Toxin-producing Phytoplankton Research Articles

Bifurcation analysis in a discrete toxin-producing phytoplankton–zooplankton model with refuge

This paper concerns a discrete-time phytoplankton–zooplankton model in which the effects of toxin produced by phytoplankton and refuges provided for phytoplankton on the interactions between phytoplankton and zooplankton are considered. We first discuss the existence and stability of fixed points. When two parameters change, it is shown that there exist some codimension-two bifurcations, including fold-flip bifurcation and strong resonance bifurcations. Moreover, we give the corresponding bifurcation diagrams, phase diagrams and maximum Lyapunov exponent diagrams. The results show that phytoplankton toxin and refuges play important roles in the occurrence and termination of algal blooms in freshwater lakes.

Impact of selective grazing on the dynamics of a diffusive plankton model with component Allee effect and additional food

In order to explore the pattern formation of non-toxic phytoplankton, toxin-producing phytoplankton, and zooplankton, a spatiotemporal plankton model is formulated by incorporating the component Allee effect, additional food, and selective grazing. For the non-spatial scenario, the qualitative analyses and numerical simulations show that the system admits rich dynamics such as Hopf bifurcation and alternative stable states. For the spatial model, the stability analyses demonstrate that the moderate component Allee effect and adequate additional food promote stable coexistence. Furthermore, our findings illustrate that selective grazing facilitates toxin-producing phytoplankton biomass. Low grazing selectivity decreases zooplankton biomass. Moderate grazing selectivity contributes to coexistence. Excessive grazing selectivity promotes the rapid reproduction of toxin-producing phytoplankton and leads to spatiotemporal chaos. In addition, the variations in the component Allee effect, additional food, and grazing selectivity give rise to the transitions of spatial patterns, which shed valuable insights into controlling plankton distribution.

Mathematical Modelling of Harmful Algal Blooms on West Coast of Sabah

Algal bloom is a condition in which there is a massive growth of algae in a certain region and it is said to be harmful when the bloom causes damage effects. Due to the tremendous impact of harmful algal bloom (HAB) on some aspects, this research proposes the mathematical modelling of an HAB model to describe the process of HAB together with population dynamics. This research considers the delay terms in the modelling since the liberation of toxic chemicals by toxin-producing phytoplankton (TPP) is not an instantaneous process in which the species need to achieve their maturity. A model of fish interaction is also being studied to show the effect of HAB on fish species. Time delay is incorporated for the mortality of fish due to the consumption of toxic zooplankton. Stability analysis is conducted and numerical simulations are applied to obtain the analytical results which highlight the critical values for the delay parameters. The existence of Hopf bifurcation is established when the delay passes the threshold value. The results of both models show that the inclusion of the delay term affects the model by stabilizing and destabilizing the model. Therefore, this research shows the effect of an inclusion delay term on the model and also gives knowledge and an understanding of the process of HAB occurrence as well as the effect of HAB on fish populations.

The impact of environmental fluctuations on a plankton model with toxin-producing phytoplankton and patchy agglomeration

In aquatic ecosystem, plankton populations are easily affected by environmental fluctuations due to the unpredictability of many physical factors such as nutrient availability, acidity, water temperature and so on. To reveal how environmental fluctuations influence plankton populations, in this paper, we develop and analyze a stochastic toxin-producing phytoplankton (TPP)-zooplankton model with patchy agglomeration. We first perform the survival analysis of the model, including the persistence and extinction as well as the existence of ergodic stationary distribution. Then, for the scenario when the model exhibits bistability between a positive equilibrium or a limit cycle and TPP-only equilibrium in the absence of noise, we further study the phenomenon of noise-induced transition from plankton coexistence to zooplankton extirpation. Also, we numerically estimate the critical values of noise intensities for the occurrence of transitions with the aids of the technique of stochastic sensitivity functions. Our research indicates that zooplankton population becomes more vulnerable and easily goes to extinction in the presence of environmental noise, and as a result, phytoplankton could benefit from the decrease of grazing pressure. This partially explains the often seen phenomenon in aquatic ecosystems that many toxin-releasing microalgal species with patchy agglomeration are more likely to cause blooms.

Dynamics of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton and impulsive perturbations

This paper describes an analytical and numerical investigation of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton (TPP) and impulsive perturbations. White noise, impulsive perturbations, and TPP were incorporated into the system to stimulate natural aquatic ecological phenomena. The aim of this paper was to analyze how these factors affect the dynamics of the system. Mathematical derivations were utilized to investigate some key threshold conditions that ensure the existence and uniqueness of a global positive solution, population extinction, and persistence in the mean. In particular, we determined if there is a positive periodic solution for the system when the toxin liberation rate reaches a critical value. The numerical results indicated that both white noise and the impulsive control parameter can directly influence population extinction and persistence in the mean. Enhancing the toxin liberation rate of TPP increases the possibility of phytoplankton survival but reduces zooplankton biomass. These results improve our understanding of the dynamics of complex of aquatic ecosystems in a fluctuating environment.

The role of harvesting in population control in the presence of correlated noise sources

In this paper, we compare the role of constant and Michaelis-Menten type harvesting in single species population control in presence of correlated noise sources. Our aim is to determine a statistical correlation between the noises in the model parameters and population size. The characteristic time scale over which the population size of prey and predator varies are very much different, this fact justifies to consider a single species model as the predator population can be chosen to be constant within the generation time of prey. Steady state probability distributions and stationary potentials of the population are determined by Fokker-Planck equations. Stochastic bifurcation analysis and mean first passage times have been computed. Noise induced critical transitions are observed depending on the strength of the noises. The extinction possibility of population in stochastic control with Michaelis-Menten type harvesting is higher than the constant harvesting. One of our key findings is the transition from bistable to tristable state for weak noises. Another valuable finding is the noise enhanced stability phenomenon for negatively correlated noises. Constant rate of harvesting is better in deterministic case whereas Michaelis-Menten type harvesting is better in stochastic case to reduce population size. The obtained results may be helpful to understand toxin producing phytoplankton blooms and its control in marine ecosystem. Moreover, the study can be useful to explain wild prey population outbreak or extinction in forest.

Dynamics of a stochastic phytoplankton–toxic phytoplankton–zooplankton system under regime switching

In this paper, a stochastic phytoplankton–toxic phytoplankton–zooplankton system with Beddington–DeAngelis functional response, where both the white noise and regime switching are taken into account, is studied analytically and numerically. The aim of this research is to study the combined effects of the white noise, regime switching, and toxin‐producing phytoplankton (TPP) on the dynamics of the system. Firstly, the existence and uniqueness of global positive solution of the system is investigated. Then some sufficient conditions for the extinction, persistence in the mean, and the existence of a unique ergodic stationary distribution of the system are derived. Significantly, some numerical simulations are carried to verify our analytical results and show that high intensity of white noise is harmful to the survival of plankton populations, but regime switching can balance the different survival states of plankton populations and decrease the risk of extinction. Additionally, it is found that an increase in the toxin liberation rate produced by TPP will increase the survival chance of phytoplankton, while it will reduce the biomass of zooplankton. All these results may provide some insightful understanding on the dynamics of phytoplankton–zooplankton systems in randomly disturbed aquatic environments.

Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System

It is well known that the evolution of natural populations is almost inevitably disturbed by various environmental factors. Various experiments have shown that the growth of phytoplankton might be affected by nutrient availability, water temperature, and light, while the development of zooplankton is more disturbed by the pH value of the seawater, water temperature, and water movement. However, it is not clear how these environmental fluctuations affect the dynamical behavior of the phytoplankton and zooplankton system. In this paper, a stochastic eco-epidemiological model for viral infection in the toxin-producing phytoplankton and zooplankton system is proposed. Firstly, the existence and uniqueness of globally positive solutions for this model is shown. Secondly, the stochastic boundedness of solutions for the model is proved. Moreover, sufficient conditions for the extinction and persistence in the mean for the phytoplankton and zooplankton are obtained by constructing appropriate stochastic Lyapunov functions and using analytical techniques. Numerical simulations are carried out to demonstrate different dynamical behaviors including coexistence, extinction of the whole plankton system, partial persistence and extinction, and their corresponding probability density curves.

Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model

In this paper, we study a reaction-diffusion nutrient-phytoplankton model with nutrient recycling delay and toxin-producing phytoplankton. For the delay-free case, we prove that the release rate of toxic chemicals by the toxin-producing phytoplankton can destabilize the system and cause periodic oscillation. For the time-delayed case, we observe that nutrient recycling delay may bring about stability switches and Hopf bifurcation. Moreover, we derive the formula for determining the direction and stability of the bifurcating periodic solutions. Finally, we give some numerical simulations to support the theoretical analyses.

Seasonal plankton succession is in accordance with phycotoxin occurrence in Disko Bay, West Greenland

Harmful algal blooms (HABs) are occurring more frequently in the world's oceans, probably as a consequence of climate change. HABs have not been considered a serious concern in the Arctic, even though the Arctic warms faster than any other region. While phycotoxins and toxin-producing phytoplankton have been found in Arctic waters on several occasions, there is a lack of information on seasonal succession of species and whether the occurrence of harmful species correlates with the presence of their respective phycotoxins. Hence, there is no baseline to assess future changes of HABs in this area. Here, we investigated two periods, from winter to spring and from the spring bloom until summer, in Disko Bay, West Greenland and followed the succession of toxins and their producers using metabarcoding, as well as analyses of particulate and dissolved toxins. We observed a typical seasonal succession with a spring bloom dominated by diatoms, followed by dinoflagellates in summer, with the two most important potentially toxic taxa found being Pseudo-nitzschia spp. and Alexandrium ostenfeldii. The Pseudo-nitzschia spp. peak correlated with a clear increase in particulate domoic acid, reaching 0.05 pg/L. Presence of Alexandrium ostenfeldii could be linked to an increase in spirolides, up to 56.4 pg/L in the particulate phase. Generally, the majority of detected dissolved toxins followed the succession pattern of the particulate toxins with a delay in time. Our results further show that Arctic waters are a suitable habitat for various toxin producers and that the strong seasonality of this environment is reflected by changing abundances of different toxins that pose a potential threat to the ecosystem and its beneficiaries.

Dynamical study of harmful algal bloom in Sundarban mangrove wetland with spatial interaction and competing effects

Sundarbans is the largest mangrove wetland ecosystem of the world with rich biodiversity suffering from deteriorated water quality due to excessive fertilization that leads to an uncontrolled increase in phytoplankton. Such eutrophication also changes the community structure and increases the harmful algal blooms (HABs). In this work, we propose an interacting population model for phytoplankton–zooplankton system in which the density of zooplankton is influenced by non-toxic phytoplankton (NTP) and toxin-producing phytoplankton (TPP) followed by Holling type II and Monod–Haldane (MH)-type functional response. The growth of zooplankton species is assumed to reduce due to toxic chemicals released by TPP population. The mathematical model of the proposed system includes the competition terms between TPP and NTP. System dynamics is studied in both cases, i.e., system with diffusion and without diffusion. For the non-diffusive system, we have investigated the condition for boundedness along with the existing criteria of all feasible equilibrium point. Stability analysis of the model system is carried out in detail for each equilibrium point. Forward and backward bifurcation diagrams are obtained for the temporal system in order to understand the behavior of different parameters that control the system dynamics. Theoretically, stability criteria and Turing instability of diffusive system are derived. In this study, we have taken a case of Sundarban mangrove wetland which is suffering from algal blooms due to the presence of toxic Dinoflagellates and Cyanophyceae. Our numerical investigation shows that the lower value of intraspecific interference of zooplankton promotes the complex spatiotemporal dynamics for the population of non-toxic, toxic phytoplankton and zooplankton. The higher value of inter-specific competition coefficient of NTP leads to reduction in zooplankton density that may cause bad health of the wetland system. This investigation renders the importance of diffusion in algal blooms by the occurrence of different Turing patterns and the role of time delay in destabilization of stationary points through the creation of limit cycles. We observed that the increasing value of diffusion coefficient of zooplankton and time allows the algal blooms to settle down from spot-strip mixture to spot patterns.

Fully automatic detection and classification of phytoplankton specimens in digital microscopy images

Background and objectiveThe proliferation of toxin-producing phytoplankton species can compromise the quality of the water sources. This contamination is difficult to detect, and consequently to be neutralised, since normal water purification techniques are ineffective. Currently, the water analyses about phytoplankton are commonly performed by the specialists with manual routine analyses, which represents a major limitation. The adequate identification and classification of phytoplankton specimens requires intensive training and expertise. Additionally, the performed analysis involves a lengthy process that exhibits serious problems of reliability and repeatability as inter-expert agreement is not always reached. Considering all those factors, the automatization of these analyses is, therefore, highly desirable to reduce the workload of the specialists and facilitate the process. MethodsThis manuscript proposes a novel fully automatic methodology to perform phytoplankton analyses in digital microscopy images of water samples taken with a regular light microscope. In particular, we propose a method capable of analysing multi-specimen images acquired using a simplified systematic protocol. In contrast with prior approaches, this enables its use without the necessity of an expert taxonomist operating the microscope. The system is able to detect and segment the different existing phytoplankton specimens, with high variability in terms of visual appearances, and to merge them into colonies and sparse specimens when necessary. Moreover, the system is capable of differentiating them from other similar objects like zooplankton, detritus or mineral particles, among others, and then classify the specimens into defined target species of interest using a machine learning-based approach. ResultsThe proposed system provided satisfactory and accurate results in every step. The detection step provided a FNR of 0.4%. Phytoplankton detection, that is, differentiating true phytoplankton from similar objects (zooplankton, minerals, etc.), provided a result of 84.07% of precision at 90% of recall. The target species classification, reported an overall accuracy of 87.50%. The recall levels for each species are, 81.82% for W. naegeliana, 57.15% for A. spiroides, 85.71% for D. sociale and 95% for the ”Other” group, a set of relevant toxic and interesting species widely spread over the samples. ConclusionsThe proposed methodology provided accurate results in all the designed steps given the complexity of the problem, particularly in terms of specimen identification, phytoplankton differentiation as well as the classification of the defined target species. Therefore, this fully automatic system represents a robust and consistent tool to aid the specialists in the analysis of the quality of the water sources and potability.

An assessment of temporal, spatial and taxonomic trends in harmful algal toxin exposure in stranded marine mammals from the U.S. New England coast.

Despite a long-documented history of severe harmful algal blooms (HABs) in New England coastal waters, corresponding HAB-associated marine mammal mortality events in this region are far less frequent or severe relative to other regions where HABs are common. This long-term survey of the HAB toxins saxitoxin (STX) and domoic acid (DA) demonstrates significant and widespread exposure of these toxins in New England marine mammals, across multiple geographic, temporal and taxonomic groups. Overall, 19% of the 458 animals tested positive for one or more toxins, with 15% and 7% testing positive for STX and DA, respectively. 74% of the 23 different species analyzed demonstrated evidence of toxin exposure. STX was most prevalent in Maine coastal waters, most frequently detected in common dolphins (Delphinus delphis), and most often detected during July and October. DA was most prevalent in animals sampled in offshore locations and in bycaught animals, and most frequently detected in mysticetes, with humpback whales (Megaptera novaeangliae) testing positive at the highest rates. Feces and urine appeared to be the sample matrices most useful for determining the presence of toxins in an exposed animal, with feces samples having the highest concentrations of STX or DA. No relationship was found between the bloom season of toxin-producing phytoplankton and toxin detection rates, however STX was more likely to be present in July and October. No relationship between marine mammal dietary preference and frequency of toxin detection was observed. These findings are an important part of a framework for assessing future marine mammal morbidity and mortality events, as well as monitoring ecosystem health using marine mammals as sentinel organisms for predicting coastal ocean changes.

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.

Automatic Detection of Freshwater Phytoplankton Specimens in Conventional Microscopy Images.

Water safety and quality can be compromised by the proliferation of toxin-producing phytoplankton species, requiring continuous monitoring of water sources. This analysis involves the identification and counting of these species which requires broad experience and knowledge. The automatization of these tasks is highly desirable as it would release the experts from tedious work, eliminate subjective factors, and improve repeatability. Thus, in this preliminary work, we propose to advance towards an automatic methodology for phytoplankton analysis in digital images of water samples acquired using regular microscopes. In particular, we propose a novel and fully automatic method to detect and segment the existent phytoplankton specimens in these images using classical computer vision algorithms. The proposed method is able to correctly detect sparse colonies as single phytoplankton candidates, thanks to a novel fusion algorithm, and is able to differentiate phytoplankton specimens from other image objects in the microscope samples (like minerals, bubbles or detritus) using a machine learning based approach that exploits texture and colour features. Our preliminary experiments demonstrate that the proposed method provides satisfactory and accurate results.

Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food

<p style='text-indent:20px;'>The article aims to investigate the dynamic transitions of a toxin-producing phytoplankton zooplankton model with additional food in a 2D-rectangular domain. The investigation is based on the dynamic transition theory for dissipative dynamical systems. Firstly, we verify the principle of exchange of stability by analysing the corresponding linear eigenvalue problem. Secondly, by using the technique of center manifold reduction, we determine the types of transitions. Our results imply that the model may bifurcate two new steady state solutions, which are either attractors or saddle points. In addition, the model may also bifurcate a new periodic solution as the control parameter passes critical value. Finally, some numerical results are given to illustrate our conclusions.

Dynamical analysis of a stochastic toxin-producing phytoplankton\u2013fish system with harvesting

In this paper, we analytically and numerically study the dynamics of a stochastic toxin-producing phytoplankton–fish system with harvesting. Mathematically, we give the existence and stability of the positive equilibrium in the deterministic system (i.e., the system without environmental noise fluctuations). In the case of the stochastic system (i.e., the system with environmental noise fluctuations), in addition to the existence and uniqueness of the positive solution, we provide the properties of the stochastic dynamics including the stochastic extinction and persistence in the mean, almost sure permanence and uniform boundedness, and the existence of ergodic stationary distribution for the phytoplankton and fish. Ecologically, via numerical analysis, we find that (1) the small random environmental fluctuations can ensure the persistence of phytoplankton and fish, but the larger one can result in the extinction of these populations; (2) an appropriate increase in harvest rate can reduce the irregular random variation of phytoplankton and fish; (3) the increase of toxin liberate rate is capable to decrease the height of probability density function of phytoplankton. These results may help us to better understand the phytoplankton–fish dynamics.

Mathematical analysis of plankton population dynamics

Harmful algal blooms (HABs) event that causes enormous economic loss and health effect raises concerns among environmentalists. In this paper, a mathematical model of interaction between nutrient, toxin-producing phytoplankton (TPP), non-toxic phytoplankton (NTP), zooplankton, and toxic chemicals is proposed to study on how the process of these HABs occurred. The model of interaction is represented by Ordinary Differential Equations (ODEs) and stability analysis of the model is conducted. Several conditions for the system to be stable around trivial and interior equilibrium point are obtained. From the analysis, it is observed that under nutrient limitation, the amounts of toxic chemicals secreted out by the TPP are increased. As a result, NTP population and zooplankton population are affected by the situation. If this situation is prolonged, this will result in the extinction of both populations. Overall, this study shows that TPP release more toxic chemicals when the nutrient is limited and gives a better understanding on the occurrence of HABs event.

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

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

Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems

In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and stability of equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations.