Food Web System Research Articles

Predicting phase and sensing phase coherence in chaotic systems with machine learning.

Recent interest in exploiting machine learning for model-free prediction of chaotic systems focused on the time evolution of the dynamical variables of the system as a whole, which include both amplitude and phase. In particular, in the framework based on reservoir computing, the prediction horizon as determined by the largest Lyapunov exponent is often short, typically about five or six Lyapunov times that contain approximately equal number of oscillation cycles of the system. There are situations in the real world where the phase information is important, such as the ups and downs of species populations in ecology, the polarity of a voltage variable in an electronic circuit, and the concentration of certain chemical above or below the average. Using classic chaotic oscillators and a chaotic food-web system from ecology as examples, we demonstrate that reservoir computing can be exploited for long-term prediction of the phase of chaotic oscillators. The typical prediction horizon can be orders of magnitude longer than that with predicting the entire variable, for which we provide a physical understanding. We also demonstrate that a properly designed reservoir computing machine can reliably sense phase synchronization between a pair of coupled chaotic oscillators with implications to the design of the parallel reservoir scheme for predicting large chaotic systems.

Ecological Models on Multi Species Interaction within Unlimited Resources

In this paper, we present a three species food web system in that two species are interacting mutually and a third species, which is a predator to the first species and host for the second species i.e. there is a commensalism interaction between second and third species. All three species considered in unbounded availability of natural resources. The analytical investigations of this ecological model are observed by employing known direct methods if not by numerical methods. This model is characterized by a system of first order nonlinear ordinary coupled differential equations. We investigate three cases: (1) The death rate of any one (say third species) species is greater than its birth rate. (2) The death rates of any two species (say second, third) are greater than their birth rates. (3) The death rates of all the species are greater than their birth rates. Further the local stability at existing equilibrium points and global stability by suitable parametric values to the model equations are examined. The numerical simulations are supporting the analytical findings. As a whole we can conclude that the ecological food systems involving such kind of interactions may exist for a long time under certain environmental conditions.

Modelling the impact of tidal range energy on species communities

Tidal energy has the potential to form a key component of the energy production in a number of countries, including the UK. Nonetheless, the deployment of tidal energy systems is associated with potential environmental impacts as prime resource sites often coincide with unique ecosystems inhabited by sensitive organisms. Previous studies have generally focused on the hydrodynamic impact of tidal energy schemes, i.e. how schemes alter the flow dynamics and sedimentary transport processes. Whilst these efforts are key in understanding environmental impacts, there is no straightforward step for translating sediment to faunal changes. Species distribution models offer methods to quantitatively predict certain possible impacts of tidal energy extraction. The River Severn is a distinguished candidate region for tidal energy in the UK featuring sites under stringent ecological protection regulations. We examine the impact of a proposed Severn tidal barrage on 14 species via the linking of hydrodynamic modelling to species distribution models. Through a selection of species that are linked via a simple food web system we extrapolate changes in prey species to the respective predator species. We show that species at lower trophic levels would be adversely affected by the barrage, but higher trophic level organisms increase in possible habitable area. Once food web relationships are acknowledged this increase in habitat area decreases, but is still net positive. Overall, all 14 species were affected, with most gaining in distribution area, and only four losing distribution area within the Severn Estuary. We conclude that a large-scale tidal barrage may have detrimental and complex impacts on species distribution, altering food web dynamics and altering food availability in the Severn Estuary. The methodology outlined herein can be transferred to the assessment and optimisation of prospective projects globally to aide in the sustainable introduction of the technology.

A nonautonomous model for the effect of environmental toxins on plankton dynamics

The increasing input of environmental toxins in aquatic systems raises concerns regarding the environmental exposure and impact of toxins on natural aquatic environments. Phytoplankton and zooplankton appear to be among the most sensitive aquatic organisms to environmental toxins. Moreover, toxin-producing phytoplankton plays an important role in regulating the real aquatic ecosystems. In this paper, the combined effects of these factors on the dynamics of phytoplankton–zooplankton interactions are investigated. The phytoplankton grows logistically, but their growth rate is suppressed due to the presence of environmental toxins. The zooplankton is assumed to be generalist and follows logistic growth in the absence of phytoplankton. Also, it is considered that toxicants in the environment are increased constantly due to different natural and human behaviors. Global sensitivity analysis helps to identify the most significant parameters that reduce the environmental toxins in the system. Among these, the input rate of environmental toxins, contact rate between phytoplankton and environmental toxins, and environmental toxins-induced growth suppression of phytoplankton have destabilizing effect on the dynamics of system, while the depletion rate of environmental toxins has stabilizing effect. Therefore, it is imperative to modulate the depletion rate of environmental toxins to prevent the crash of the aquatic food web system. Further, we incorporate seasonal variations in the model, letting the parameters become functions of time. Sufficient conditions for the existence and stability of positive periodic solutions are obtained. We also derive conditions for existence, uniqueness and stability of a positive almost periodic solution. Large values of time-dependent toxin release by phytoplankton and input rate of environmental toxins induce periodic solutions of the nonautonomous system while the corresponding autonomous system exhibits a stable focus. Interestingly, our nonautonomous system exhibits bursting patterns for two slow rationally related excitation frequencies. Finally, we convert our deterministic autonomous model into stochastic model by introducing additive noise term. We find that the stability of the system gets disturbed in the presence of environmental fluctuation.

On an Impulsive Food Web System with Mutual Interference and Distributed Time Delay

In this paper, we present a predator-prey system with mutual interference and distributed time delay and study its dynamical behavior. Based on the existence and universality of mutual interference among species, it is necessary to further study an impulsive food web system. By using stability theory, slight perturbation technique, and comparison theorem, we obtain some theoretical results of the system, such as boundedness and permanence. Moreover, numerical experiments are used to verify the theoretical results and to explore the dynamical behavior of the system, which exhibits rich dynamical behavior such as chaotic oscillation, periodic oscillation, symmetry-breaking bifurcations, chaotic crises, and period bifurcation. Finally, we give some practical guidelines for biological systems based on the theoretical results and numerical experiments of the system.

An ecological application of sustainability and sustainizability over sets

AbstractThe sustainability over sets and sustainizability over sets concepts have been recently introduced as sustainable system analysis and synthesis tools, respectively, with broad flexibility in incorporating human input. In this work, these two concepts are applied to an ecological food web system, describing the flow of biomass among different organisms of an ecosystem with 10 compartments aggregated in five trophic levels. The obtained results first show that this ecosystem is not sustainable over any set, imposing upper and lower numerical bounds on the population of each species, and accounting for sinusoidal variations in plant growth. It is subsequently established that the system can be sustainized over such sets through appropriate external actions.Statement of industrial relevanceBy presenting a mathematical viewpoint for ecological sustainability of food web structures, the presented article can be informative to researchers working on environmental sustainability, and in particular on assessing and ensuring the sustainability of processes involving microbial populations and remediation/treatment of solid or aqueous waste processes.

Hopf bifurcation and chaos control for a Leslie\u2013Gower type generalist predator model

This paper is concerned with chaos control and bifurcations of the Leslie–Gower type generalist predator model in a tri-trophic food web system with the time-delayed feedback control. First, the distribution of the roots of the related characteristic equations is analyzed by the polynomial theorem, the conditions to guarantee the existence of Hopf bifurcation are given by choosing the time delay as a bifurcation parameter. Then, the explicit formula for direction of Hopf bifurcation and stability of periodic solutions bifurcating are determined by using the normal form theory and center manifold theorem. Finally, the correctness of our theoretical analysis is verified by some numerical simulation.

The dynamics of nutrient, toxic phytoplankton, nontoxic phytoplankton and zooplankton model

<p>The objective of this paper is to study the dynamical behavior of an aquatic food web system. A mathematical model that includes nutrients, phytoplankton and zooplankton is proposed and analyzed. It is assumed that, the phytoplankton divided into two compartments namely toxic phytoplankton which produces a toxic substance as a defensive strategy against predation by zooplankton, and a nontoxic phytoplankton. All the feeding processes in this food web are formulating according to the Lotka-Volterra functional response. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability conditions of all possible equilibrium points are established. The occurrence of local bifurcation and Hopf bifurcation are investigated. Finally, numerical simulation is used to study the global dynamics of this model.</p>

Exploring stochasticity and imprecise knowledge based on linear inequality constraints.

This paper explores the stochastic dynamics of a simple foodweb system using a network model that mimics interacting species in a biosystem. It is shown that the system can be described by a set of ordinary differential equations with real-valued uncertain parameters, which satisfy a set of linear inequality constraints. The constraints restrict the solution space to a bounded convex polytope. We present results from numerical experiments to show how the stochasticity and uncertainty characterizing the system can be captured by sampling the interior of the polytope with a prescribed probability rule, using the Hit-and-Run algorithm. The examples illustrate a parsimonious approach to modeling complex biosystems under vague knowledge.

Removal of Agricultural Non-Point Source Pollutants by Artificial Aquatic Food Web System: A Study Case of the Control of Cynobacterial Bloom in Jiyu River

An artificial aquatic food web (AAFW) system was designed to remove the non-point source pollutants in eutrophic Jiyu river. A certain amount of Scenedesmus obliquus and Daphnia pulex was cultured in the system for the control of serious cyanobacterial bloom. The AAFW system was a continuous-flow system including one storage basin of 3 m3 capacity with polluted river water (the total nitrogen-TN: 4.49 mg⋅l-1; the total phosphorus-TP: 0.192 mg⋅l-1), one phytoplankton tank of 3 m3 capacity with an initial concentrations of S. obliquus about 5.8 × 103 ind⋅l-1, and one zooplankton growth chamber of 1.5 m3 capacity with an initial abundance of D. pulex about 22.5 ind⋅l-1. The system was optimized by setting hydraulic retention time of phytoplankton tank as 5 days and the experiments were operated for 45 days. Compared with the polluted river, TN and TP were removed about 28% and 47% by the AAFW system, respectively. The biomass of phytoplankton decrease from 6.33 mg⋅l-1 to 1.48 mg⋅l-1 and the percentage of cyanobacteria decrease from 43.93% to 2.36%, the biomass of Crustacean zooplankton increase from 0.34 mg⋅l-1 to 1.53 mg⋅l-1 and the percentage of D. pulex increase from 19.19% to 57.62%. Our results indicated that the AAFW system not only is an efficient, flexible system for reducing nutrient levels in tributary rivers, but also has an ability to control the cyanobacteria bloom and rebuilding the aquatic ecosystem from the polluted river water.

Spiral periodic structures in a parameter plane of an ecological model

We investigate a parameter plane of a set of three autonomous, ten-parameter, first-order nonlinear ordinary differential equations, which models a tri-trophic food web system. By using Lyapunov exponents, bifurcation diagrams, and trajectories in the phase-space, to numerically characterize the dynamics of the model in a parameter plane, we show that it presents typical periodic structures embedded in a chaotic region, forming a spiral structure that coils up around a focal point while period-adding bifurcations take place.

Temporal variability of the microbial food web (viruses to ciliates) under the influence of the Black Sea Water inflow (N. Aegean, E. Mediterranean)

Τhe entire pelagic microbial food web was studied during the winter-spring period in the frontal area of the North Aegean Sea. Abundance of viruses, heterotrophic bacteria, cyanobacteria, auto- and hetero-trophic flagellates, and ciliates, as well as bacterial production, were measured at three stations (MD1, MD2, MD3) situated along a N-S transect between the area directly influenced by the inflowing Black Sea water and the area covered by the Levantine water. Samples were collected in December 2009, and January, March, April, and May 2011. Station MD1 exhibited the highest values of abundance and integrated biomass of all microbial groups and bacterial production during all months, and MD3 the lowest. Bacteria dominated the total integrated biomass at all stations and months, followed by cyanobacteria, auto-, hetero-trophic flagellates and ciliates. On a temporal scale, the microbial food web was less important in March as all microbial parameters at all stations showed the lowest values. After the phytoplankton bloom in March, the heterotrophic part of the microbial food web (mainly) strongly increased, though the intensity of the phenomenon was diminished from North to South. Pico-sized plankton was found to be heterotrophic whereas nanoplankton was autotrophic. It seems that the influence of the Black Sea water on station MD1, permanent throughout the study period of early winter to late spring, was reflected in all microbial populations studied, and produced a more productive pelagic food web system, with potential consequences for the upper trophic levels.

Bridging the gap between marine biogeochemical and fisheries sciences; configuring the zooplankton link

Exploring climate and anthropogenic impacts on marine ecosystems requires an understanding of how trophic components interact. However, integrative end-to-end ecosystem studies (experimental and/or modelling) are rare. Experimental investigations often concentrate on a particular group or individual species within a trophic level, while tropho-dynamic field studies typically employ either a bottom-up approach concentrating on the phytoplankton community or a top-down approach concentrating on the fish community. Likewise the emphasis within modelling studies is usually placed upon phytoplankton-dominated biogeochemistry or on aspects of fisheries regulation. In consequence the roles of zooplankton communities (protists and metazoans) linking phytoplankton and fish communities are typically under-represented if not (especially in fisheries models) ignored. Where represented in ecosystem models, zooplankton are usually incorporated in an extremely simplistic fashion, using empirical descriptions merging various interacting physiological functions governing zooplankton growth and development, and thence ignoring physiological feedback mechanisms. Here we demonstrate, within a modelled plankton food-web system, how trophic dynamics are sensitive to small changes in parameter values describing zooplankton vital rates and thus the importance of using appropriate zooplankton descriptors. Through a comprehensive review, we reveal the mismatch between empirical understanding and modelling activities identifying important issues that warrant further experimental and modelling investigation. These include: food selectivity, kinetics of prey consumption and interactions with assimilation and growth, form of voided material, mortality rates at different age-stages relative to prior nutrient history. In particular there is a need for dynamic data series in which predator and prey of known nutrient history are studied interacting under varied pH and temperature regimes.

Decreasing Excess Biomass from Municipal Wastewater Using an Artificial Food Web System

AbstractIn this biotechnology research, an artificial food web composed of bacteria, Chlorella, and Daphnia magna was used to remove organic loading by enriching the activated biomass and simultaneously reducing the production of excess biomass from synthetic municipal wastewater. In the continuous-flow experiment under optimal conditions, almost 49.99% and 14.42% of the bacteria were reduced in the Chlorella chamber and the D. magna chamber, respectively, and 90.91% of the Chlorella was grazed by Daphnia in the D. magna chamber. Meanwhile, the removal rates of chemical oxygen demand (COD), total nitrogen (TN), and total phosphorus (TP) were 85.95%, 47.02%, and 39.78%, respectively, where 73.68%, 10.67%, and 1.60% of COD, 19.94%, 25.59%, and 1.49% of TN, 15.71%, 7.28%, and 16.79% of TP were removed in the bacterial chamber, Chlorella chamber, and D. magna chamber, respectively. This study would promote the understanding of using a pure food chain for maximal reduction of excess biomass in a large-scale tr...

Improving the Effectiveness of a Nutrient Removal System Composed of Microalgae and Daphnia by an Artificial Illumination

For determining the effect of illumination on nutrient removal in an artificial food web (AFW) system, we launched a pilot continuous-flow system. The system consisted of a storage basin, a phytoplankton growth chamber, and a zooplankton growth chamber. A 25,000 Lux AFW-light emitting diode (LED) on system and an AFW-LED off system were separately operated for 10 days. In the AFW-LED on system, the maximum chlorophyll-a concentration of the phytoplankton chamber was four times higher than that of the AFW-LED off system. With artificial nighttime illumination, the microalgae became both smaller and more nutritious; the microalgae became high quality food for the zooplankton, Daphnia magna. Consequently, this zooplankton became more efficient at extracting nutrients and grew more densely than in the AFW-LED off system condition. In the LED-on condition, the amounts of total nitrogen (TN) and total phosphorus (TP) flowing into the system for 10 days were 84.7 g and 20.4 g, and the amounts flowing out were 19.5 g (23%) and 4.0 g (20%), respectively. In contrast, in the LED-off condition, 83.8 g and 20.6 g of TN and TP flowed into the system while 38.8 g (46%) and 6.8 g (33%) flowed out, respectively. Artificial illumination significantly improves the removal rate of nutrients in an AFW system.

Geometry of the Poincaré compactification of a four-dimensional food-web system

In this paper, the behavior of dynamics ‘at infinity’ of a four-dimensional autonomous food web system has been investigated. For this, a topological method has been developed to understand the geometry of the Poincaré compactification which investigate the behavior of the vector field at infinity. The global phase portrait has been shown on the Poincaré disc.

Dynamics of Leslie–Gower type generalist predator in a tri-trophic food web system

In this paper, the dynamics of a tri-trophic food web system consists of Leslie–Gower type generalist predator has been explored. The system is bounded under certain conditions. The Hopf-bifurcation has been established in the phase planes. The bifurcation diagrams exhibit coexistence of all three species in the form of periodic/chaotic solutions. The “snail-shell” chaotic attractor has very high Lyapunov exponents. The coexistence in the form of stable equilibrium is also possible for lower values of parameters. The two-parameter bifurcation diagrams are drawn for critical parameters.

Ecotoxicity of the veterinary pharmaceutical ivermectin tested in a soil multi-species (SMS) system

The present study tests the effect of antiparasitic compound ivermectin in a constructed food-web system, a soil multi-species (SMS) higher tier test system. Mutualism, competition and predation within the SMS system were introduced by the addition of five collembolan species, one enchytraeid and a predatory mite species. Bait lamina sticks were incorporated as a measure of functional toxicity, attempting to the integrated feeding activity of the invertebrates. The study showed that on the community level all treatments were significantly affecting the community abundance and composition and that the decrease in abundance corresponded well with increasing exposure concentration for all species. Since all concentrations had significant adverse effect on the community structure, the community-based no-effect-concentration is below the lowest test concentration of 0.25 mg kg−1, whereas the EC10 for the individual species were as low as 0.05 mg kg−1. The bait lamina respond was only affected at the highest exposure concentration.

Omnivory, vertical food‐web structure and system productivity: stable isotope analysis of freshwater planktonic food webs

Summary1. The energetic hypothesis proposes that the vertical structure of food webs should increase in height with increasing system productivity. I measured the trophic positions and extent of trophic separation between the invertebrate planktivores Mysis relicta and Chaoborus spp. and their putative zooplankton prey along a gradient of lake productivity with the use of stable nitrogen isotopes.2. In lakes of low productivity, these planktivores were found to be herbivorous, becoming omnivorous at intermediate lake productivities, and only able to be truly zooplanktivorous as lakes approached mesotrophy. A subsequent secondary analysis of literature data revealed that the strength of top‐down trophic cascades among these organisms increased with lake productivity as reflected by relationships between the abundance of planktivores and that of phytoplankton.3. Increased omnivory under conditions of low productivity, effectively shortening the vertical structure of food webs as predicted by the energetic hypothesis, may produce increased community stability.

영양흐름모형을 이용한 1994년 신지도 해양생태계 해석

1994년 신지도 해양생태계에서 관측된 자료를 이용 Ecopath 영양흐름 모델을 구축하였다. 모델은 생체량과 먹이 조성 자료를 이용하여 우점종의 개체군 역학, 주요 영양흐름의 경로, 생태적 특성을 해석하여 다른 해양 생태계와 비교하였다. 계를 구성하는 그룹은 17개로서 해조류, 식물플랑크톤, 동물플랑크톤, 복족류, 다모류, 이매패류, 극피동물, 갑각류, 두족류, 망둑어, 양태, 홍어, 보구치, 베도라치, 장어, 가자미 및 유기쇄설물을 포함한다. 실험결과 영양단계는 일차생산자와 유기쇄설물로부터 최고 소비자인 가자미 그룹에 이르기까지 1.0~4.0의 범위를 보였다. 계의 총생체량(B)은 0.1 <TEX>$kgWW/m^2$</TEX>, 총순일차생산량(PP)과 총통과흐름(TST)은 각기 1.6, 3.4 <TEX>$kgWW/m^2/yr$</TEX>이며, TST는 총소비 7%, 총이출 43%, 총호흡(TR) 4%, 총유기쇄설물전환 46%의 합으로 구성된다. PP/TR은 0.012, PP/B는 0.015, 잡식지수는 0.12, 핀순환지수는 0.7%, 평균경로거리는 2.15, 지배용량(A)과 발전용량(C)은 각기 4.1과 8.2 <TEX>$kgWW/m^2/yr$</TEX> bits이며, 상대지배용량(A/C)은 51%를 보였다. 특히 본 연구는 영양상호영향 해석에서 간접적인 경로를 통한 영향을 4가지 형태로 구분하여 기술하였다. 총통과흐름 기운데 총이출이 높은 것은 계가 반폐쇄된 만과 다르게 물질 교환이 크다는 의미이며, 연구해역이 신지도, 조약도, 생일도로 둘러싸인 수로를 통해 강한 조류가 미치는 지역임을 보아 쉽게 알 수 있다. 생태계 이론 및 순환지수 가운데 총생체량, 총통과흐름, PP/TR, 핀순환지수, 평균경로 거리, 잡식지수는 비교적 낮게 산출되었는데, 이는 오덤의 이론에 따라 계가 충분히 성숙하지 못한 근거로 해석되었고, 정보지수인 상대지배용량이 크게 산출된 것은 계가 최대로 발전할 수 있는 용량이 작다는 것으로 해석되었다. 이상의 결과로 보아 연구해역은 영양물질의 외부 유출이 커 계가 발전할 수 있는 가능성은 한정되고 현재 발전하고 있는 단계인 것으로 판단되었다. 본 연구는 신지도 해양생태계의 영양흐름 구조와 생태계 특성을 해석한 시험연구로서 향후 생태계의 변화를 비교하거나 관리에 유용할 것으로 판단된다. A balanced trophic model for Sinjido marine ecosystem was constructed using ECOPATH model and data obtained 1994 in the region. The model integrates available information on biomass and food spectrum, and analyses ecosystem properties, dynamics of the main species populations and the key trophic pathways of the system, and then compares these results with those of other marine environments. The model comprises 17 groups of benthic algae, phytoplankton, zooplankton, gastropoda, polychaeta, bivalvia, echinodermata, crustacean, cephalopoda, goby, flatfish, rays and skates, croaker, blenny, conger, flatheads, and detritus. The model shows trophic levels of 1.0~4.0 from primary producers and detritus to top predator as flathead group. The model estimates total biomass(B) of 0.1 <TEX>$kgWW/m^2$</TEX>, total net primary production(PP) of 1.6 <TEX>$kgWW/m^2/yr$</TEX>, total system throughput(TST) of 3.4 <TEX>$kgWW/m^2/yr$</TEX> and TST's components of consumption 7%, exports 43%, respiratory flows 4% and flows into detritus 46%. The model also calculates PP/TR of 0.012, PP/B of 0.015, omnivory index(OI) of 0.12, Fin's cycling index(FCI) of 0.7%, Fin's mean path length(MPL) of2.11, ascendancy(A) of 4.1 <TEX>$kgWW/m^2/yr$</TEX> bits, development capacity(C) of 8.2 <TEX>$kgWW/m^2/yr$</TEX> bits and A/C of 51%. In particular this study focuses the analysis of mixed trophic impacts and describes the indirect impact of a groupb upon another through mediating one based on 4 types. A large proportion of total export in TST means higher exchange rate in the study region than in semi enclosed basins, which seems by strong tidal currents along the channels between islands, called Sinjido, Choyakdo and Saengildo. Among ecosystem theory and cycling indices, B, TST, PP/TR, FCI, MPL and OI are shown low, indicating the system is not fully mature according to Odum's theory. Additionally, high A/C reveals the maximum capacity of the region is small. To sum up, the study region has high exports of trophic flow and low capacity to develop, and reaches a development stage in the moment. This is a pilot research applied to the Sinjido in terms of trophic flow and food web system such that it may be helpful for comparison and management of the ecosystem in the future.