Bloom dynamics under the effects of periodic driving forces

Phytoplankton bloom received considerable attention for many decades. Different approaches have been used to explain the bloom phenomena. In this paper, we study a Nutrient-Phytoplankton-Zooplankton (NPZ) model consisting of a periodic driving force in the growth rate of phytoplankton due to solar radiation and analyse the dynamics of the corresponding autonomous and non-autonomous systems in different parametric regions. Then we introduce a novel aspect to extend the model by incorporating another periodic driving force into the growth term of the phytoplankton due to sea surface temperature (SST), a key point of innovation. Temperature dependency of the maximum growth rate (μmax) of the phytoplankton is modelled by the well-known Q10 formulation: [Formula: see text] , where μ0 is maximum growth at 0oC. Stability conditions for all three equilibrium points are expressed in terms of the new parameter ρ2, which appears due to the incorporation of periodic driving forces. System dynamics is explored through a detailed bifurcation analysis, both mathematically and numerically, with respect to the light and temperature dependent phytoplankton growth response. Bloom phenomenon is explained by the saddle point bloom mechanism even when the co-existing equilibrium point does not exist for some values of ρ2. Solar radiation and SST are modelled using sinusoidal functions constructed from satellite data. Our results of the proposed model describe the initiation of the phytoplankton bloom better than an existing model for the region 25-35° W, 40-45° N of the North Atlantic Ocean. An improvement of 14 days (approximately) is observed in the bloom initiation time. The rate of change method (ROC) is applied to predict the bloom initiation.

Nutrient enrichment and phytoplankton toxicity influence a diversity of complex dynamics in a fear-induced plankton-fish model

In this paper, we contemplate the dynamics of an aquatic system consisting of three interacting species, phytoplankton, zooplankton, and fish. We assume that the evading risk of fish predation induces fear in zooplankton species, which affects its growth dynamics radically. On the other hand, zooplankton develop an anti-predator defense by taking temporary refuge. Interestingly, the system potentially exhibits multi-stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including multiple saddle-node and transcritical bifurcations with varying levels of nutrients, strength of phytoplankton toxicity, zooplankton refuge size and the cost of fear imposed by fish population. Further, by adding Gaussian white noise, we have extended the deterministic system to its stochastic version. We find that white noise appears to regulate the survival and extinction of model species. Comprehensive numerical simulations are consistent with mathematical results prognosticated by linear analysis. Overall, our study may provide a new insight into the mechanisms of emergence and mitigation of plankton blooms.

Stability switches and chaos induced by delay in a reaction-diffusion nutrient-plankton model

In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats.

A discrete-time nutrients-phytoplankton-oysters mathematical model of a bay ecosystem

Populations are generally censused daily, weekly, monthly or annually. In this paper, we introduce a discrete-time nutrients-phytoplankton-oysters (NPO) model that describes the interactions of nutrients, phytoplankton and oysters in a bay ecosystem. We compute the threshold parameter R N for persistence of phytoplankton with or without oysters. When R N < 1 , then both phytoplankton and oysters populations go extinct. However, when R N > 1 , we show that the model may exhibit two scenarios: (1) a locally asymptotically stable equilibrium with positive values of nutrients and phytoplankton with oysters missing, and (2) a locally asymptotically stable interior equilibrium with positive values of nutrients, phytoplankton and oysters. We use sensitivity analysis to study the impact of human and environmental factors on the model. We use examples to illustrate that some human activities and environmental factors can force the interior equilibrium to undergo a Neimark-Sacker bifurcation which generates phytoplankton blooms with oscillations in oysters population and nutrients level.

Toxicity-mediated regime shifts in a contaminated nutrient-plankton system

In this article, we contemplate the dynamics of a three-tier system of nutrient, phytoplankton, and zooplankton with a gestation delay of discrete type and a distributed delay in nutrient recycling. Phytoplankton secretion-mediated alteration in the grazing pattern of zooplankton is encapsulated by a Monod-Haldane functional response. We carry out global sensitivity analysis for identifying the crucial model parameters having a significant impact on zooplankton density. The system potentially exhibits bistable configurations under identical ecological conditions by allowing different bifurcation scenarios, including multiple saddle-node and transcritical bifurcations with varying input rates of nutrients and inhibitory effects of phytoplankton against zooplankton. We observe that the gestation delay in zooplankton is responsible for the emergence of noxious bloom events. Interestingly, when the delay parameter crosses a threshold, the system experiences chaotic disorder, which prognosticates the onset of irregular bloom. Furthermore, by adding Gaussian white noise, we have extended the deterministic model to its stochastic counterpart. We found that white noise appears to regulate the survival and extinction of interacting populations. Comprehensive numerical simulations are consistent with mathematical results prognosticated by linear analysis.

High-resolution metagenomic reconstruction of the freshwater spring bloom

BACKGROUND

The phytoplankton spring bloom in freshwater habitats is a complex, recurring, and dynamic ecological spectacle that unfolds at multiple biological scales. Although enormous taxonomic shifts in microbial assemblages during and after the bloom have been reported, genomic information on the microbial community of the spring bloom remains scarce.

RESULTS

We performed a high-resolution spatio-temporal sampling of the spring bloom in a freshwater reservoir and describe a multitude of previously unknown taxa using metagenome-assembled genomes of eukaryotes, prokaryotes, and viruses in combination with a broad array of methodologies. The recovered genomes reveal multiple distributional dynamics for several bacterial groups with progressively increasing stratification. Analyses of abundances of metagenome-assembled genomes in concert with CARD-FISH revealed remarkably similar in situ doubling time estimates for dominant genome-streamlined microbial lineages. Discordance between quantitations of cryptophytes arising from sequence data and microscopic identification suggested the presence of hidden, yet extremely abundant aplastidic cryptophytes that were confirmed by CARD-FISH analyses. Aplastidic cryptophytes are prevalent throughout the water column but have never been considered in prior models of plankton dynamics. We also recovered the first metagenomic-assembled genomes of freshwater protists (a diatom and a haptophyte) along with thousands of giant viral genomic contigs, some of which appeared similar to viruses infecting haptophytes but owing to lack of known representatives, most remained without any indication of their hosts. The contrasting distribution of giant viruses that are present in the entire water column to that of parasitic perkinsids residing largely in deeper waters allows us to propose giant viruses as the biological agents of top-down control and bloom collapse, likely in combination with bottom-up factors like a nutrient limitation.

CONCLUSION

We reconstructed thousands of genomes of microbes and viruses from a freshwater spring bloom and show that such large-scale genome recovery allows tracking of planktonic succession in great detail. However, integration of metagenomic information with other methodologies (e.g., microscopy, CARD-FISH) remains critical to reveal diverse phenomena (e.g., distributional patterns, in situ doubling times) and novel participants (e.g., aplastidic cryptophytes) and to further refine existing ecological models (e.g., factors affecting bloom collapse). This work provides a genomic foundation for future approaches towards a fine-scale characterization of the organisms in relation to the rapidly changing environment during the course of the freshwater spring bloom. Video Abstract.

Nitrogen and Iron Availability Drive Metabolic Remodeling and Natural Selection of Diverse Phytoplankton during Experimental Upwelling

Nearly half of carbon fixation and primary production originates from marine phytoplankton, and much of it occurs in episodic blooms in upwelling regimes. Here, we simulated blooms limited by nitrogen and iron by incubating Monterey Bay surface waters with subnutricline waters and inorganic nutrients and measured the whole-community transcriptomic response during mid- and late-bloom conditions. Cell counts revealed that centric and pennate diatoms (largely Pseudo-nitzschia and Chaetoceros spp.) were the major blooming taxa, but dinoflagellates, prasinophytes, and prymnesiophytes also increased. Viral mRNA significantly increased in late bloom and likely played a role in the bloom's demise. We observed conserved shifts in the genetic similarity of phytoplankton populations to cultivated strains, indicating adaptive population-level changes in community composition. Additionally, the density of single nucleotide variants (SNVs) declined in late-bloom samples for most taxa, indicating a loss of intraspecific diversity as a result of competition and a selective sweep of adaptive alleles. We noted differences between mid- and late-bloom metabolism and differential regulation of light-harvesting complexes (LHCs) under nutrient stress. While most LHCs are diminished under nutrient stress, we showed that diverse taxa upregulated specialized, energy-dissipating LHCs in low iron. We also suggest the relative expression of NRT2 compared to the expression of GSII as a marker of cellular nitrogen status and the relative expression of iron starvation-induced protein genes (ISIP1, ISIP2, and ISIP3) compared to the expression of the thiamine biosynthesis gene (thiC) as a marker of iron status in natural diatom communities. IMPORTANCE Iron and nitrogen are the nutrients that most commonly limit phytoplankton growth in the world's oceans. The utilization of these resources by phytoplankton sets the biomass available to marine systems and is of particular interest in high-nutrient, low-chlorophyll (HNLC) coastal fisheries. Previous research has described the biogeography of phytoplankton in HNLC regions and the transcriptional responses of representative taxa to nutrient limitation. However, the differential transcriptional responses of whole phytoplankton communities to iron and nitrogen limitation has not been previously described, nor has the selective pressure that these competitive bloom environments exert on major players. In addition to describing changes in the physiology of diverse phytoplankton, we suggest practical indicators of cellular nitrogen and iron status for future monitoring.

Uncertainty quantification for ecological models with random parameters

There is often considerable uncertainty in parameters in ecological models. This uncertainty can be incorporated into models by treating parameters as random variables with distributions, rather than fixed quantities. Recent advances in uncertainty quantification methods, such as polynomial chaos approaches, allow for the analysis of models with random parameters. We introduce these methods with a motivating case study of sea ice algal blooms in heterogeneous environments. We compare Monte Carlo methods with polynomial chaos techniques to help understand the dynamics of an algal bloom model with random parameters. Modelling key parameters in the algal bloom model as random variables changes the timing, intensity and overall productivity of the modelled bloom. The computational efficiency of polynomial chaos methods provides a promising avenue for the broader inclusion of parametric uncertainty in ecological models, leading to improved model predictions and synthesis between models and data.

Dynamical Analysis of Nutrient-Phytoplankton-Zooplankton Model with Viral Disease in Phytoplankton Species under Atangana-Baleanu-Caputo Derivative

A mathematical model of the nutrient-phytoplankton-zooplankton associated with viral infection in phytoplankton under the Atangana-Baleanu derivative in Caputo sense is investigated in this study. We prove the theoretical results for the existence and uniqueness of the solutions by using Banach’s and Sadovskii’s fixed point theorems. The notion of various Ulam’s stability is used to guarantee the context of the stability analysis. Furthermore, the equilibrium points and the basic reproduction numbers for the proposed model are provided. The Adams type predictor-corrector algorithm has been applied for the theoretical confirmation to establish the approximate solutions. A variety of numerical plots corresponding to various fractional orders between zero and one are presented to describe the dynamical behavior of the fractional model under consideration.

Comparative metagenomics of phytoplankton blooms after nutrient enrichment of oligotrophic marine waters

Increasing anthropogenic pressures on the coastal marine environments impact these ecosystems via a variety of mechanisms including nutrient loading, leading to eutrophication and increases in algal blooms. Here, we use a metagenomics approach to assess the taxonomic and functional changes of the microbial community throughout a nutrient enriched mesocosm phytoplankton bloom. We tested four different nutrient treatments consisting of either nitrate and phosphate or nitrate, phosphate and silicate, administered on the first day or continuously for the first two weeks of the experiment. Our results show a shift in the taxonomic composition of the community over time that is dependent on the nutrient addition regime. Significant differences in the functional potential of the communities were detected, with an interaction between bloom period (pre-bloom, bloom and post-bloom) and nutrient treatment (p = 0.004). A sharp drop in functional similarity was observed in the first week in all treatments and after 20 days had not returned to pre-bloom levels. Changes within energy metabolism pathways showed a remarkable enrichment of the dissimilatory nitrate reduction pathway in the post-bloom period. Eukaryotic oxidative phosphorylation and photosynthetic antenna proteins were more abundant during the bloom, especially in the continuous treatment with silicate. Our results suggest that continuous (i.e. chronic) nutrient enrichment has a larger effect on the functioning of marine systems compared to a single (i.e acute) addition. A deep understanding of the functional and taxonomic shifts in the community during blooms is essential to reverse or mitigate human impacts on coastal environments.

Hopf Bifurcation Analysis of a Diffusive Nutrient–Phytoplankton Model with Time Delay

In this paper, we studied a nutrient–phytoplankton model with time delay and diffusion term. We studied the Turing instability, local stability, and the existence of Hopf bifurcation. Some formulas are obtained to determine the direction of the bifurcation and the stability of periodic solutions by the central manifold theory and normal form method. Finally, we verify the above conclusion through numerical simulation.

A nonautonomous mathematical model to assess the impact of algae on the abatement of atmospheric carbon dioxide

The world’s oceans have played an important role in sequestering atmospheric carbon dioxide through solubility and the action of algae. Fixation of atmospheric carbon dioxide by photoautotrophic algal cultures has the potential to diminish the release of carbon dioxide into the atmosphere, thereby helping to alleviate the trend toward global warming. This work investigates the role of algae in controlling the level of atmospheric carbon dioxide. Partial Rank Correlation Coefficients (PRCCs) technique is used to address how the concentration of atmospheric carbon dioxide is affected by changes in a specific parameter disregarding the uncertainty over the rest of the model parameters. Parameters related to algal growth are shown to significantly reduce the level of atmospheric CO2. Further, we explore the dynamics of nonautonomous system by incorporating the seasonal variations of some ecologically important model parameters. Our nonautonomous system exhibits globally attractive positive periodic solution, and also the appearance of double periodic solution is observed. Moreover, by letting the seasonally forced parameters as almost periodic functions of time, we show almost periodic behavior of the system. Our findings suggest that the policy makers should focus on continuous addition of nutrients in the ocean to accelerate the algal growth thereby reducing the level of carbon dioxide in the atmosphere.

Macro-Nutrient Stoichiometry of Glacier Algae From the Southwestern Margin of the Greenland Ice Sheet

Glacier algae residing within the surface ice of glaciers and ice sheets play globally significant roles in biogeochemical cycling, albedo feedbacks, and melt of the world's cryosphere. Here, we present an assessment of the macro-nutrient stoichiometry of glacier algal assemblages from the southwestern Greenland Ice Sheet (GrIS) margin, where widespread glacier algal blooms proliferate during summer melt seasons. Samples taken during the mid-2019 ablation season revealed overall lower cellular carbon (C), nitrogen (N), and phosphorus (P) content than predicted by standard microalgal cellular content:biovolume relationships, and elevated C:N and C:P ratios in all cases, with an overall estimated C:N:P of 1,997:73:1. We interpret lower cellular macro-nutrient content and elevated C:N and C:P ratios to reflect adaptation of glacier algal assemblages to their characteristic oligotrophic surface ice environment. Such lower macro-nutrient requirements would aid the proliferation of blooms across the nutrient poor cryosphere in a warming world. Up-scaling of our observations indicated the potential for glacier algal assemblages to accumulate ∼ 29 kg C km2 and ∼ 1.2 kg N km2 within our marginal surface ice location by the mid-ablation period (early August), confirming previous modeling estimates. While the long-term fate of glacier algal autochthonous production within surface ice remains unconstrained, data presented here provide insight into the possible quality of dissolved organic matter that may be released by assemblages into the surface ice environment.

Dynamics induced by environmental stochasticity in a phytoplankton-zooplankton system with toxic phytoplankton

Environmental stochasticity and toxin-producing phytoplankton (TPP) are the key factors that affect the aquatic ecosystems. To investigate the effects of environmental stochasticity and TPP on the dynamics of plankton populations, a stochastic phytoplankton-zooplankton system with two TPP is studied theoretically and numerically in this paper. Theoretically, we first prove that the system possesses a unique and global positive solution with positive initial values, and then derive some sufficient conditions guaranteeing the extinction and persistence in the mean of the system. Significantly, it is shown that the system has a stationary distribution when toxin liberation rate reaches some a critical value. Additionally, numerical analysis shows that the white noise can affect the survival of plankton populations directly. Furthermore, it has been observed that the increasing one toxin liberation rate can increase the survival chance of phytoplankton and reduce the biomass of zooplankton, but the combined effects of two liberation rates on the changes in plankton populations are stronger than that of controlling any one of the two TPP.

Modelling and parameter inference of predator-prey dynamics in heterogeneous environments using the direct integral approach

Most bacterial habitats are topographically complex in the micro scale. Important examples include the gastrointestinal and tracheal tracts, and the soil. Although there are myriad theoretical studies that explore the role of spatial structures on antagonistic interactions (predation, competition) among animals, there are many fewer experimental studies that have explored, validated and quantified their predictions. In this study, we experimentally monitored the temporal dynamic of the predatory bacterium Bdellovibrio bacteriovorus, and its prey, the bacterium Burkholderia stabilis in a structured habitat consisting of sand under various regimes of wetness. We constructed a dynamic model, and estimated its parameters by further developing the direct integral method, a novel estimation procedure that exploits the separability of the states and parameters in the model. We also verified that one of our parameter estimates was consistent with its known, directly measured value from the literature. The ability of the model to fit the data combined with realistic parameter estimates indicate that bacterial predation in the sand can be described by a relatively simple model, and stress the importance of prey refuge on predation dynamics in heterogeneous environments.

DIFFUSIVE THREE SPECIES PLANKTON MODEL IN THE PRESENCE OF TOXIC PREY: APPLICATION TO SUNDARBAN MANGROVE WETLAND

The bloom of toxin producing phytoplankton (TPP) is an environmental issue due to its negative impact on fresh water and marine ecology. In this paper, such a phenomenon is modeled using the reaction–diffusion equations. The spatiotemporal interaction among non-toxin producing phytoplankton (NTP), TPP, and zooplankton has been considered with Holling type II and III functional responses. The stability analysis for non-spatial and spatial model system is carried out and numerical simulations are performed for a fixed set of parameter values, which is realistic to planktonic dynamics. It has been observed that on increasing the reduction rate of zooplankton, the system shows cyclic to stable behavior. The result shows that the predators which avoid to toxic prey promote the bloom. Non-Turing patchy pattern has also been observed on time evolution. In this work, we have taken the case study of Sundarban mangrove wetland which is suffering from algal bloom due to the presence of toxic Dinoflagellates and Cyanophyceae. Through the numerical simulation, it has been shown that the higher value of reduction rate of zooplankton ([Formula: see text]) is responsible for bad health of the wetland system.

Bifurcation behaviors analysis of a plankton model with multiple delays

A mathematical model describing the dynamics of toxin producing phytoplankton–zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.

Spatial dynamics of a nutrient-phytoplankton system with toxic effect on phytoplankton

The production of toxins by some species of phytoplankton is known to have several economic, ecological, and human health impacts. However, the role of toxins on the spatial distribution of phytoplankton is not well understood. In the present study, the spatial dynamics of a nutrient-phytoplankton system with toxic effect on phytoplankton is investigated. We analyze the linear stability of the system and obtain the condition for Turing instability. In the presence of toxic effect, we find that the distribution of nutrient and phytoplankton becomes inhomogeneous in space and results in different patterns, like stripes, spots, and the mixture of them depending on the toxicity level. We also observe that the distribution of nutrient and phytoplankton shows spatiotemporal oscillation for certain toxicity level.

Delay-induced instability in a nutrient-phytoplankton system with flow

In this paper, a nutrient-phytoplankton system described by a couple of advection-diffusion-reaction equations with delay was studied analytically and numerically. The aim of this research was to provide an understanding of the impact of delay on instability. Significantly, delay cannot only induce instability, but can also promote the formation of spatial pattern via a Turing-like instability. In addition, the theoretical analysis indicates that the flow (advection term) may lead to instability when the delay term exists. By comparison, diffusion cannot result in Turing instability when flow does not exist. Results of numerical simulation were consistent with the analytical results.

Effect of demographic noise in a phytoplankton-zooplankton model of bloom dynamics

An extension of the Truscott-Brindley model [Bull. Math. Biol. 56, 981 (1994)] is derived to account for the effect of demographic fluctuations. In the presence of seasonal forcing and sufficiently shallow water conditions, the fluctuations induced by the discreteness of the zooplankton component appear sufficient to cause switching between the bloom and no-bloom cycles predicted at the mean-field level by the model. The destabilization persists in the thermodynamic limit of a water basin infinitely extended in the horizontal direction.

Successional dynamics in the seasonally forced diamond food web

Plankton seasonal succession is a classic example of nonequilibrium community dynamics. Despite the fact that it has been well studied empirically, it lacks a general quantitative theory. Here we investigate a food web model that includes a resource, two phytoplankton, and a shared grazer-the diamond food web-in a seasonal environment. The model produces a number of successional trajectories that have been widely discussed in the context of the verbal Plankton Ecology Group model of succession, such as a spring bloom of a good competitor followed by a grazer-induced clear-water phase, setting the stage for the late-season dominance of a grazer-resistant species. It also predicts a novel, counterintuitive trajectory where the grazer-resistant species has both early- and late-season blooms. The model often generates regular annual cycles but sometimes produces multiyear cycles or chaos, even with identical forcing each year. Parameterizing the model, we show how the successional trajectory depends on nutrient supply and the length of the growing season, two key parameters that vary among water bodies. This model extends nonequilibrium theory to food webs and is a first step toward a quantitative theory of plankton seasonal succession.

Recurring plankton bloom dynamics modeled via toxin-producing phytoplankton

A simple nutrient-phytoplankton model is proposed and analyzed in the presence of toxic chemicals released by toxin-producing phytoplankton (TPP) to understand the dynamics of seasonally recurring bloom phenomena. We observe that the presence of toxic chemicals helps to explain the bloom phenomenon. We have further studied our proposed system by varying the toxin liberation rate. Our model displays a wide range of dynamical behaviours, from simple cyclical blooms to irregular chaotic blooms. We also observe skipping phenomenon. The effect of toxic chemicals released by TPP cannot, thus, be ignored in 'bottom-up' models.

Water temperature and mixing depth affect timing and magnitude of events during spring succession of the plankton

In many lakes, the most conspicuous seasonal events are the phytoplankton spring bloom and the subsequent clear-water phase, a period of low-phytoplankton biomass that is frequently caused by mesozooplankton (Daphnia) grazing. In Central European lakes, the timing of the clear-water phase is linked to large-scale climatic forcing, with warmer winters being followed by an earlier onset of the clear-water phase. Mild winters may favour an early build-up of Daphnia populations, both directly through increased surface temperatures and indirectly by reducing light limitation and enhancing algal production, all being a consequence of earlier thermal stratification. We conducted a field experiment to disentangle the separate impacts of stratification depth (affecting light supply) and temperature on the magnitude and timing of successional events in the plankton. We followed the dynamics of the phytoplankton spring bloom, the clear-water phase and the spring peak in Daphnia abundance in response to our experimental manipulations. Deeper mixing delayed the timing of all spring seasonal events and reduced the magnitudes of the phytoplankton bloom and the subsequent Daphnia peak. Colder temperatures retarded the timing of the clear-water phase and the subsequent Daphnia peak, whereas the timing of the phytoplankton peak was unrelated to temperature. Most effects of mixing depth (light) and temperature manipulations were independent, effects of mixing depth being more prevalent than effects of temperature. Because mixing depth governs both the light climate and the temperature regime in the mixed surface layer, we propose that climate-driven changes in the timing and depth of water column stratification may have far-reaching consequences for plankton dynamics and should receive increased attention.

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.

Chaos in a periodically forced chemostat with algal mortality

We study the possibility of chaotic dynamics in the externally driven Droop model. This model describes a phytoplankton population in a chemostat under periodic nutrient supply. Previously, it has been proven under very general assumptions, that such systems are not able to exhibit chaotic dynamics. We show that the simple introduction of algal mortality may lead to chaotic oscillations of algal density in the forced chemostat. Our numerical simulations show that the existence of chaos is intimately related to plankton overshooting in the unforced model. We provide a simple measure, based on stability analysis, for estimating the amount of overshooting. These findings are not restricted to the Droop model but also hold for other chemostat models with mortality. Our results suggest periodically driven chemostats as a simple model system for the experimental verification of chaos in ecology.

What Minimal Models Cannot Tell: A Comment on “A Model of Phytoplankton Blooms”

Huppert et al. analyzed a simple model describing bottom-up control of phytoplankton blooms. While we appreciate the mathematical aspects of this article, we feel that the fit of their model to data of Lake Kinneret is overly optimistic because the time axis was rescaled in an arbitrary way. Furthermore, one of the main conclusions of the article (bottom-up control is more likely to occur than top-down control) cannot, in our opinion, be drawn from a minimal model because such a model focuses on one explanation. It cannot be used to reveal the relative importance of alternative explanations.

Coastal oceanography sets the pace of rocky intertidal community dynamics

The structure of ecological communities reflects a tension among forces that alter populations. Marine ecologists previously emphasized control by locally operating forces (predation, competition, and disturbance), but newer studies suggest that inputs from large-scale oceanographically modulated subsidies (nutrients, particulates, and propagules) can strongly influence community structure and dynamics. On New Zealand rocky shores, the magnitude of such subsidies differs profoundly between contrasting oceanographic regimes. Community structure, and particularly the pace of community dynamics, differ dramatically between intermittent upwelling regimes compared with relatively persistent down-welling regimes. We suggest that subsidy rates are a key determinant of the intensity of species interactions, and thus of structure in marine systems, and perhaps also nonmarine communities.