly influenced biomass composition and indirectly influenced trophic networks. Water quality, including dissolved oxygen and flow velocity; habitat characteristics, such as riffles, cobble-gravel substrate, and seasonal floodplain; and biological indicators, including the relative contributions (%) of decapods, insectivorous fish, and insect scrapers to biomass composition, had significant (P < 0.05) positive impacts on system maturity (evaluated by omnivory, connectance, and cycling indices). In the future, it will be possible to evaluate the health of river ecosystems by monitoring representative environmental factors, which could be a cost-effective approach to system-level improvement.

The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

This paper aims to study the role of a prey refuge that depends on both prey and predator species on the dynamics of a food web model. It is assumed that the food transfer among the web levels occurs according to Lotka-Volterra functional response. The solution properties, such as existence, uniqueness, and uniform boundedness, are discussed. The local, as well as the global, stabilities of the solution of the system are investigated. The persistence of the system is studied with the assistance of average Lyapunov function. The local bifurcation conditions that may occur near the equilibrium points are established. Finally, numerical simulation is used to confirm our obtained results. It is observed that the system has only one type of attractors that is a stable point, while periodic dynamics do not exist even on the boundary planes.

Spatial distribution of zooplankton in response to ecological dynamics in tropical shallow lake: insight from Lake Malombe, Malawi

This study assessed zooplankton density and Chl-a amount to understand their spatial and seasonal variation in Lake Malombe. Samples were collected for analysis during the hot, dry season (HDS) and cool, dry, windy season (CDWS). The zooplankton identified were Tropodiaptomus cunningtoni (TC), Mesocyclops aequatorialis aequatorialis (MAA), Thermocyclops neglectus (TN), Bosmina longirostris (BL), Diaphanosoma spp. (DS), and Nauplii. These zooplankton groups belong to copepods, Cyclopidae, Cladocera, Ctenopod, and Rotifers. Chl-a exhibited a substantial seasonal variation, with the highest concentration observed in HDS and lowest in CDWS. Zooplankton such as T. cunningtoni, M. aeq. aequatorialis, T. neglectus, B. longirostris, Diaphanosoma spp, Nauplii, and Rotifer increased during the HDS. The water temperatures (WT), pH, Dissolved Oxygen (DO), and Chl-a positively correlated with all zooplankton densities. Sodium (Na+) and Potassium (K+) ions positively correlated with TC, MAA, DS, Nauplii, and Rotifers. Chloride ion (Cl-) positively correlated with DS, Rotifers, while Carbonate ion (CO3 2-) positively correlated with TC. Bicarbonate (HCO3 -) correlated positively with DS and Rotifers, while TDS correlated negatively with BL, Nauplii, and Rotifers. Nitrite affected zooplankton density negatively, while SRP had a positive effect. The study revealed that physical-chemical variables, some significant ions, and Chl-a are the most critical factors influencing the spatial and seasonal variation of zooplankton density in the lake. These findings demonstrate the interaction between physical-chemical variables, Chl-a, and zooplankton and highlight the significance of ecological understanding of the complex dynamics of the food web system in shallow tropical lakes such as Lake Malombe- under the changing climate.

Impact of awareness on environmental toxins affecting plankton dynamics: a mathematical implication

The widespread problem of water pollution due to enhanced concentration of anthropogenic effluents is becoming a global issue. Public environmental awareness may be a plausible factor for the control of toxicants in the aquatic medium. The present paper is devoted to study the impact of awareness among human on reduction of environmental toxins affecting planktonic system. The provision of awareness among people helps to maintain the ecological balance of the system by reducing the input rate of toxicants through anthropogenic sources. The conditions for existence and local asymptotic stability of all feasible steady states of the system are derived. Our study reveals that the system is stable for low or high input rate of toxicants, but for intermediate ranges, the system produces oscillations by destroying the stable dynamics. Moreover, for very large level of pollutants, zooplankton disappears from the system. Importantly, the limited supply of additional food to zooplankton prevents the crash of aquatic food web system. Sensitivity results evoke that environmental toxins can be reduced to a low level by imparting awareness among human, thereby maintaining the rhythm of the planktonic ecosystem.

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.