Plankton-toxin interaction with a variable input nutrient

A simple model of phytoplankton–zooplankton interaction with a periodic input nutrient is presented. The model is then used to study a nutrient–plankton interaction with a toxic substance that inhibits the growth rate of plankton populations. The effects of the toxin upon the existence, magnitude, and stability of the periodic solutions are discussed. Numerical simulations are also provided to illustrate analytical results and to compare more complicated dynamical behaviour.     

Omnivory by Planktivores Stabilizes Plankton Dynamics, but May Either Promote or Reduce Algal Biomass

Classical models of phytoplankton–zooplankton interaction show that with nutrient enrichment such systems may abruptly shift from limit cycles to stable phytoplankton domination due to zooplankton predation by planktivorous fish. Such models assume that planktivorous fish eat only zooplankton, but there are various species of filter-feeding fish that may also feed on phytoplankton. Here, we extend these classical models to systematically explore the effects of omnivory by planktivorous fish. Our analysis indicates that if fish forage on phytoplankton in addition to zooplankton, the alternative attractors predicted by the classical models disappear for all realistic parameter settings, even if omnivorous fish have a strong preference for zooplankton. Our model also shows that the level of fish biomass above which zooplankton collapse should be higher when fish are omnivorous than when fish are zooplanktivorous. We also used the model to explore the potential effects of the now increasingly common practice of stocking lakes with filter-feeding fish to control cyanobacteria. Because omnivorous filter-feeding fish forage on phytoplankton as well as on the main grazers of phytoplankton, the net effect of such fish on the phytoplankton biomass is not obvious. Our model suggests that there may be a unimodal relationship between the biomass of omnivorous filter-feeding fish and the biomass of phytoplankton. This implies that to manage for reductions in phytoplankton biomass, heavy stocking or strong reduction of such fish is best.     

Oscillations in plankton models with nutrient recycling

Plankton--nutrient interaction models with both instantaneous and delayed nutrient recycling are considered. The system consists of three components: autotrophic phytoplankton, herbivorous zooplankton and dissolved limiting nutrient. Local stability of the equilibria is analysed. It is shown that the positive equilibrium loses its stability when the nutrient input concentration passes through a critical value and the Hopf bifurcation occurs that induces oscillations of the populations. Numerical simulations are carried out to illustrate the obtained results.     

Phytoplankton–zooplankton dynamics in periodic environments taking into account eutrophication

In this paper, we derive and analyze a mathematical model for the interactions between phytoplankton and zooplankton in a periodic environment, in which the growth rate and the intrinsic carrying-capacity of phytoplankton are changing with respect to time and nutrient concentration. A threshold value: “Predator’s average growth rate” is introduced and it is proved that the phytoplankton–zooplankton ecosystem is permanent (both populations survive cronically) and possesses a periodic solution if and only if the value is positive. We use TP (Total Phosphorus) concentration to mark the degree of eutrophication. Based on experimental data, we fit the growth rate function and the environmental carrying capacity function with temperature and nutrient concentration as independent variables. Using measured data of temperature on water bodies we fit a periodic temperature function of time, and this leads the growth rate and intrinsic carrying-capacity of phytoplankton to be periodic functions of time. Thus we establish a periodic system with TP concentration as parameter. The simulation results reveal a high diversity of population levels of the ecosystem that are mainly sensitive to TP concentration and the death-rate of zooplankton. It illustrates that the eruption of algal bloom is mainly resulted from the increasing of nutrient concentration while zooplankton only plays a role to alleviate the scale of algal bloom, which might be used to explain the mechanism of algal bloom occurrence in many natural waters. What is more, our results provide a better understanding of the traditional manipulation method.     

Competing predators for a prey in a chemostat model with periodic nutrient input

A system of ordinary differential equations is used to model the interactions of n competing predators on a single prey population in a chemostat environment with a periodic nutrient input. In the case of one or no predators, criteria for the existence of periodic solutions are given. In the general case, conditions for all populations to persist are derived.Research is in part based on a Ph.D. thesis submitted to the Faculty of Graduate Studies, University of AlbertaResearch is partly supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A4823     

Phytoplankton food quality control of planktonic food web processes

We developed a mechanistic model of nutrient, phytoplankton, zooplankton and fish interactions to test the effects of phytoplankton food quality for herbivorous zooplankton on planktonic food web processes. When phytoplankton food quality is high strong trophic cascades suppress phytoplankton biomass, the zooplankton can withstand intense zooplanktivory, and energy is efficiently transferred through the food web sustaining higher trophic level production. Low food quality results in trophic decoupling at the plant-animal interface, with phytoplankton biomass determined primarily by nutrient availability, zooplankton easily eliminated by fish predation, and poor energy transfer through the food web. At a given nutrient availability, food quality and zooplanktivory interact to determine zooplankton biomass which in turn determines algal biomass. High food quality resulted in intense zooplankton grazing which favored fast-growing phytoplankton taxa, whereas fish predation favored slow-growing phytoplankton. These results suggest algal food quality for herbivorous zooplankton can strongly influence the nature of aquatic food web dynamics, and can have profound effects on water quality and fisheries production. Handling editor: D. Hamilton     

Role of infochemical mediated zooplankton grazing in a phytoplankton competition model

Infochemicals released by marine phytoplankton play important roles in food web interactions by influencing the feeding behavior and selectivity of zooplanktonic predators. Recent modeling efforts have focused on the role of such chemicals as toxic grazing deterrents in phytoplankton competition. However, infochemicals may also be utilized as grazing cues, leading predators to profitable foraging patches. Here we investigate the role of infochemical mediated zooplankton grazing in a standard 3-species phytoplankton competition model, with the aim of further elucidating the ecological role of phytoplankton derived infochemicals. We then extend this to consider a more realistic 4-species model. The models produce a range of solutions depending on the strength of competition and microzooplankton grazing selectivity. Our key result is that infochemical chemoattractants, which increase the susceptibility of the producer to grazing, can provide a refuge for both competing phytoplankton species by attracting carnivorous copepods to consume microzooplankton grazers in a multi-trophic interaction. Our results indicate that infochemicals potentially have important consequences for the dynamics of marine food webs.     

A nonautonomous model for the effects of refuge and additional food on the dynamics of phytoplankton-zooplankton system

In this paper, a mathematical model for the interacting dynamics of phytoplankton-zooplankton is proposed. The phytoplankton have the ability to take refuge and release toxins to avoid over predation by zooplankton. The zooplankton are provided some additional food to persist in the system. The phytoplankton are assumed to be affected directly by external toxic substances whereas zooplankton are affected indirectly by feeding on the affected phytoplankton. We incorporate seasonal variations in the model, assuming the level of nutrients, refuge and the rate of toxins released by phytoplankton as functions of time. Our results show that when high toxicity and refuge cause extinction of zooplankton, providing additional food supports the survival of zooplankton population and controls the phytoplankton population. Prey refuge and additional food have stabilizing effects on the system; higher values of the former results in extinction of zooplankton whereas phytoplankton disappear for larger values of the latter. Seasonality in nutrients level and toxins released by phytoplankton generate higher periodic solutions while time-dependent refuge of phytoplankton causes the occurrence of a period-three solution. The possibility of finding additional food for zooplankton may push back the ecosystem to a simple stable state from a complex dynamics.     

Patchiness in a minimal nutrient — phytoplankton model

We present a minimal two-component model that can exhibit various types of spatial patterns including patchiness. The model, comprising nutrients and phytoplankton, includes the effect of nutrient uptake by phytoplankton as a Holling type II functional response, and also includes the effect of zooplankton grazing on phytoplankton as a Holling type II non-dynamical term. The mean-field model without the diffusion and advection terms shows both bistability and limit-cycle oscillations as a few parameters such as the input rate of nutrients and the maximum feeding rate of zooplankton are changed. If the parameter values are chosen from the limit-cycle oscillation region, the corresponding reaction-advection-diffusion equations show spatial pattern formations by the combined effects of advection and diffusion by turbulent stirring and mixing, and biological interactions. As the nutrient input is increased, the system behaviour changes from the extinction of the entire phytoplankton to the formation of filamentous patterns, patchiness patterns and homogeneous distributions. These observations suggest that the spatial pattern of phytoplankton can function as an indicator to evaluate the eutrophication level in aquatic ecosystems.     

Effects of an invasive consumer on zooplankton communities are unaltered by nutrient inputs

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Biological control of phytoplankton by the subtropical submerged macrophytes Egeria densa and Potamogeton illinoensis: a mesocosm study

1. In temperate regions, submerged macrophytes can hamper phytoplankton blooms. Such an effect could arise directly, for instance via allelopathy, or indirectly, via competition for nutrients or the positive interaction between submerged macrophytes and zooplankton grazing. However, there is some evidence that the positive interaction between submerged macrophytes and zooplankton grazing is less marked in warmer regions, where the interaction is less well studied, and that negative effects of higher water plants on phytoplankton biomass are weaker. 2. We carried out two consecutive mesocosm experiments in Uruguay (subtropical South America) to study the effects of two common submerged macrophytes from this region (Egeria densa and Potamogeton illinoensis) on phytoplankton biomass, in the absence of zooplankton grazing. We compared phytoplankton development between different macrophyte treatments (no macrophytes, artificial macrophytes, real Egeria and real Potamogeton). We used artificial macrophytes to differentiate between physical effects (i.e. shading, sedimentation and competition with periphyton) and biological effects (i.e. nutrient competition and allelopathy). 3. In Experiment 1, we found no evidence for physical effects of macrophytes on phytoplankton biomass, but both macrophyte species seemed to exert strong biological effects on phytoplankton biomass. Only Egeria affected phytoplankton community structure, particularly tempering the dominance of Scenedesmus. Nutrient addition assays revealed that only Egeria suppressed phytoplankton through nutrient competition. 4. We performed a second mesocosm experiment with the same design, but applying saturating nutrient conditions as a way of excluding the effects of competition for nutrients. This experiment showed that both macrophytes were still able to suppress phytoplankton through biological mechanisms, providing evidence for allelopathic effects. Our results indicate that both common macrophytes are able to keep phytoplankton biomass low, even in the absence of zooplankton grazing.     

Harmful algal blooms: combining excitability and competition

Harmful algal blooms (HABs) characterized by a large concentration of toxic species appear rather rarely, but have a severe impact on the whole ecosystem. To study on possible trigger mechanisms for the emergence of HABs, we consider a nutrient-phytoplankton-zooplankton model to find the conditions under which a toxic phytoplankton species is able to form a bloom by winning the competition against its nontoxic competitor. The basic mechanism is related to the excitability of the system, i.e., the ability to develop a large response on certain perturbations. In a large class of models, a HAB results from a combined effect of nutrient enrichment and selective predation on different phytoplankton populations by zooplankton. We show that the severity of HAB is controlled by nutrient enrichment and zooplankton abundance, while the frequency of its occurrence depends on the strength of selectivity of predation. Thereby the intricate interplay between excitability, competition, and selective grazing pressure builds the backbone of the mechanism of the emergence of HABs.     

A coupled plankton system with instantaneous and delayed predation

We present two simple plankton population models: one has instantaneous predation, another has delayed predation. The models consist of two coupled differential equations representing the interaction between phytoplankton and herbivorous zooplankton with additional effect of zooplankton predation by a constant fish population. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species, and address the stability and bifurcation under different density of fish, with or without the maturation time delay. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.     

A coupled plankton system with instantaneous and delayed predation

We present two simple plankton population models: one has instantaneous predation, another has delayed predation. The models consist of two coupled differential equations representing the interaction between phytoplankton and herbivorous zooplankton with additional effect of zooplankton predation by a constant fish population. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species, and address the stability and bifurcation under different density of fish, with or without the maturation time delay. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.     

Studies on the gut contents of leptestheriella maduraiensis (Conchostraca: Branchiopoda) Nayar and Nair

Studies on the food and feeding habits of Leptestheriella maduraiensis Nayar & Nair have shown that the organisms are nonselective algal and detrital filter feeders. They utilise available food in almost similar proportions as in the overlying pond water and it is found from the present studies that the phytoplankton (Bacillariophyceae, Chlorophyceae and Cyanophyceae) form the major part of the gut (48.9%), followed by detritus (38.6%), zooplankton (11.1%) and miscellaneous items (1 .4%).Formed part of a thesis approved for the degree of Ph.D. of the Madurai University, 1973.Formed part of a thesis approved for the degree of Ph.D. of the Madurai University, 1973.     

外源输入对大亚湾大鹏澳浮游生物影响的模拟研究

本文通过建立一个简单的浮游植物、浮游动物和营养盐动力学数值模型,根据大亚湾大鹏澳秋季一个月的连续观测资料,利用线性回归分析法来求得上述动力学数值模型的一些主要参数,结果表明,降雨及陆源输入是导致该海区营养盐增加的一个重要因子;根据上述参数进行的数值模拟结果与实测结果基本吻合,同时也表明,降雨及陆源输入对该海区浮游植物和浮游动物的分布规律影响较大。     

Effects of water-column mixing on bacteria,phytoplankton, and rotifers under different levels of herbivory in a shallow eutrophic lake

Water-column mixing is known to have a decisive impact on plankton communities. The underlying mechanisms depend on the size and depth of the water body, nutrient status and the plankton community structure, and they are well understood for shallow polymictic and deep stratified lakes. Two consecutive mixing events of similar intensity under different levels of herbivory were performed in enclosures in a shallow, but periodically stratified, eutrophic lake, in order to investigate the effects of water-column mixing on bacteria abundance, phytoplankton abundance and diversity, and rotifer abundance and fecundity. When herbivory by filter-feeding zooplankton was low, water-column mixing that provoked a substantial nutrient input into the euphotic zone led to a strong net increase of bacteria and phytoplankton biomass. Phytoplankton diversity was lower in the mixed enclosures than in the undisturbed ones because of the greater contribution of a few fast-growing species. After the second mixing event, at a high biomass of filter-feeding crustaceans, the increase of phytoplankton biomass was lower than after the first mixing, and diversity remained unchanged because enhanced growth of small fast-growing phytoplankton was prevented by zooplankton grazing. Bacterial abundance did not increase after the second mixing, when cladoceran biomass was high. Changes in rotifer fecundity indicated a transmission of the phytoplankton response to the next trophic level. Our results suggest that water-column mixing in shallow eutrophic lakes with periodic stratification has a strong effect on the plankton community via enhanced nutrient availability rather than resuspension or reduced light availability. This fuels the basis of the classic and microbial food chain via enhanced phytoplankton and bacterial growth, but the effects on biomass may be damped by high levels of herbivory. Received: 3 May 1999 / Accepted: 13 April 2000     

Examination of the role of detritus food quality,phytoplankton intracellular storage capacity,and zooplankton stoichiometry on planktonic dynamics

Nutrient stoichiometric ratios are primary driving factors of planktonic food web dynamics. Ecological stoichiometry theory postulates the elemental ratios of consumer species to be homeostatic, while primary-producer stoichiometry may vary with ambient nutrient availability. The notion of phytoplankton intracellular storage is far from novel, but remains largely unexplored in modeling studies of population dynamics. We constructed a seasonally-unforced, zero-dimensional, nutrient–phytoplankton–zooplankton–detritus (NPZD) model that considers dynamic phytoplankton phosphorus reserves and quasi-dynamic zooplankton stoichiometry. A generic food quality term is used to express seston biochemical composition, ingestibility, and digestibility. We examined the sensitivity of the planktonic food web patterns to light and nutrient availability, zooplankton mortality, and detritus food quality as well as to phytoplankton intracellular storage and zooplankton stoichiometry. Our results reinforce earlier findings that high quality seston exerts a stabilizing effect on food web dynamics. However, we also found that the combination of low algal and high detritus food quality with high zooplankton mortality yielded limit cycles and multiple steady states, suggesting that the heterogeneity characterizing seston nutritional quality may have more complicated ecological ramifications. Our numerical experiments identify resource competition strategies related to nutrient transport rates and internal nutrient quotas that may be beneficial for phytoplankton to persevere in resource-limiting habitats. We also highlight the importance of the interplay between optimal stoichiometry and the factors controlling homeostatic rigidity in zooplankton. In particular, our predictions show that the predominance of phosphorus-rich and tightly-homeostatic herbivores in nutrient-enriched environments with low seston food quality can potentially result in high phytoplankton abundance, high phytoplankton-to-zooplankton ratios, and acceleration of oscillatory dynamics. Generally, our modeling study emphasizes the impact of both intracellular/somatic storage and food quality on prey–predator interactions, pinpointing an important aspect of food web dynamics usually neglected by the contemporary modeling studies.     

Response of phytoplankton and bacteria to nutrients and zooplankton: a mesocosm experiment

Although both nutrient inputs and zooplankton grazing are importantto phytoplankton and bacteria in lakes, controversy surroundsthe relative importance of grazing pressure for these two groupsof organisms. For phytoplankton, the controversy revolves aroundwhether zooplankton grazers, especially large cladocerans likeDaphnia, can effectively reduce phytoplankton populations regardlessof nutrient conditions. For bacteria, little is known aboutthe balance between possible direct and indirect effects ofboth nutrients and zooplankton grazing. However, there is evidencethat bacteria may affect phytoplankton responses to nutrientsor zooplankton grazing through direct or apparent competition.We performed a mesocosm experiment to evaluate the relativeimportance of the effects of nutrients and zooplankton grazingfor phytoplankton and bacteria, and to determine whether bacteriamediate phytoplankton responses to these factors. The factorialdesign crossed two zooplankton treatments (unsieved and sieved)with four nutrient treatments (0, 0.5, 1.0 and 2.0 µgphosphorus (P) l^–1 day^–1 together with nitrogen(N) at a N:P ratio of 20:1 by weight). Weekly sieving with 300µm mesh reduced the average size of crustacean zooplanktonin the mesocosms, decreased the numbers and biomass of Daphnia,and increased the biomass of adult copepods. Nutrient enrichmentcaused significant increases in phytoplankton chlorophyll a(4–5x), bacterial abundance and production (1.3x and 1.6x,respectively), Daphnia (3x) and total zooplankton biomass (2x).Although both total phytoplankton chlorophyll a and chlorophylla in the <35 µm size fraction were significantly lowerin unsieved mesocosms than in sieved mesocosms, sieving hadno significant effect on bacterial abundance or production.There was no statistical interaction between nutrient and zooplanktontreatments for total phytoplankton biomass or bacterial abundance,although there were marginally significant interactions forphytoplankton biomass <35 µm and bacterial production.Our results do not support the hypothesis that large cladoceransbecome less effective grazers with enrichment; rather, the differencebetween phytoplankton biomass in sieved versus unsieved zooplanktontreatments increased across the gradient of nutrient additions.Furthermore, there was no evidence that bacteria buffered phytoplanktonresponses to enrichment by either sequestering P or affectingthe growth of zooplankton.     

The effect of a lake fertilization on the stability and material utilization of a limnetic ecosystem

The interaction between the phytoplankton, zooplankton and fish populations and certain abiotic environmental factors, was investigated in an oligotrophic Norwegian lake during a 5-yr period (1974–1978). The effects of adding artificial fertilizer in 1975 and 1976 were also studied. When cladoceran dominated, the zooplankton community was able to maintain a more or less constant phytoplankton biomass and a rather low phytoplankton production even when nutrient levels were raised. In years when rotifers were dominant, algal biomass and productivity increased, despite the amount of added nutrients being lower. The regression for the relationship between daily phytoplankton P/B and daily herbivore zooplankton P/B indicated that these trophic levels were highly interdependent. A change, from large-sized to smaller herbivorous zooplankton, due to fish predation, also led to an increase in phytoplankton turnover. The investigations show that planktivorous fish may be the key factor which determines the stability of limnetic systems and controls the material transfer from the algae to the higher trophic level.