Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer

Phytoplankton-chytrid-zooplankton dynamics via a reaction-diffusion-advection mycoloop model

Mycoloop is an important aquatic food web composed of phytoplankton, chytrids (one dominant group of parasites in aquatic ecosystems), and zooplankton. Chytrids infect phytoplankton and fragment them for easy consumption by zooplankton. The free-living chytrid zoospores are also a food resource for zooplankton. A dynamic reaction-diffusion-advection mycoloop model is proposed to describe the Phytoplankton-chytrid-zooplankton interactions in a poorly mixed aquatic environment. We analyze the dynamics of the mycoloop model to obtain dissipativity, steady state solutions, and persistence. We rigorously derive several critical thresholds for phytoplankton or zooplankton invasion and chytrid transmission among phytoplankton. Numerical diagrams show that varying ecological factors affect the formation and breakup of the mycoloop, and zooplankton can inhibit chytrid transmission among phytoplankton. Furthermore, this study suggests that mycoloop may either control or cause phytoplankton blooms.

Modelling phytoplankton-virus interactions: phytoplankton blooms and lytic virus transmission

A dynamic reaction-diffusion model of four variables is proposed to describe the spread of lytic viruses among phytoplankton in a poorly mixed aquatic environment. The basic ecological reproductive index for phytoplankton invasion and the basic reproduction number for virus transmission are derived to characterize the phytoplankton growth and virus transmission dynamics. The theoretical and numerical results from the model show that the spread of lytic viruses effectively controls phytoplankton blooms. This validates the observations and experimental results of Emiliana huxleyi-lytic virus interactions. The studies also indicate that the lytic virus transmission cannot occur in a low-light or oligotrophic aquatic environment.

Distinct differences of vertical phytoplankton community structure in mainstream and a tributary bay of the Three Gorges Reservoir, China

The vertical distribution of phytoplankton plays a crucial role in shaping the dynamics and structure of aquatic communities. In highly dynamic reservoir systems, water level fluctuations significantly affect the physiochemical conditions and the phytoplankton community. However, the specific effects on the vertical characteristics of phytoplankton between the mainstream and the tributary bay of the reservoir remain unstudied. This study investigated the vertical aspects of phytoplankton density, biomass, α and β diversity through monthly sampling over two years in the mainstream (Chang Jiang, CJ) and a tributary bay (Xiang Xi, XX) of the Three Gorges Reservoir in China. Phytoplankton density and biomass were significantly higher in XX, indicating an increased risk of algal blooms in the tributary. The phytoplankton community in CJ showed more stable species-environment relationships, a lower Shannon index and a higher evenness index, suggesting a relatively simple structure and a more uniform distribution of phytoplankton among different water layers. Conversely, XX showed greater differences between water layers (higher β diversity), with significant negative correlations with water level and positive correlations with DO difference, dissolved silica (DSi) difference, and stratification. Peak phytoplankton density and biomass, as well as high β diversity in XX, occurred during periods of decreased water levels with strong stratification in spring and summer. A structural equation model complemented by path analysis revealed that a decrease in water level could increase β diversity either directly through internal processes with extended residence time or indirectly by modifying stratification and the vertical distribution of DSi in XX. Therefore, a proposed water quality management strategy for XX was to increase the water level or reduce β diversity by implementing artificial mixing during stratification periods. Overall, this study lies in its comprehensive investigation of the vertical characteristics of the phytoplankton community in both the mainstream and the tributary bay of the Three Gorges Reservoir, elucidating the significant impact of water level fluctuations and providing insights for targeted water quality management strategies in the tributary bay to mitigate potential ecological impacts.

Asymmetrical resource competition in aquatic producers: Constant cell quota versus variable cell quota

In a shallow aquatic environment, a mathematical model with variable cell quota is proposed to characterize asymmetric resource competition for light and nutrients among aquatic producers. We investigate the dynamics of asymmetric competition models with constant and variable cell quotas and obtain the basic ecological reproductive indexes for aquatic producer invasions. The similarities and differences between the two types of cell quotas for dynamical properties and influences on asymmetric resource competition are explored through theoretical and numerical analysis. These results contribute to further revealing the role of constant and variable cell quotas in aquatic ecosystems.

Dynamics of autotroph-mixotroph interactions with the intraguild predation structure

A mathematical model with the intraguild predation structure is proposed to describe the interactions of autotrophs and mixotrophs containing light and nutrients in a well-mixed aquatic ecosystem. The dissipation, existence and stability of equilibria of the model are proved, and the ecological reproductive indexes for the extinction, survival and coexistence of autotrophs and mixotrophs are established. We also consider the influence of Holling type functional responses and abiotic factors on the coexistence and biomass of autotrophs and mixotrophs. It is shown that the intraguild predation structure is beneficial to phytoplankton biodiversity and provides an explanation for the phytoplankton paradox.

Effects of solar irradiance noise on a complex marine trophic web

The analysis of experimental data of the solar irradiance, collected on the marine surface, clearly highlights the intrinsic stochasticity of such an environmental parameter. Given this result, effects of randomly fluctuating irradiance on the population dynamics of a marine ecosystem are studied on the basis of the stochastic 0-dimensional biogeochemical flux model. The noisy fluctuations of the irradiance are formally described as a multiplicative Ornstein-Uhlenbeck process, that is a self-correlated Gaussian noise. Nonmonotonic behaviours of the variance of the marine populations' biomass are found with respect to the intensity and the autocorrelation time of the noise source, manifesting a noise-induced transition of the ecosystem to an out-of-equilibrium steady state. Moreover, evidence of noise-induced effects on the organic carbon cycling processes underlying the food web dynamics are highlighted. The reported results clearly show the profound impact the stochastic environmental variables can have on both the populations and the biogeochemistry at the basis of a marine trophic network.

Effects of large-scale advection and small-scale turbulent diffusion on vertical phytoplankton dynamics

Turbulence has been recognized as a factor of paramount importance for the survival or extinction of sinking phytoplankton species. However, dealing with its multiscale nature in models of coupled fluid and biological dynamics is a formidable challenge. Advection by coherent structures, such as those related to winter convection and Langmuir circulation, is also recognized to play a role in the survival and localization of phytoplankton. In this work we revisit a theoretically appealing model for phytoplankton vertical dynamics, and numerically investigate how large-scale fluid motions affect the survival conditions and the spatial distribution of the biological population. For this purpose, and to work with realistic parameter values, we adopt a kinematic flow field to account for the different spatial and temporal scales of turbulent motions. The dynamics of the population density are described by an advection-reaction-diffusion model with a spatially heterogeneous growth term proportional to sunlight availability. We explore the role of fluid transport by progressively increasing the complexity of the flow in terms of spatial and temporal scales. We find that, due to the large-scale circulation, phytoplankton accumulates in downwelling regions and its growth is reduced, confirming previous indications in slightly different conditions. We then explain the observed phenomenology in terms of a plankton filament model. Moreover, by contrasting the results in our different flow cases, we show that the large-scale coherent structures have an overwhelming importance. Indeed, we find that smaller-scale motions only quite weakly affect the dynamics, without altering the general mechanism identified. Such results are relevant for parametrizations in numerical models of phytoplankton life cycles in realistic oceanic flow conditions.

A model of algal growth depending on nutrients and inorganic carbon in a poorly mixed water column

A reaction-diffusion-advection model is proposed to describe the growth of algae depending on both nutrients and inorganic carbon in a poorly mixed water column. Nutrients from the water bottom and inorganic carbon from the water surface form an asymmetric resource supply mechanism for the algal growth. The existence and stability of semi-trivial steady state and positive steady state of the model are proved, and a threshold condition for the regime shift from extinction to survival of algae is established. The influence of environmental parameters on the vertical distribution of algae is investigated in the water column. It is shown that the vertical distribution of algae can exhibit many different profiles under the combined limitation of nutrients and inorganic carbon.

Exploring the role of spatial and stoichiometric heterogeneity in the top-down control in eutrophic planktonic ecosystems

Understanding the impact of eutrophication on the dynamics of aquatic food webs, remains a long-term challenge in ecology. Mathematical models generally predict the destabilisation of such webs, under increasing eutrophication levels, with large oscillations of species densities that can result in their extinction. This is at odds with a number of ecological observations that show stable dynamics even for high nutrient loads. The apparent discrepancy between theory and observations is known as the Rosenzweig's 'paradox of enrichment' and various solutions to the problem have been proposed over the years. In this study, we explore the stabilisation of dynamics of a tri-trophic plankton model in a eutrophic environment which occurs as a result of interplay of space heterogeneity, ecological stoichiometry, and food taxis of predators. We build a variety of models of increasing complexity, to explore various scenarios of phytoplankton growth, zooplankton food-dependent vertical movement, and different stoichiometric limitations of zooplankton. We show that the synergy among the vertical gradient in phytoplankton growth, phytoplankton structuring in terms of their stoichiometric ratio, and food-dependent vertical movement of zooplankton, would result in a postponing of destabilisation of eutrophic systems as compared to a well-mixed system. Our approach reveals a high complexity of the bifurcation structure of the system when key model parameters, such as the degree of eutrophication and light shading, are varied. We find coexistence of limit cycles and stable equilibria and that the possibility of multiple attractors in the system can result in hysteresis phenomena when the nutrient load is manipulated. These results are relevant and should be taken into account in lake restoration programs.

Temporal and spatial characteristics of potential energy anomaly in Lake Taihu

In this study, water temperature and meteorological data in Lake Taihu from June 11 to July 6, 2013, are collected to calibrate and verify the unstructured grid finite-volume community ocean model (FVCOM) coupled with a heat exchange module. The spatial and temporal variations of potential energy anomalies (PEA) in the lake, simulated by the calibrated FVCOM, are analyzed to explore the stratification and de-stratification processes in water body. The temporal variation of PEA primarily follows the diurnal cycles of solar radiation, while the spatial heterogeneity of PEA is jointly determined by solar radiation and vertical shear of horizontal velocity coupled with the topography of the lake. The maxima of PEA in the lake are not greater than 4 J/m³ in the summer and even smaller along shore regions and near the Pingtaishan station. This study is helpful to improve understanding of the effect of physical processes on the algae bloom in Lake Taihu.

Trait selection and co-existence of phytoplankton in partially mixed systems: Trait based modelling and potential of an aggregated approach

Trait selection and co-existence in phytoplankton communities in partially mixed water columns is investigated using trait based modelling. In the models employed, trait selection results from phytoplankton competition for two limiting resources, light and nutrients. The study employs spatially resolved models, in which the phytoplankton community is represented as a large number of trait-groups characterized by fixed trait combinations (trade-offs). Results from the trait-group resolving model (RM) are compared to results from an aggregated trait based model with adaptive traits (AM). Differences in specific production resulting from a trade-off between the half saturation constants of light and nutrients are sufficient to support evolutionary stable co-existence confirming that co-existence does not require differences in resource consumption. If abiotic conditions lead to the selection of a single trait group in RM, AM provides excellent approximations of the development of total biomass, average community trait and trait variance in the phytoplankton community. However, if selection leads to bimodal trait distributions, e.g. to co-existence of two trait groups (or species), functionally important properties of the phytoplankton community cannot be adequately represented by the aggregated information provided by AM. Because the increase in variance due to the development of bimodal trait distributions cannot be distinguished from an increase in variance due to an increase in trait diversity, the development of trait variance in AM models is not a reliable measure of trait diversity. Furthermore, AM may not provide reliable simulations of trophic interactions if the performance of the consumers depends on the traits of their resources. However, AM may support exploration of the consequences of environmental conditions and of the parameterization of species for co-existence within communities.

EXPLORING THE ROLE OF VERTICAL HETEROGENEITY IN THE STABILIZATION OF PLANKTONIC ECOSYSTEMS UNDER EUTROPHICATION

Understanding plankton dynamics in marine and lake ecosystems under eutrophication is currently a hot topic in the literature. Simple theoretical models predict appearance of large amplitude oscillations of species densities in nutrient-rich waters; however, such predictions do not always correspond to field observations. Recent models taking into account heterogeneity of the growth rate of phytoplankton and active food-searching behavior of zooplankton demonstrated that grazers can efficiently control phytoplankton densities at low values even for a high nutrient stock. In this paper, we extend the previous modeling findings on the role of fast-moving plankton grazers by exploring a more realistic case where the limiting nutrient is a dynamical variable. Thus, the growth of phytoplankton across the water column depends on both light attenuation and dynamical depletion of nutrients. We also consider a more realistic scenario of a depth-dependent vertical turbulent diffusion. Most of the previous results on stabilization of planktonic ecosystems still hold; however, some alternative mechanisms of bloom suppression can also be possible. In particular, we demonstrate that the foraging of zooplankton according to the ideal free distribution (IFD) of food (which was previously considered to be a crucial condition for stabilization) may be less stabilizing than random foraging of zooplankton. We also show that stable top-down control in the ecosystem would be highly dependent on values of vertical diffusion and on the nutrient concentration in deep layers.

Spatio-temporal dynamics of a planktonic system and chlorophyll distribution in a 2D spatial domain: matching model and data

Field data on chlorophyll distribution are investigated in a two-dimensional spatial domain of the Mediterranean Sea by using for phytoplankton abundances an advection-diffusion-reaction model, which includes real values for physical and biological variables. The study exploits indeed hydrological and nutrients data acquired in situ, and includes intraspecific competition for limiting factors, i.e. light intensity and phosphate concentration. As a result, the model allows to analyze how both the velocity field of marine currents and the two components of turbulent diffusivity affect the spatial distributions of phytoplankton abundances in the Modified Atlantic Water, the upper layer of the water column of the Mediterranean Sea. Specifically, the spatio-temporal dynamics of four phytoplankton populations, responsible for about 80% of the total chlorophyll a, are reproduced. Results for phytoplankton abundances obtained by the model are converted in chlorophyll a concentrations and compared with field data collected in twelve marine sites along the Cape Passero (Sicily)- Misurata (Libya) transect. Statistical checks indicate a good agreement between theoretical and experimental distributions of chlorophyll concentration. The study can be extended to predict the spatio-temporal behaviour of the primary production, and to prevent the consequent decline of some fish species in the Mediterranean Sea.

How diffusivity, thermocline and incident light intensity modulate the dynamics of deep chlorophyll maximum in Tyrrhenian Sea

During the last few years theoretical works have shed new light and proposed new hypotheses on the mechanisms which regulate the spatio-temporal behaviour of phytoplankton communities in marine pelagic ecosystems. Despite this, relevant physical and biological issues, such as effects of the time-dependent mixing in the upper layer, competition between groups, and dynamics of non-stationary deep chlorophyll maxima, are still open questions. In this work, we analyze the spatio-temporal behaviour of five phytoplankton populations in a real marine ecosystem by using a one-dimensional reaction-diffusion-taxis model. The study is performed, taking into account the seasonal variations of environmental variables, such as light intensity, thickness of upper mixed layer and profiles of vertical turbulent diffusivity, obtained starting from experimental findings. Theoretical distributions of phytoplankton cell concentration was converted in chlorophyll concentration, and compared with the experimental profiles measured in a site of the Tyrrhenian Sea at four different times (seasons) of the year, during four different oceanographic cruises. As a result we find a good agreement between theoretical and experimental distributions of chlorophyll concentration. In particular, theoretical results reveal that the seasonal changes of environmental variables play a key role in the phytoplankton distribution and determine the properties of the deep chlorophyll maximum. This study could be extended to other marine ecosystems to predict future changes in the phytoplankton biomass due to global warming, in view of devising strategies to prevent the decline of the primary production and the consequent decrease of fish species.

Depth of the biomass maximum affects the rules of resource competition in a water column

The theory of resource competition in spatially extended systems with resources and biomass fluxes is far from trivial. Here, we analyze the competition between two phytoplankton species for light and a nutrient in a weakly mixed water column. We develop a general framework for such an analysis and show that the competition outcome can be largely understood from a single parameter, the slope of the invasion threshold in the plane of resources. Using this approach, we show that the competition outcome crucially depends on the depth of the biomass maximum. Under eutrophic conditions, when the phytoplankton production peaks on the surface, species composition depends on the ratio of resource supplies, and the competition outcome follows the “classic” rule: coexistence is possible if each competitor has the greatest effect on its most limiting resource. By contrast, in oligotrophic systems, characterized by deep biomass maxima, the absolute level of resource supplies drives species composition, and coexistence becomes more feasible if each competitor mostly consumes its least limiting resource. Finally, when the production peaks in the subsurface, good nutrient competitors are favored. Our findings are supported by empirical data.

Retrieval of vertical particle concentration profiles by optical remote sensing: a model study

Water-leaving radiance is subject to depth variability of the water constituents. The optical penetration depth is strongly dependent on the wavelength λ, which allows to retrieve a non-uniform vertical profile of an optically-active constituent CTSM(z) from remote-sensing reflectance Rrs(λ,Cz). We define the apparent particle concentration CTSM,app(λ) of a vertically homogeneous water column whose Rrs(λ,Cconst) matches Rrs(λ,Cz). Subsequently, we define a vertically-weighted averaged particle concentration CTSM,ave(λ), only dependent on CTSM(z), and retrieve CTSM(z) by minimizing the error between CTSM,app(λ) and CTSM,ave(λ) with genetic algorithms. We conclude that the retrieval is excellent if the sub-surface maximum lays close to the surface or the background concentration of CTSM(z) is low. Conversely, results worsen for opposite conditions, due to insufficient signal strength from superimposed sub-surface maxima.

Dynamics of two picophytoplankton groups in mediterranean sea: analysis of the deep chlorophyll maximum by a stochastic advection-reaction-diffusion model

A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for the cell concentrations of the two picophytoplankton groups. The results are converted into chlorophyll a and divinil chlorophyll a concentrations and compared with experimental data collected in two different sites of the Sicily Channel (southern Mediterranean Sea). The comparison shows that real distributions are well reproduced by theoretical profiles. Specifically, position, shape and magnitude of the theoretical deep chlorophyll maximum exhibit a good agreement with the experimental values.

The nutrient-load hypothesis: patterns of resource limitation and community structure driven by competition for nutrients and light

Resource competition theory predicts that the outcome of competition for two nutrients depends on the ratio at which these nutrients are supplied. Yet there is considerable debate whether nutrient ratios or absolute nutrient loads determine the species composition of phytoplankton and plant communities. Here we extend the classical resource competition model for two nutrients by including light as additional resource. Our results suggest the nutrient-load hypothesis, which predicts that nutrient ratios determine the species composition in oligotrophic environments, whereas nutrient loads are decisive in eutrophic environments. The underlying mechanism is that nutrient enrichment shifts the species interactions from competition for nutrients to competition for light, which favors the dominance of superior light competitors overshadowing all other species. Intermediate nutrient loads can generate high biodiversity through a fine-grained patchwork of two-species and three-species coexistence equilibria. Depending on the species traits, however, competition for nutrients and light may also produce multiple alternative stable states, suppressing the predictability of the species composition. The nutrient-load hypothesis offers a solution for several discrepancies between classical resource competition theory and field observations, explains why eutrophication often leads to diversity loss, and provides a simple conceptual framework for patterns of biodiversity and community structure observed in nature.