A model of phytoplankton blooms

A simple model that describes the dynamics of nutrient-driven phytoplankton blooms is presented. Apart from complicated simulation studies, very few models reported in the literature have taken this "bottom-up" approach. Yet, as discussed and justified from a theoretical standpoint, many blooms are strongly controlled by nutrients rather than by higher trophic levels. The analysis identifies an important threshold effect: a bloom will only be triggered when nutrients exceed a certain defined level. This threshold effect should be generic to both natural blooms and most simulation models. Furthermore, predictions are given as to how the peak of the bloom Pmax is determined by initial conditions. A number of counterintuitive results are found. In particular, it is shown that increasing initial nutrient or phytoplankton levels can act to decrease Pmax. Correct predictions require an understanding of such factors as the timing of the bloom and the period of nutrient buildup before the bloom.     

Asymptotics of Conduction Velocity Restitution in Models of Electrical Excitation in the Heart

We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh–Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified “caricature” of Noble (J. Physiol. Lond. 160:317–352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177–210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler–Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method.     

Trophic exploitation in grassland food chains: simple models and a field experiment

This study provides insight into the importance of top carnivores (top-down control) and nutrient inputs (bottom-up control) in structuring food chains in a terrestrial grassland system. Qualitative predictions about food chain structure are generated using 4 simple models, each differing in assumptions about some key component in the population dynamics of the herbivore trophic level. The four model systems can be classified broadly into two groups (1) those that assume plant resource intake by herbivores is limited by search rate and handling time as described by classic Lotka-Volterra models; and (2) those that assume plant resource intake by herbivores is limited externally by the supply rate of resources as described by alternatives to Lotka-Volterra formulations. The first class of models tends to ascribe greater importance to top-down control of food chain structure whereas the second class places greater weight on bottom-up control. I evaluated the model predictions using experimentally assembled grassland food chains in which I manipulated nutrient inputs and carnivore (wolf spider) abundance to determine the degree of top-down and bottom-up control of grassland plants and herbivores (grasshoppers). The experimental results were most consistent with predictions of the second class of models implying a predominance of bottom-up control of food chain structure.     

Community Assembly in Marine Phytoplankton: Application of Recent Models to Harmful Dinoflagellate Blooms

The habitat preferences of dinoflagellate bloom species alongan onshore–offshore, mixing-nutrient gradient, their associatedlife-form (morphotype) characteristics and adaptive strategieswere evaluated from the perspective of Margalef's Mandala andReynolds Intaglio. Nine different mixingnutrient habitats andassociated dinoflagellate life-form types having distinctivemorphotype features and habitat preferences are distinguishable.Reynolds Intaglio provided greater fidelity to actual in situdinoflagellate community assembly than the Mandala. We suggestthat the correlation between degree of mixing and nutrient levelspresumed in the Mandala is not the essential interaction inthe selection of life forms and their succession. A more significantaspect of the turbulence axis is the degree of vertical, micro-habitatstructural differentiation that it permits. Three primary adaptivestrategies consistent with C-S-R strategies recognized amongfreshwater phytoplankton species characterize the componentdinoflagellate species: invasive, small- to intermediate-sizedcolonist species (C) which often predominate in chemically-disturbedwater bodies; acquisitive, larger-celled, nutrient stresstolerantspecies (S); and disturbance-tolerant ruderal species (R) tolerantof shear/stress forces in physically-disturbed water masses(fronts, upwelling relaxations, current entrainment). It issuggested that harmful algal bloom community assembly and dynamicsreflect two basic selection features—life-form and species-specificselection, that commonly held life-form properties overridephylogenetic properties in bloom-species selection, and thatthe latter is often stochastic, rather than singular. The highdegree of unpredictability of individual species blooms is consistentwith stochastic selection, e.g. bloom species are often selectedas a result of being in the right place at the right time atsuitable inoculum levels. A focus on the life-form properties,habitat preference and stochastic selection of bloom specieswould appear to be more viable and realistic than current ecologicalinvestigative approaches.     

Phytoplankton blooms and fish recruitment rate

The relationships between phytoplankton and zooplankton productionand fish larval survival to recruitment are examined by linkingtwo generic models. It is first demonstrated that the phytoplankton–zooplanktonmodels can be appropriately combined with a zooplankton–larvae–recruitmentmodel. The combined model reveals some general principles. Recruitmenttends to be a domed-shaped function of initial fish egg production.‘Bloom’ phytoplankton conditions are important forhigh recruitments. The timing and duration of fish egg productionis important in determining recruitment through their impacton the phytoplankton bloom. It is argued that optimal recruitmentwould be obtained if the duration of larval feeding was lessthan the duration of the phytoplankton bloom; a hypothesis whichis testable.     

A model for seasonal phytoplankton blooms

We analyse a generic bottom-up nutrient phytoplankton model to help understand the dynamics of seasonally recurring algae blooms. The deterministic model displays a wide spectrum of dynamical behaviours, from simple cyclical blooms which trigger annually, to irregular chaotic blooms in which both the time between outbreaks and their magnitudes are erratic. Unusually, despite the persistent seasonal forcing, it is extremely difficult to generate blooms that are both annually recurring and also chaotic or irregular (i.e. in amplitude) even though this characterizes many real time-series. Instead the model has a tendency to 'skip' with outbreaks often being suppressed from 1 year to the next. This behaviour is studied in detail and we develop analytical expressions to describe the model's flow in phase space, yielding insights into the mechanism of the bloom recurrence. We also discuss how modifications to the equations through the inclusion of appropriate functional forms can generate more realistic dynamics.     

Diet-induced obesity is linked to marked but reversible alterations in the mouse distal gut microbiome

We have investigated the interrelationship between diet, gut microbial ecology, and energy balance using a mouse model of obesity produced by consumption of a prototypic Western diet. Diet-induced obesity (DIO) produced a bloom in a single uncultured clade within the Mollicutes class of the Firmicutes, which was diminished by subsequent dietary manipulations that limit weight gain. Microbiota transplantation from mice with DIO to lean germ-free recipients promoted greater fat deposition than transplants from lean donors. Metagenomic and biochemical analysis of the gut microbiome together with sequencing and metabolic reconstructions of a related human gut-associated Mollicute (Eubacterium dolichum) revealed features that may provide a competitive advantage to members of the bloom in the Western diet nutrient milieu, including import and processing of simple sugars. Our study illustrates how combining comparative metagenomics with gnotobiotic mouse models and specific dietary manipulations can disclose the niches of previously uncharacterized members of the gut microbiota.     

An unusual bloom of the dinoflagellate Akashiwo sanguinea off the central Oregon, USA, coast in autumn 2009

An algal bloom caused by the dinoflagellate Akashiwo sanguinea was observed in October–November 2009 along the central Oregon coast (44.6°N), off Newport, Oregon, U.S.A. In this paper, the conditions are described which led to the development and demise of this bloom. The bloom was observed for 1 month from 5-October until 4-November with the peak of abundance on 19-October (347,615 cells L⁻¹). The A. sanguinea bloom followed September blooms of the diatoms Pseudo-nitzschia spp, Chaetoceros debilis, and the dinoflagellate Prorocentrum gracile. The bloom occurred when nitrate and silicate concentrations were <2 μM and <8 μM, respectively, and when the water column was stratified. This A. sanguinea dinoflagellate bloom event was closely related to the anomalous upwelling conditions in 2009: upwelling ceased early, at the end of August, whereas a normal upwelling continues into early October. This relaxation extended to near the end of September as a prolonged downwelling event, but then active upwelling reappeared in October and November. The explanation for the occurrence of the A. sanguinea bloom in October may be related to a combination of a prior diatom bloom, a stratified water column with low nutrient concentration in September, and an active upwelling event in October. As for the ultimate source of the cells, the hypothesis is that the seed stock for the A sanguinea bloom off Oregon was southward transport of cells from the Washington coast where a massive bloom of A. sanguinea was first observed in September 2009.     

Investigating the Use of a Bayesian Network to Model the Risk of Lyngbya majuscula Bloom Initiation in Deception Bay,Queensland, Australia

Modelling the risk factors driving an environmental problem can be problematic when published data describing variables and their interactions are sparse. In such cases, expert opinion forms a vital source of information. Here we demonstrate the utility of a Bayesian Net (BN) model to integrate available information in a risk analysis setting. As an example, we use this methodology to explore the major factors influencing initiation of Lyngbya majuscula blooms in Deception Bay, Queensland, Australia. Over the past decade Lyngbya blooms have increased in both frequency and extent on seagrass beds in Deception Bay, with a range of adverse effects. This model was used to identify the main factors that could trigger a Lyngbya bloom. The five factors found to have the greatest effect on Lyngbya bloom initiation were: the available nutrient pool, water temperature, redox state of the sediments, current velocity, and light. Scenario analysis was also conducted to determine the sensitivity of the model to different combinations of variable states. The model has been used to identify knowledge gaps and therefore to direct additional research efforts in Deception Bay. With minor changes the model can be used to better understand the factors triggering Lyngbya blooms in other coastal regions.     

Modeling microzooplankton and macrozooplankton dynamics within a coastal upwelling system

A simple nutrient–phytoplankton–zooplankton (NPZ)pelagic ecosystem model coupled to a two-dimensional primitiveequation circulation model with explicit mixed-layer physicsis configured in a coastal setting to study the biological responseto idealized wind-driven upwelling conditions. Conventionalecosystem model parameterization, which assumes macrozooplanktonas the target grazers, leads to upwelling-induced phytoplanktonblooms that exhaust available nutrient supply and whose zonalscale increases with wind duration. Offshore zooplankton maximaresult from upwelled water with greater total nitrogen concentrationsthan initial ambient surface water. Substantial vertical mixingin the surface boundary layer sets the vertical scale of theproductivity. Phytoplankton sinking contributes to a nearshoreaccumulation of total nitrogen, and enhances the magnitude andduration of the phytoplankton bloom. The system responds differentlywhen the zooplankton are parameterized to represent microzooplankton.The phytoplankton and zooplankton maxima have more limited zonalextent, are more independent of the duration of wind forcing,and near-surface nutrient levels remain high over most of thedomain. When winds are relaxed, the diminished offshore transportreveals the underlying biological oscillations in the microzooplankton-parameterizedecosystem, and reduced vertical mixing decouples surface fromsubsurface dynamics. In contrast, the macrozooplankton systemrelaxes to a steady state supporting limited phytoplankton andlarge zooplankton levels in the upwelling region.     

Analysis of an excitable dendritic spine with an activity-dependent stem conductance

 Dendritic spines are the major target for excitatory synaptic inputs in the vertebrate brain. They are tiny evaginations of the dendritic surface consisting of a bulbous head and a tenuous stem. Spines are considered to be an important locus for plastic changes underlying memory and learning processes. The findings that synaptic morphology may be activity-dependent and that spine head membrane may be endowed with voltage-dependent (excitable) channels is the motivation for this study. We first explore the dynamics, when an excitable, yet morphologically fixed spine receives a constant current input. Two parameter Andronov–Hopf bifurcation diagrams are constructed showing stability boundaries between oscillations and steady-states. We show how these boundaries can change as a function of both the spine stem conductance and the conductance load of the attached dendrite. Building on this reference case an idealized model for an activity-dependent spine is formulated and analyzed. Specifically we examine the possibility that the spine stem resistance, the tunable “synaptic weight” parameter identified by Rall and Rinzel, is activity-dependent. In the model the spine stem conductance depends (slowly) on the local electrical interactions between the spine head and the dendritic cable; parameter regimes are found for bursting, steady states, continuous spiking, and more complex oscillatory behavior. We find that conductance load of the dendrite strongly influences the burst pattern as well as other dynamics. When the spine head membrane potential exhibits relaxation oscillations a simple model is formulated that captures the dynamical features of the full model. Received: 10 January 1997/Revised version: 25 March 1997     

A test of three alternative pathways for consumer regulation of primary productivity

The pathways linking consumer effects to primary productivity (PPR) are likely to vary among taxa because of species-specific trophic and functional differences. Thus, it is necessary to understand the dynamics of consumer–PPR interactions so that effects of species loss on ecosystem function can be addressed from a mechanistic approach. In this study, I used three fish taxa (orangethroat darter, Etheostoma spectabile; western mosquitofish, Gambusia affinis; and bullhead minnow, Pimephales vigilax) as model consumers with different trophic and functional characteristics to test alternative mechanisms for consumer regulation of PPR (i.e., trophic cascade, terrestrial nutrient translocation, and sedimentary nutrient translocation). Experiments were conducted in stream mesocosms fitted with a combination of fish and terrestrial insect barriers to address relative importance of consumer-driven top-down and bottom-up control of PPR. A predatory invertivore, orangethroat darter, increased PPR through an apparent trophic cascade by localized reduction of benthic grazing invertebrate densities (i.e., top-down). A surface feeding insectivore, western mosquitofish, consumed terrestrial insects on the stream surface, increasing PPR by enhancing allochthonous nutrients in the mesocosms (i.e., bottom-up). A benthic omnivore, bullhead minnow, consumed benthic food items, resulting in increased PPR by enhancing availability of autochthonous nutrients via translocation of sedimentary nutrients (i.e., bottom-up). However, under specific environmental contexts, this species also consumed terrestrial invertebrates, potentially affecting PPR through terrestrial nutrient translocation as well. In this study, the trophic and functional characteristics of different species resulted in alternative pathways that increased PPR, suggesting that in natural ecosystems multiple consumer-driven pathways may be influencing PPR simultaneously and could potentially be important for temporal persistence of ecosystem function in changing environments.     

Positive feedbacks between bottom-up and top-down controls promote the formation and toxicity of ecosystem disruptive algal blooms: A modeling study

Harmful algal blooms that disrupt and degrade ecosystems (ecosystem disruptive algal blooms, EDABs) are occurring with greater frequency and severity with eutrophication and other adverse anthropogenic alterations of coastal systems. EDAB events have been hypothesized to be caused by positive feedback interactions involving differential growth of competing algal species, low grazing mortality rates on EDAB species, and resulting decreases in nutrient inputs from grazer-mediated nutrient cycling as the EDAB event progresses. Here we develop a stoichiometric nutrient–phytoplankton–zooplankton (NPZ) model to test a conceptual positive feedback mechanism linked to increased cell toxicity and resultant decreases in grazing mortality rates in EDAB species under nutrient limitation of growth rate. As our model EDAB alga, we chose the slow-growing, toxic dinoflagellate Karenia brevis, whose toxin levels have been shown to increase with nutrient (nitrogen) limitation of specific growth rate. This species was competed with two high-nutrient adapted, faster-growing diatoms (Thalassiosira pseudonana and Thalassiosira weissflogii) using recently published data for relationships among nutrient (ammonium) concentration, carbon normalized ammonium uptake rates, cellular nitrogen:carbon (N:C) ratios, and specific growth rate. The model results support the proposed positive feedback mechanism for EDAB formation and toxicity. In all cases the toxic bloom was preceded by one or more pre-blooms of fast-growing diatoms, which drew dissolved nutrients to low growth rate-limiting levels, and stimulated the population growth of zooplankton grazers. Low specific grazing rates on the toxic, nutrient-limited EDAB species then promoted the population growth of this species, which further decreased grazing rates, grazing-linked nutrient recycling, nutrient concentrations, and algal specific growth rates. The nutrient limitation of growth rate further increased toxin concentrations in the EDAB algae, which further decreased grazing-linked nutrient recycling rates and nutrient concentrations, and caused an even greater nutrient limitation of growth rate and even higher toxin levels in the EDAB algae. This chain of interactions represented a positive feedback that resulted in the formation of a high-biomass toxic bloom, with low, nutrient-limited specific growth rates and associated high cellular C:N and toxin:C ratios. Together the elevated C:N and toxin:C ratios in the EDAB algae resulted in very high bloom toxicity. The positive feedbacks and resulting bloom formation and toxicity were increased by long water residence times, which increased the relative importance of grazing-linked nutrient recycling to the overall supply of limiting nutrient (N).     

东海原甲藻与中肋骨条藻的种间竞争数值模拟

研究探讨了两个零维箱式模型在东海典型赤潮藻东海原甲藻和中肋骨条藻竞争与演替研究中的应用。模型在采用不同接种密度下的单种培养实验数据进行参数校正后,被用来模拟不同N/P条件下单种培养实验以及两藻种共培养竞争实验,并以实验数据对其结果进行了验证。模拟结果表明,在单种培养条件下,模型能够较好地重现两种藻在不同N/P环境中的生长及对营养盐的利用;共培养实验的模拟结果显示,在所有初始细胞密度比例条件下,中肋骨条藻的最终密度均会超过东海原甲藻,且PO4的消耗主要源于中肋骨条藻的利用,与实验结果一致,表明模型能够很好地体现两种藻的竞争结果及对营养盐的竞争关系;由于模型不足以模拟除营养盐竞争以外的藻间相互作用,模拟结果未体现东海原甲藻细胞数迅速衰减这一现象,有待进一步研究。     

Continuous plankton records: seasonal variations in the distribution and abundance of plankton in the North Atlantic Ocean and the North Sea

Charts are presented of the seasonal variations in the distributionof four phytoplankton and five zooplankton taxa in the NorthAtlantic and the North Sea. The main factors determining theseasonal variations appear to be the distribution of the mainoverwintering stocks, the current system and, in some instances,temperature control of the rate of population increase. Informationis presented about the variation with latitude (over the rangefrom 34° N to 65 ° N) of the seasonal regime of theplankton. On the assumption that there is a relationship betweennutrient supply and vertical temperature stratification themain features of this variability can be interpreted. In thesouth (to about 43° N) nutrient limitation plus grazingappear to be dominant, resulting in a bimodal seasonal cycleof phytoplankton. North of about 60° N the system appearsto be limited by the size of the phytoplankton stocks beinggrazed primarily by Calanus Finmarchicus and Euphausiacea. Inan extensive zone, from about 44° N to 60° N, it wouldappear that the spring bloom of phytoplankton is under-exploitedby grazing while in summer the zooplankton graze the daily productionof the phytoplankton, the stocks of which are probably maintainedby in situ nutrient regeneration. The implications, for at leastthis mid-latitude zone, that rates and fluxes of processes,as opposed to density dependent interactions between stocks,play a major role in the dynamics of the seasonal cycle is consistentwith previously reported observations suggesting that physicalenvironmental factors play a major role in determining year-to-yearfluctuations in the abundance of the plankton.     

Basic mechanisms responsible for calcium signalling in neuronal cells

Calcium ions are the most universal intracellular messengers transmitting signals from the plasmalemma of excitable cells to the intracellular structures and triggering or modulating in this way most cellular functions. The molecular mechanisms responsible for injection of Ca ions into the cytoplasm during cellular activity and for producting transient elevations of their cytoplasmic free level (calcium “transient,” or “signals”) have been a subject of extensive investigation in numerous laboratories during last three decades. In a short review it is impossible to summarize the results obtained; two extensive publications on this subject have appeared already from our laboratory [1, 2]. Therefore, here the main attention will be paid to the most recent data from our laboratory concerning different aspects of the mechanisms forming calcium signals in neuronal cells.     

A mesocosm study of Phaeocystis globosa (Prymnesiophyceae) population dynamics: II. Significance for the microbial community

The impact of Phaeocystis globosa population decline on the microbial community was studied during a mesocosm experiment, with irradiance regime and inorganic N:P ratios (4, 16, and 44) as controlling factors. Heterotrophic bacterial activity was closely related to enhanced (viral) lysis rates of P. globosa cells and disintegration of the colonies. Up to 85% of the bacterial C demand could be supplied by P. globosa-specific cellular C release. The bacterial populations with high DNA content became dominant (>70% of total). The bacterial community showed a rapid shift in composition to take advantage of the changing conditions during the demise of the P. globosa bloom. Members of the Alphaproteobacteria and the Bacteroidetes group emerged directly upon bloom decay. Multidimensional scaling analysis in conjunction with DGGE fingerprinting implied that clustering was more related to the availability of organic carbon (the collapse of the P. gobosa bloom) than to the nature of the phytoplankton growth-controlling nutrient. Reduced irradiance delayed the development of the P. globosa population and subsequently changes in the bacterial community composition. Disintegration of P. globosa colonies resulted in the formation of transparent exopolymeric particles (TEP) and aggregates, more so under P-depletion than under N-deficient conditions. The colonial matrix transformed into big aggregates under P-depleted conditions but remained largely as ghost colonies under N-depleted conditions. In the mesocosm with initial nitrogen and phosphorus supplied in the Redfield ratio, features intermediate to conditions with either N- or P-depletion were observed. It was hypothesized that TEP affected microbial population dynamics directly through bacterial colonization and indirectly through scavenging of predators and viruses.     

How does eutrophication affect the role of grazers in harmful algal bloom dynamics?

Population dynamics of harmful algal bloom species are regulated both from the “bottom-up” by factors that affect their growth rate and from the “top-down” by factors that affect their loss rates. While it might seem apparent that eutrophication would have the greatest impact on factors affecting growth rates of phytoplankton (nutrient supply, light availability) the roles of top-down controls, including grazers and pathogens, cannot be ignored in studies of harmful bloom dynamics. Lags between the growth of phytoplankton and zooplankton populations, or disruption of zooplankton populations by adverse environmental conditions may be important factors in the initiation of plankton blooms under eutrophic conditions. Grazers that avoid feeding on harmful species and actively graze on competing species may also play important roles in bloom initiation. Grazers that are not affected by phytoplankton toxins and have growth rates comparable to phytoplankton (e.g. protozoan grazers) may have the potential to control the initiation of blooms. If the inhibition of grazers varies with cell density for blooms of toxic phytoplankton, eutrophication may increase the chances of blooms reaching threshold densities for grazer inhibition. In addition, secondary effects of eutrophication, including hypoxia and change in pH may adversely affect grazer populations, and further release HAB species from top-down control. The Texas brown tide (Aureoumbra lagunensis) blooms provide evidence for the role of grazer disruption in bloom initiation and the importance of high densities of brown tide cells in continued suppression of grazers.