Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: A mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.     

The effects of seston food quality on planktonic food web patterns

In planktonic food webs, the conversion rate of plant material to herbivore biomass is determined by a variety of factors such as seston biochemical/elemental composition, phytoplankton cell morphology, and colony architecture. Despite the overwhelming heterogeneity characterizing the plant–animal interface, plankton population models usually misrepresent the food quality constraints imposed on zooplankton growth. In this study, we reformulate the zooplankton grazing term to include seston food quality effects on zooplankton assimilation efficiency and examine its ramifications on system stability. Using different phytoplankton parameterizations with regards to growth strategies, light requirements, sinking rates, and food quality, we examined the dynamics induced in planktonic systems under varying zooplankton mortality/fish predation, light conditions, nutrient availability, and detritus food quality levels. In general, our analysis suggests that high food quality tends to stabilize the planktonic systems, whereas unforced oscillations (limit cycles) emerge with lower seston food quality. For a given phytoplankton specification and resource availability, the amplitude of the plankton oscillations is primarily modulated from zooplankton mortality and secondarily from the nutritional quality of the alternative food source (i.e., detritus). When the phytoplankton community is parameterized as a cyanobacterium-like species, conditions of high nutrient availability combined with high zooplankton mortality led to phytoplankton biomass accumulation, whereas a diatom-like parameterization resulted in relatively low phytoplankton to zooplankton biomass ratios highlighting the notion that high phytoplankton food quality allows the zooplankton community to sustain relatively high biomass and to suppress phytoplankton biomass to low levels. During nutrient and light enrichment conditions, both phytoplankton and detritus food quality determine the extent of the limit cycle region, whereas high algal food quality increases system resilience by shifting the oscillatory region towards lower light attenuation levels. Detritus food quality seems to regulate the amplitude of the dynamic oscillations following enrichment, when algal food quality is low. These results highlight the profitability of the alternative food sources for the grazer as an important predictor for the dynamic behavior of primary producer–grazer interactions in nature.     

The development of a multi-species algal ecodynamic model for urban surface water systems and its application

An ecodynamic model that can simulate four phytoplankton species has been developed to deal with the unique characteristics of urban river systems which has manmade river profile, flow controlled by gates, severe eutrophication status, and fragile aquatic ecosystem. The ecodynamic model was developed referencing two typical models: the water quality simulation model WASP and ecological model CAEDYM. The model can simulate 11 state variables: dissolved oxygen, carbonaceous biochemical oxygen demand, ammonia nitrogen, nitrate nitrogen, organic nitrogen, inorganic phosphorus, organic phosphorus and four phytoplankton species with zooplankton as a boundary condition. The ecodynamic model was applied to Sihai section of the Beijing urban river system, where serious algal blooms broke out in recent years. The dominant phytoplankton species are Cyanophyta, Chlorophyta, Bacillariophyta, and Cryptophyta. Site-specific data on geometry, meteorology, pollution sources, and existing ecosystem parameters were collected and used for model calibration and verification The model results mimic observed trends of water quality and phytoplankton species succession and can be used for forecasting algal blooms as well as assessment of river management measures.     

Water management strategies against toxic Microcystis blooms in the Dutch delta.

To prevent flooding of the Dutch delta, former estuaries have been impounded by the building of dams and sluices. Some of these water bodies, however, experience major ecological problems. One of the problem areas is the former Volkerak estuary that was turned into a freshwater lake in 1987. From the early 1990s onward, toxic Microcystis blooms dominate the phytoplankton of the lake every summer. Two management strategies have been suggested to suppress these harmful algal blooms: flushing the lake with fresh water or reintroducing saline water into the lake. This study aims at an advance assessment of these strategies through the development of a mechanistic model of the population dynamics of Microcystis. To calibrate the model, we monitored the benthic and pelagic Microcystis populations in the lake during two years. Field samples of Microcystis were incubated in the laboratory to estimate growth and mortality rates as functions of light, temperature, and salinity. Recruitment and sedimentation rates were measured in the lake, using traps, to quantify benthic-pelagic coupling of the Microcystis populations. The model predicts that flushing with fresh water will suppress Microcystis blooms when the current flushing rate is sufficiently increased. Furthermore, the inlet of saline water will suppress Microcystis blooms for salinities exceeding 14 g/L. Both management options are technically feasible. Our study illustrates that quantitative ecological knowledge can be a helpful tool guiding large-scale water management.     

Role of standard incidence in an eco-epidemiological system: A mathematical study

Ecology and epidemiology are two major fields of study in their own right, but they have some common features. [Chattopadhyay, J., Pal, S., El Abdllaoui, A., 2003. Classical predator–prey system with infection of prey population—a mathematical model. Math. Meth. Appl. Sci. 26, 1211–1222] considered a predator–prey model with disease in the prey population. They analyzed the system based on the assumption that horizontal incidence follows simple mass action incidence. Mass action incidence is appropriate for a constant population, but for a large population, standard incidence is more appropriate. The complicated dynamics around (0, 0, 0) arise because of standard incidence. The conditions under which the population reaches the origin either by following the axis or in a spiral pattern were determined. Numerical experiments were performed to observe the dynamics of the system with mass action incidence and standard incidence. This investigation showed that the infection rate plays a crucial role for predicting the behavior of the dynamics in the long run.     

Phytoplankton carbon dynamics during a winter-spring diatom bloom in an enclosed marine ecosystem: primary production,biomass and loss rates

Phytoplankton production, standing crop, and loss processes (respiration, sedimentation, grazing by zooplankton, and excretion) were measured on a daily basis during the growth, dormancy and decline of a winter-spring diatom bloom in a large-scale (13 m³) marine mesocosm in 1987. Carbonspecific rates of production and biomass change were highly correlated whereas production and loss rates were unrelated over the experimental period when the significant changes in algal biomass characteristic of phytoplankton blooms were occurring. The observed decline in diatom growth rates was caused by nutrient limitation. Daily phytoplankton production rates calculated from the phytoplankton continuity equation were in excellent agreement with rates independently determined using standard ¹⁴C techniques. A carbon budget for the winter bloom indicated that 82.4% of the net daytime primary production was accounted for by measured loss processes, 1.3% was present as standing crop at the end of the experiment, and 16.3% was unexplained. Losses via sedimentation (44.8%) and nighttime phytoplankton respiration (24.1%) predominated, while losses due to zooplankton grazing (10.7%) and nighttime phytoplankton excretion (2.8%) were of lesser importance. A model simulating daily phytoplankton biomass was developed to demonstrate the relative importance of the individual loss processes.     

A hydrodynamic and water quality modeling study of spatial and temporal patterns of phytoplankton growth in a stratified lake with buoyant incoming flow

A three-dimensional hydrodynamic and water quality model was applied to Lake Paldang, a lake in South Korea that is stratified by incoming flows. The spatial and temporal patterns of phytoplankton growth in this lake were determined from the model. The model was calibrated and verified using data measured under different hydrological conditions. The model results were in reasonable agreement with the field measurements, in both the calibration and verification phases. The distributions of water quality and residence time in the lake and phytoplankton response to changes in nutrient loads were examined with the model, and the influence of the hydrodynamics on phytoplankton response was analyzed. The simulation results indicated that Lake Paldang is an essentially phosphorus-limited system, but that phytoplankton growth is limited by low water temperature and short residence time during the winter and the summer monsoon period, respectively. The results of sensitivity analyses also suggested that the hydrodynamics within the lake may have an indirect influence on phytoplankton responses to changes in the limiting nutrient loads, and that reducing phosphorus loading from Kyoungan Stream should be a high priority policy for controlling algal blooms during the pre- and post-monsoon periods. From this study, it was concluded that the three-dimensional water quality model incorporating hydrodynamic processes could successfully simulate phytoplankton response to changes in nutrient loads and that it could become a useful tool for identifying the essential factors determining phytoplankton growth and for developing the best management policy for algal blooms in Lake Paldang.     

Description and use of an improved method for determining estuarine zooplankton grazing rates on phytoplankton

A method of rapidly determining zooplankton grazing rates on natural mixed phytoplankton populations using ¹⁴C is described. The method simplifies the design of grazing experiments as the grazing time can be kept short enough to prevent recycling of the isotope, and growth of the phytoplankton substrate. Very high specific activity, ¹⁴C-labelled phytoplankton concentrated either by centrifugation or sieving, may be used either as the sole grazing substrate, or as a tracer in natural mixed phytoplankton. Zooplankton, confined in glass jars at either ambient, or higher than ambient concentrations, are permitted to feed on the phytoplankton for periods of 30 min and 2 h, and are then separated by sieving. The zooplankton community grazing rate, or, if the samples are sorted into species, the individual species grazing rates, can be determined after scintillation counting of the zooplankton. The rate of appearance of ¹⁴C-labelled phytoplankton in the zooplankton is an estimate of the grazing rate, and the slope of the line joining the grazing rates at various phytoplankton concentrations gives an estimate of the grazing rate constant for the zooplankton population. The method provides a quick way of obtaining both zooplankton population, and individual species grazing rates on natural mixed phytoplankton. In two experiments, labelled phytoplankton was used as the sole grazing substrate in concentrations ranging between 0.4 and 5 times ambient levels. Grazing rate constants, for net-caught zooplankton concentrated to 46 times (Experiment 1) and 28 times (Experiment, 2) ambient estuarine levels were-0.14and-0.12 of the phytoplankton standing stock per day, respectively. There was a linear increase in the amount of phytoplankton grazed with an increase in phytoplankton concentration up to four times ambient phytoplankton levels. When tracer amounts of labelled phytoplankton were added to samples containing both phytoplankton and zooplankton at ambient concentrations the grazing rate constants were-0.28 and-0.42 of the phytoplankton standing stock per day. We conclude that zooplankton grazing was the major control factor of phytoplankton population size during October–November 1975 in South West Arm, Port Hacking, near Sydney, Australia.     

Population dynamics of Müllerian mimicry under interspecific competition

We ask what the effects of mutualism on population dynamics of two competitive species are. We model the population dynamics of mutualistic interactions with positive density- and frequency-dependences. We specifically assume the dynamics of Müllerian mimicry in butterflies, where the mortality of both species is reduced depending on the relative frequency of the other species. We assume that the two species are under Lotka–Volterra density-dependent competition. The equilibria are compared with the cases of competition alone. Unlike the traditional model of positive density-dependence, population explosion does not appear in the current dynamics, but the new equilibrium is simply achieved. It is because the effects of positive density- or frequency-dependence are restricted to parts of mortality. Both positive density- and frequency-dependences do promote coexistence of the mimetic species. However, the two models show a distinctive difference for coexistence. The effects of positive density-dependence are rather limited. In contrast, positive frequency-dependence always promotes coexistence, irrespective of environmental conditions. The results may imply that the evolutionary origin of Müllerian mimicry may depend on frequency-dependence (and density-dependence), but that its current population dynamics may depend solely on density-dependence. The role of frequency- and density-dependences on evolutionary dynamics is an open question.     

A resource-based approach to modelling the dynamics of interacting populations

The procedure for modelling the growth of single-species populations [Sakanoue, S., 2007. Extended logistic model for growth of single-species populations. Ecol. Model. 205, 159–168] is improved to be applicable to the study of the dynamics of interacting populations. The improved procedure is based on three assumptions: resource availability changes with population size as a variable, resource supply to populations and population demand for resources are defined as functions of resource availability and population size, and the variables of resource availability and population size shift in the supply function attracted to the demand function. These assumptions are organized into three equations. The equations can generate the dynamics models of plant, herbivore, and detritivore populations, and their own resources. The models can be used to describe prey–predator dynamics. They naturally contain nonlinear terms for the predator’s numerical and functional responses. Depending on the terms, the fluctuations in resource availability and population size stabilize. The three equations can also generate the dynamics models of different populations consuming the same resources. The analysis of zero isoclines of the models shows that a superior population can be simply defined as one with a higher intrinsic rate of natural increase, that a stable coexistence may be realized with the intraspecific interference or the interspecific facilitation of superiors, and that the interspecific interference or the intraspecific facilitation of inferiors may make the coexistence unstable and the inferiors winners depending on their initial population size.     

Optimization of exergy and implications of body sizes of phytoplankton and zooplankton in an aquatic ecosystem model

Size appears to be an important parameter in ecological processes. All physiological processes vary with body size ranging from small microorganisms to higher mammals. In this model, five state variables — phosphorus, detritus, phytoplankton, zooplankton and fish are considered. We study the implications of body sizes of phytoplankton and zooplankton for total system dynamics by optimizing exergy as a goal function for system performance indicator. The rates of different sub-processes of phytoplankton and zooplankton are calculated, by means of allometric relationships of their body sizes. We run the model with different combinations of body sizes of phytoplankton and zooplankton and observe the overall biomass of phytoplankton, zooplankton and fish. The highest exergy values in different combinations of phytoplankton and zooplankton size indicate the maximum biomass of fish with relative proportions of phytoplankton and zooplankton. We also test the effect of phosphorus input conditions corresponding to oligotrophic, mesotrophic, eutrophic system on its dynamics. The average exergy to be maximized over phytoplankton and zooplankton size was computed when the system reached a steady state. Since this state is often a limit cycle, and the exergy copies this behaviour, we averaged the exergy computed for 365 days (duration of 1 year) in the stable period of the run. In mesotrophic condition, maximum fish biomass with relative proportional ratio of phytoplankton, zooplankton is recorded for phytoplankton size class 3.12 (log V μm³ volume) and zooplankton size 4 (log V μm³ volume). In oligotrophic condition the highest average exergy is obtained in between phytoplankton size 1.48 (log V μm³ volume) and zooplankton size 4 (log V μm³ volume), whereas in eutrophic condition the result shows the highest exergy in the combination of phytoplankton size 5.25 (log V μm³ volume) and zooplankton size 4 (log V μm³ volume).     

Estimating the critical phosphorus loading of shallow lakes with the ecosystem model PCLake: Sensitivity, calibration and uncertainty

There is a vast body of knowledge that eutrophication of lakes may cause algal blooms. Among lakes, shallow lakes are peculiar systems in that they typically can be in one of two contrasting (equilibrium) states that are self-stabilizing: a ‘clear’ state with submerged macrophytes or a ‘turbid’ state dominated by phytoplankton. Eutrophication may cause a switch from the clear to the turbid state, if the P loading exceeds a critical value. The ecological processes governing this switch are covered by the ecosystem model PCLake, a dynamic model of nutrient cycling and the biota in shallow lakes. Here we present an extensive analysis of the model, using a three-step procedure. (1) A sensitivity analysis revealed the key parameters for the model output. (2) These parameters were calibrated on the combined data on total phosphorus, chlorophyll-a, macrophytes cover and Secchi depth in over 40 lakes. This was done by a Bayesian procedure, giving a weight to each parameter setting based on its likelihood. (3) These weights were used for an uncertainty analysis, applied to the switchpoints (critical phosphorus loading levels) calculated by the model. The model was most sensitive to changes in water depth, P and N loading, retention time and lake size as external input factors, and to zooplankton growth rate, settling rates and maximum growth rates of phytoplankton and macrophytes as process parameters. The results for the ‘best run’ showed an acceptable agreement between model and data and classified nearly all lakes to which the model was applied correctly as either ‘clear’ (macrophyte-dominated) or ‘turbid’ (phytoplankton-dominated). The critical loading levels for a standard lake showed about a factor two uncertainty due to the variation in the posterior parameter distribution. This study calculates in one coherent analysis uncertainties in critical phosphorus loading, a parameter that is of great importance to water quality managers.     

The dynamics of phytoplankton blooms in puget sound a fjord in the Northwestern United States

This paper describes a quantitative investigation of relationships between the growth of phytoplankton, and climatic and hydrodynamci conditions in temperate fjords with marked tides, as exemplified by Puget Sound, Washington (USA). Algal growth in the open waters of the central basin of the Sound is dominated by a number of intense blooms beginning in late April or May and recurring throughout the summer. Rarely, and only briefly, does nitrate become exhausted. The phytoplankton production rate in the central basin of Puget Sound is about 465 g C m^-2 year^-1. During the springs of 1966 and 1967, oceanographic measurements were carried out at a mid-channel station with sufficient frequency to allow investigation of physical and biological processes with time scales of the order of a day. The principal investigative tool is a numerical model in which the hydrodynamical conditions are represented by an approximate analysis of the gravitational convection mode of circulation. Algal concentration is represented as a continous function of space and time in the model which ascribes changes in phytoplankton density to variations in photosynthetic and respiratory activity, algal sinking, grazing by herbivores, and to mixing and advection. Computations adequately reproduce the principal features of phytoplankton concentrations observed during 75 days and 35 days in the springs of 1966 and 1967, respectively. Numerical experiments assess the relative importance of various processes which govern the level of primary production in Puget Sound. It is concluded that phytoplankton growth is limited by a combination of factors, including vertical advection and turbulence, modulation of underwater light intensity by self-shading and inorganic particulates, sinking of algal cells, and occasional rapid horizontal advection of the population from the area by sustained winds. The high primary productivity of the Sound is due to intensive upward transport of nitrate by the estuarine mechanism. These results should be generally applicable to other temperate fjords because of the largely conventional choice of the biological functions.     

Does biodiversity of estuarine phytoplankton depend on hydrology?

Phytoplankton growth in estuaries is controlled by factors such as flushing, salinity tolerance, light, nutrients and grazing. Here, we show that biodiversity of estuarine phytoplankton is related to flushing, and illustrate this for some European estuaries.The implications for the definition of reference conditions for quality elements in estuaries of different types are examined, leading to the conclusion that constraints on the number of estuarine and coastal types that may be defined for management purposes require that quality classes take into account natural variability within types, in order to be ecologically meaningful. We develop a screening model to predict the growth rate required for a phytoplankton species to be present under different flushing conditions and apply it to estuaries in the EU and US to show how changes in physical forcing may alter biodiversity. Additional results are presented on the consequences for eutrophication, showing that changes in residence time may interact with species-specific nutrient uptake rates to cause shifts in species composition, potentially leading to effects such as harmful algal blooms.We discuss applications for integrated coastal zone management, and propose an approach to normalization of estuarine phytoplankton composition as regards species numbers.     

Annual cycles of phytoplankton community-structure and bloom dynamics in the Neuse River Estuary, North Carolina

The spatiotemporal distributions of major phytoplankton taxa were quantified to estimate the relative contribution of different microalgal groups to biomass and bloom dynamics in the eutrophic Neuse River Estuary, North Carolina, USA. Biweekly water samples and ambient physical and chemical data were examined at sites along a salinity gradient from January 1994 through December 1996. Chemosystematic photopigments (chlorophylls and carotenoids) were identified and quantified using high-performance liquid chromatography (HPLC). A recently-developed factor-analysis procedure (CHEMTAX) was used to partition the algal group-specific chlorophyll a (chl a) concentrations based on photopigment concentrations. Results were spatially and temporally integrated to determine the ecosystem-level dynamics of phytoplankton community-constituents. Seasonal patterns of phytoplankton community-composition changes were observed over the 3 yr. Dinoflagellates reached maximum abundance in the late winter to early spring (January to March), followed by a spring diatom bloom (May to July). Cyanobacteria were more prevalent during summer months and made a large contribution to phytoplankton biomass, possibly in response to nutrient-enriched freshwater discharge. Cryptomonad blooms were not associated with a particular season, and varied from year to year. Chlorophyte abundance was low, but occasional blooms occurred during spring and summer. Over the 3 yr period, the total contribution of each algal group, in terms of chl a, was evenly balanced, with each contributing nearly 20% of the total chl a. Cryptomonad, chlorophyte, and cyanobacterial dynamics did not exhibit regular seasonal bloom patterns. High dissolved inorganic-nitrogen loading during the summer months promoted major blooms of cryptomonads, chlorophytes, and cyanobacteria. Received: 12 September 1997 / Accepted: 12 December 1997     

浮游植物程序性细胞死亡研究进展

浮游植物是水生生态系统的基础,在生物地化循环中起着非常重要的作用,浮游植物的死亡势必引起水生生态系统的改变。近年来的研究表明,浮游植物的死亡是浮游植物水华衰退的一个重要原因。浮游植物中是否存在与后生动物类似的程序性细胞死亡（Programmed cell death,PCD）途径,也因此成了一个热点问题。文章对近年来浮游植物死亡表型、PCD生化证据、诱发条件、分子基础方面研究进行了总结。大量证据表明,浮游植物中存在类似细胞凋亡、类凋亡、自噬等途径的PCD,但Caspase基因除具有死亡执行者功能外,还可能具有看家功能。活性氧（ROS）和一氧化氮（NO）在浮游植物PCD过程中可能起到死亡信号分子的作用。部分浮游植物的PCD可以改善种群生存,但其生态学意义总体而言仍存在许多争论。     

Simple predator–prey interactions control dynamics in a plankton food web model

A plankton food web model is analysed using interaction parameter values appropriate to the upper mixed layer of the high latitude oceans. The dynamics of this four-variable system are analysed in terms of the dynamics of much simpler two-variable predator–prey subsystems. Thus, the food web's robust, periodic, four-dimensional dynamics are explained by means of two-dimensional spirals and limit cycles. These dynamical subsystems are coupled by means of an omnivore that transfers control of the dynamics between the two predator–prey subsystems. The food web may substantially decouple the predator–prey subsystems so that the oscillating phytoplankton/zooplankton blooms exhibit population collapses when bacterial ‘breathers’ briefly dominate after growing dramatically from low background levels. This regular bloom/breather behaviour becomes benignly chaotic when the system is mildly forced by the annual cycle of the sun's irradiance.     

Succession patterns of phytoplankton blooms: directionality and influence of algal cell size

Using four replicate microcosms in the laboratory, we induced a phytoplankton bloom by enclosing a natural community sampled from Masnou Harbor (N.E. Spain) in November 1987, and examined the pattern of algal succession during the bloom. Good replicability of the temporal patterns of the community biomass and the abundance of most species demonstrated that succession was a directional, non-random process. The successional pathway observed (small flagellates » small centric diatoms » small flagellates) resembled that observed by other authors studying phytoplankton blooms. This pattern differed from previous models of algal succession in that dinoflagellates never comprised a substantial fraction of the community biomass, and in that algal cell size did not tend to increase along the successional sequence. Algal cell size, however, was an important determinant of phytoplankton community structure, since it constrained the density, but not the biomass, achievable by the different species. We suggest that there is not a single, general pattern of phytoplankton succession, but that distinction should be made, at least between seasonal and bloom patterns of phytoplankton succession.     

Modelling the effects of green macroalgae blooms on the population dynamics of Cyathura carinata (Crustacea: Isopoda) in an eutrophied estuary

A population dynamics model was developed to simulate the effects of benthic macroalgae blooms (mostly Enteromorpha spp.) on the productivity of Cyathura carinata (Crustacea: Isopoda), a possible keystone species in the benthic communities of the Mondego estuary. The model describes C. carinata population dynamics, as well as the relationships between Enteromorpha biomass, Enteromorpha decaying rates, organic matter content in the sediments and detritus consumption by C. carinata, a detritic feeder. Model results support the idea that seasonal blooms of Enteromorpha determine a significant increase of organic matter content in the sediments, due to macroalgae decay, which initially contributes to enhance C. carinata consumption and growth rates, determining a significant increase in the biomass. Nevertheless, later, following the algae bloom, C. carinata biomass decreases, and reaches its lowest value, close to 0, when the algae crash. This effect is probably related with strong anoxic conditions, especially during night, due to high algal decomposition rates. In accordance with the model, migration of new individuals from adjacent areas must occur in order to recolonise the area affected by the algae bloom. Therefore, it seems reasonable to conclude that macroalgae blooms that are limited in space may favour C. carinata populations, but extensive blooms affecting the whole area of distribution of this species will determine its disappearance.