Nonlinear dynamics of plankton ecosystem with impulsive control and environmental fluctuations

It is well known that the density of plankton populations always increases and decreases or keeps invariant for a long time, and the variation of plankton density is an important factor influencing the real aquatic environments, why do these situations occur? It is an interesting topic which has become the common interest for many researchers. As the basis of the food webs in oceans, lakes, and reservoirs, plankton plays a significant role in the material circulation and energy flow for real aquatic ecosystems that have a great effect on the economic and social values. Planktonic blooms can occur in some environments, however, and the direct or indirect adverse effects of planktonic blooms on real aquatic ecosystems, such as water quality, water landscape, aquaculture development, are sometimes catastrophic, and thus planktonic blooms have become a challenging and intractable problem worldwide in recent years. Therefore, to understand these effects so that some necessary measures can be taken, it is important and meaningful to investigate the dynamic growth mechanism of plankton and reveal the dynamics mechanisms of formation and disappearance of planktonic blooms. To this end, based on the background of the ecological environments in the subtropical lakes and reservoirs, this dissertation research takes mainly the planktonic algae as the research objective to model the mechanisms of plankton growth and evolution. In this dissertation, some theories related to population dynamics, impulsive control dynamics, stochastic dynamics, as well as the methods of dynamic modeling, dynamic analysis and experimental simulation, are applied to reveal the effects of some key biological factors on the dynamics mechanisms of the spatial-temporal distribution of plankton and the termination of planktonic blooms, and to predict the dynamics evolutionary processes of plankton growth. The main results are as follows: Firstly, to discuss the prevention and control strategies on planktonic blooms, an impulsive reaction-diffusion hybrid system was developed. On the one hand, the dynamic analysis showed that impulsive control can significantly influence the dynamics of the system, including the ultimate boundedness, extinction, permanence, and the existence and uniqueness of positive periodic solution of the system. On the other hand, some experimental simulations were preformed to reveal that impulsive control can lead to the extinction and permanence of population directly. More precisely, the prey and intermediate predator populations can coexist at any time and location of their inhabited domain, while the top predator population undergoes extinction when the impulsive control parameter exceeds some a critical value, which can provide some key arguments to control population survival by means of some reaction-diffusion impulsive hybrid systems in the real life. Additionally, a heterogeneous environment can affect the spatial distribution of plankton and change the temporal-spatial oscillation of plankton distribution. All results are expected to be helpful in the study of dynamic complex of ecosystems. Secondly, a stochastic phytoplankton-zooplankton system with toxic phytoplankton was proposed and the effects of environmental stochasticity and toxin-producing phytoplankton (TPP) on the dynamics mechanisms of the termination of planktonic blooms were discussed. The research illustrated that white noise can aggravate the stochastic oscillation of plankton density and a high-level intensity of white noise can accelerate the extinction of plankton and may be advantageous for the disappearance of harmful phytoplankton, which imply that the white noise can help control the biomass of plankton and provide a guide for the termination of planktonic blooms. Additionally, some experimental simulations were carried out to reveal that the increasing toxin liberation rate released by TPP can increase the survival chance of phytoplankton population and reduce the biomass of zooplankton population, but the combined effects of those two toxin liberation rates on the changes in plankton are stronger than that of controlling any one of the two TPP. All results suggest that both white noise and TPP can play an important role in controlling planktonic blooms. Thirdly, we established a stochastic phytoplankton-toxic producing phytoplankton-zooplankton system under regime switching and investigated how the white noise, regime switching and TPP affect the dynamics mechanisms of planktonic blooms. The dynamical analysis indicated that both white noise and toxins released by TPP are disadvantageous to the development of plankton and may increase the risk of plankton extinction. Also, a series of experimental simulations were carried out to verify the correctness of the dynamical analysis and further reveal the effects of the white noise, regime switching and TPP on the dynamics mechanisms of the termination of planktonic blooms. On the one hand, the numerical study revealed that the system can switch from one state to another due to regime shift, and further indicated that the regime switching can balance the different survival states of plankton density and decrease the risk of plankton extinction when the density of white noise are particularly weak. On the other hand, an increase in the toxin liberation rate can increase the survival chance of phytoplankton but reduce the biomass of zooplankton, which implies that the presence of toxic phytoplankton may have a positive effect on the termination of planktonic blooms. These results may provide some insightful understanding on the dynamics of phytoplankton-zooplankton systems in randomly disturbed aquatic environments. Finally, a stochastic non-autonomous phytoplankton-zooplankton system involving TPP and impulsive perturbations was studied, where the white noise, impulsive perturbations and TPP are incorporated into the system to simulate the natural aquatic ecological phenomena. The dynamical analysis revealed some key threshold conditions that ensure the existence and uniqueness of a global positive solution, plankton 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. Some experimental simulations also revealed that both white noise and impulsive control parameter can directly influence the plankton extinction and persistence in the mean. Significantly, enhancing the toxin liberation rate released by TPP increases the possibility of phytoplankton survival but reduces the zooplankton biomass. All these results can improve our understanding of the dynamics of complex of aquatic ecosystems in a fluctuating environment

Nonlinear Dynamics of a Toxin-Phytoplankton-Zooplankton System with Self- and Cross-Diffusion

A nonlinear system describing the interaction between toxin-producing phytoplankton and zooplankton was investigated analytically and numerically, where the system was represented by a couple of reaction-diffusion equations. We analyzed the effect of self- and cross-diffusion on the system. Some conditions for the local and global stability of the equilibrium were obtained based on the theoretical analysis. Furthermore, we found that the equilibrium lost its stability via Turing instability and patterns formation then occurred. In particular, the analysis indicated that cross-diffusion can play an important role in pattern formation. Subsequently, we performed a series of numerical simulations to further study the dynamics of the system, which demonstrated the rich dynamics induced by diffusion in the system. In addition, the numerical simulations indicated that the direction of cross-diffusion can influence the spatial distribution of the population and the population density. The numerical results agreed with the theoretical analysis. We hope that these results will prove useful in the study of toxic plankton systems

Investigations of Phytoplankton Diversity in Chesapeake Bay

Characterizing the diversity of a community in relation to environmental conditions and ecosystem functions are core concepts in ecology. While decades of research have led to a growing comprehension of diversity in many ecosystems, our understanding in aquatic habitats and microbial organisms remains relatively limited. Phytoplankton represent a diverse and important group that contribute approximately half of global primary productivity and are intrinsically connected to changing environmental conditions, especially in systems as dynamic as estuaries. To better understand the ecological processes governing phytoplankton composition and diversity, spatial and temporal patterns of environmental parameters and their relation to the algal community of Chesapeake Bay were analyzed using data collected over a 25 year period (1985-2009). The phytoplankton community of Chesapeake Bay, containing 1480 taxa was characterized as one of high richness and low evenness, with a single species accounting for at least half of the biomass in almost one third of all samples examined. High gamma-diversity was attributed to seasonal succession of dominant flora and spatial heterogeneity along the estuarine gradient with high species turnover between salinity regions. Alpha-diversity was greatest in freshwater and polyhaline regions, and minimal in lower mesohaline waters. Multivariate ordination analysis identified regional differences corresponded to salinity, turbidity, and nutrient gradients, with lowest richness in regions of intermediate salinity, total nitrogen and phosphorus concentrations and highest dissolved organic nitrogen. Temporal factors included negative impacts of streamflow related nutrient increases leading to greater algal abundance and lower diversity particularly within the polyhaline Bay. Results indicate that greater algal biomass was associated with higher richness and lower evenness, and may be associated with lower ecosystem stability, with greater variance in inter-annual phytoplankton biomass. To address short-term environmental variability including nutrient loading, daily sampling of the Lafayette River, was conducted in spring 2006. During consecutive blooms of Cryptomonas sp. and Gymnodinium instriatum up to 99% of total biomass was due to the individual bloom species, although species richness was not significantly reduced. Time lag correlations indicated that the Cryptomonas sp. bloom was related to precipitation related increases in dissolved inorganic nitrogen concentrations, while the G. instriatum bloom followed periods of reduced nitrogen concentrations that were accompanied by an algal community of high richness and low evenness. Based on its connectivity to both environmental and biological variables, phytoplankton diversity is recognized as a significant indicator of ecosystem condition, with high species richness and evenness as potential goals for restoration efforts

An integrated modelling approach to investigate the dynamics of Planktothrix rubescens blooming in a medium-sized pre-alpine lake (North Italy)

In a medium-sized pre-alpine lake (Lake Pusiano, North Italy) the cyanobacterium Planktothrix rubescens has strongly dominated the phytoplankton assemblage since 2000 despite improvements in water quality, similarly to what happened in many pre-alpine lakes. The ecological success of the ubiquitous harmful species has been ascribed to largely depend on its eco-physiological traits, lakes re-oligotrophication (and increasing N:P ratios) as well as climate oscillations. Whatever the viewpoint, it has been the dominating algal species over the last two decades but the scientific community is debating about the crucial factors determining the dynamics. A great difficulty is certainly the comprehension of the effects due to human pressures at different scales. Also the natural changes and the interactions within the ecosystem may cause a high uncertainty. The present research focused on the necessity to solve some of the most paradoxical features about P.rubescens large success. An intensive field campaign was conducted to evaluate distributions of phytoplankton taxa, as well as P. rubescens, using spectrally-resolved fluorescence measurements and cell enumeration. These provided a high spatially and temporally resolved database, suitable to calibrate and validate a coupled three-dimensional hydrodynamic and ecological model for lakes ecosystem. The simulations revealed the fundamental role of physiological features. They led to characteristic vertical patterns of distribution, notably a deep chlorophyll maximum, and a visible influence of lake hydrodynamic processes, particularly during high-discharge inflows in summer stratification. The simulations were used to examine growth-limiting factors that help to explain its increased prevalence during a re-oligotrophication phase. A long-term series (1960-2010), assessed over measured data, was reconstructed for some ecological indicators. A natural external phosphorus load was simulated by a hydrological and nutrients transport model (SWAT), after it was calibrated on a natural sub-basin. Data by a paleolimnological survey were used to initialize the lake ecological model to reproduce the past conditions. A specific statistical technique (Spectral Singular Analysis) was used to isolate the trend of air temperature daily series, avoiding the periodic climatic fluctuations. Four different scenarios were simulated to characterize different levels of local and global pressure on lake ecology, combining each alternative driver into the lake model. The integrated lake-basin tool was also proposed as a dynamic tool to simulate the biogeochemical cycle in an alternative pristine ecological state. The output for phosphorus reference conditions was compared to the results by the most traditional methods (previously assessed for subalpine lakes). After decades of lake eutrophication, the simulated temperatures warming did not enhance P. rubescens blooming. Conversely, a positive relation was found when the pressure from the catchment (e.g. phosphorus pollution) was switched off by the simulation, as emerged by the Mann-Kendall statistics on daily model output. In other words, the global warming may have different effects on P. rubescens dynamics, depending on the trophic evolution of a lake. The simulation of a pristine condition projected the lake into an oligo-mesotrophy, as the results of equilibrium between the external phosphorus loading and the trasformations across the internal exchanging pools. The simulation of lake transparency and productivity depicted a good ecological state, but the hypolimnetic waters remained anoxic during the thermal stratification, as confirmed by the paleolimnological survey (to pre-industrial age). P. rubescens persisted in that conditions, but its growth resulted strongly limited by low phosphorus concentration, resulting in a low productivity

Individual-based modelling of cyanobacteria blooms: Physical and physiological processes

Lakes and reservoirs throughout the world are increasingly adversely affected by cyanobacterial harmful algal blooms (CyanoHABs). The development and spatiotemporal distributions of blooms are governed by complex physical mixing and transport processes that interact with physiological processes affecting the growth and loss of bloom-forming species. Individual-based models (IBMs) can provide a valuable tool for exploring and integrating some of these processes. Here we contend that the advantages of IBMs have not been fully exploited. The main reasons for the lack of progress in mainstreaming IBMs in numerical modelling are their complexity and high computational demand. In this review, we identify gaps and challenges in the use of IBMs for modelling CyanoHABs and provide an overview of the processes that should be considered for simulating the spatial and temporal distributions of cyanobacteria. Notably, important processes affecting cyanobacteria distributions, in particular their vertical passive movement, have not been considered in many existing lake ecosystem models. We identify the following research gaps that should be addressed in future studies that use IBMs: 1) effects of vertical movement and physiological processes relevant to cyanobacteria growth and accumulations, 2) effects and feedbacks of CyanoHABs on their environment; 3) inter and intra-specific competition of cyanobacteria species for nutrients and light; 4) use of high resolved temporal-spatial data for calibration and verification targets for IBMs; and 5) climate change impacts on the frequency, intensity and duration of CyanoHABs. IBMs are well adapted to incorporate these processes and should be considered as the next generation of models for simulating CyanoHABs

Simulating Behavioral Microcystin Impairment in Fish

Fish experiencing blooms of the cyanobacteria genera Microcystis and Anabaena acquire microcystin and saxitoxin through ingestion of contaminated food and absorption of dissolved toxin. Even low chronic doses induce sensory and motor impairment—the impact of which is unquantified in wild populations. Here, I introduce Lagrangian particle models for cyanobacteria and fish which test the hypotheses that impairment symptoms suppress movement and growth. This is implemented within the Finite-Volume Coastal Ocean Model (FVCOM). Cyanobacteria particles move vertically according to mixing and buoyancy (a function of cellular reservoirs). Fish navigate the horizontal domain, foraging in high growth areas, and fleeing when toxin increases. The framework is demonstrated here for the case of juvenile fish encountering Microcystis aeruginosa in an idealized Louisiana estuary. Self-shading reduces bloom growth, and causes algae to collect at the surface. Turbulent diffusivity is insufficient to break up this layer, so dissolved toxin becomes surface-intensified. Fish seek high growth areas in this environment, and dietary uptake increases. This triggers flight and swimming impairment. As cyanobacteria excrete microcystin, absorption forces fish to become intoxicated even in areas of lower toxic risk. Repeated flight means fish spend more time in suboptimal areas, with final growth reduced up to 6.6%. In vivo, this would be exacerbated by physiological stress and the metabolic cost of toxin removal. Collective movement (group diffusivity) is suppressed nearly 50% during wide-spread intoxication. Simulations show that within a certain parameter space, both movement and growth are suppressed relative to the control case as expected. However, additional experiments resulted in higher growth, indicating the methods are sensitive to model parameterization. Ultimately, these are sandbox cases, which will require carefully-designed lab and field experiments before predictive capability can be assumed

Fluid Mechanics of Plankton

The cooperation between plankton biologists and fluid dynamists has enhanced our knowledge of life within the plankton communities in ponds, lakes, and seas. This book assembled contributions on plankton–flow interactions, with an emphasis on syntheses and/or predictions. However, a wide range of novel insights, reasonable scenarios, and founded critiques are also considered in this book

Do bacteria thrive when the ocean acidifies? Results from an off-­shore mesocosm study

Marine bacteria are the main consumers of the freshly produced organic matter. In order to meet their carbon demand, bacteria release hydrolytic extracellular enzymes that break down large polymers into small usable subunits. Accordingly, rates of enzymatic hydrolysis have a high potential to affect bacterial organic matter recycling and carbon turnover in the ocean. Many of these enzymatic processes were shown to be pH sensitive in previous studies. Due to the continuous rise in atmospheric CO2 concentration, seawater pH is presently decreasing at a rate unprecedented during the last 300 million years with so-far unknown consequences for microbial physiology, organic matter cycling and marine biogeochemistry. We studied the effects of elevated seawater pCO2 on a natural plankton community during a large-scale mesocosm study in a Norwegian fjord. Nine 25m-long Kiel Off-Shore Mesocosms for Future Ocean Simulations (KOSMOS) were adjusted to different pCO2 levels ranging from ca. 280 to 3000 µatm by stepwise addition of CO2 saturated seawater. After CO2 addition, samples were taken every second day for 34 days. The first phytoplankton bloom developed around day 5. On day 14, inorganic nutrients were added to the enclosed, nutrient-poor waters to stimulate a second phytoplankton bloom, which occurred around day 20. Our results indicate that marine bacteria benefit directly and indirectly from decreasing seawater pH. During both phytoplankton blooms, more transparent exopolymer particles were formed in the high pCO2 mesocosms. The total and cell-specific activities of the protein-degrading enzyme leucine aminopeptidase were elevated under low pH conditions. The combination of enhanced enzymatic hydrolysis of organic matter and increased availability of gel particles as substrate supported higher bacterial abundance in the high pCO2 treatments. We conclude that ocean acidification has the potential to stimulate the bacterial community and facilitate the microbial recycling of freshly produced organic matter, thus strengthening the role of the microbial loop in the surface ocean