Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system

The study of time-fractional problems with derivatives in terms of Caputo is a recent area of study in biological models. In this article, fractional differential equations with phytoplankton-toxic phytoplankton-zooplankton (PTPZ) system were solved using the Laplace transform method (LTM), the Adomain decomposition method (ADM), and the differential transform method (DTM). This study demonstrates the good agreement between the results produced by using the specified computational techniques. The numerical results displayed as graphs demonstrate the accuracy of the computational methods. The approaches that have been established are thus quite relevant and suitable for solving nonlinear fractional models. Meanwhile, the impact of changing the fractional order of a time derivative and time $t$ on populations of phytoplankton, toxic-phytoplankton, and zooplankton has been examined using graphical representations. Furthermore, the stability analysis of the LTM approach has been discussed

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

Analysis of mechanisms of phytoplankton layer formation, maintenance and dissipation in a tropical reservoir

The mechanisms of thin phytoplankton layers development were investigated in the tropical La Fe reservoir in terms of the balance between convergence processes acting to thin the layers and turbulent diffusion acting to dissipate them. Our approach included the analysis of field data collected in a field campaign during September 2012, the calibration of the hydrodynamic and ecological model ELCOM-CAEDYM, and the application of a scaling analysis in order to understand and define the processes involved in the formation, maintenance and dissipation of the observed thin layers in the reservoir. Based on the scaling analysis applied to identify the mechanisms participating in the layering process, we defined in situ growth as the primarily mechanism involved in the formation of the layers. The influx of nutrients due to horizontal intrusions and vertical turbulent fluxes influenced this mechanism. Other analyzed mechanisms were convergent swimming and buoyancy of phytoplankton cells. The stratification of the water column together with the dissipation rates responsible to the turbulence around the layers defined local region with favorable conditions to the development of thin layers. Further studies are needed in order to characterize more precisely the mechanisms involved in the development of phytoplankton layers in this reservoir and other environments.Resumen: Los mecanismos responsables de la formación de capas delgadas de fitoplancton en el embalse tropical La Fe fueron investigados en términos del balance entre los procesos de convergencia que actúancomprimiendo las capas y los procesos difusivos que actúan disipándolas . Nuestro planteamiento incluye el análisis de datos de campo medidos en una campaña de campo realizada en Septiembre de 2012, la calibración del modelo hidrodinámico y ecológico ELCOM -CAEDYM y la parametrización de los mecanismos analizados con el fin de entender y definir los procesos involucrados en la formación, permanencia y disipación de las capas de fitoplancton observadas en el embalse Basados en la parametrización desarrollada para identificar los mecanismos participantes en la formación de las capas de fitoplancton, definimos el crecimiento in situ de las células de fitoplancton como el principal mecanismo responsable de la formación de las capas. El flujo de nutrientes debido a la intrusión horizontal y a los flujos turbulentos en la vertical influenció este mecanismo. Los otros mecanismos analizados están relacionados con el desplazamiento y la boyancia de las células de fitoplancton en la columna de agua . La estratificación de la columna de agua junto con las velocidades de disipación responsables de la turbulencia alrededor de las capas definieron region es locales con condiciones favorables para el desarrollo de las capas delgadas de fitoplancton. Se necesitan más studios para caracterizar más precisamente los mecanismos que participan en el desarrollo de las capas de fitoplancton en este embalse y en otros escenarios.Maestrí

Ecological features of harmful algal blooms in coastal upwelling ecosystems

Upwelling regions are the most complex habitats in which dinoflagellates produce red tides, but the flora is not unique. Many species also bloom in nutrient-enriched, non-upwelling systems, share the collective  dinoflagellate trait of low-nutrient affinity, and can achieve relatively fast growth rates. Blooms occur over the range of nutrient – mixing – advection combinations found in upwelling habitats, rather than being restricted to the high-nutrient high-irradiance low-turbulence conditions posited by Margalef’s classical Mandala and its Bowman et al. and Pingree versions. The bloom species are primarily ruderal strategists (R-species), which typify “mixing – drift” life-forms adapted to the velocities associated with frontal zones, entrainment within coastal currents, and vertical mixing during upwelling relaxations. Collectively, dinoflagellates appear capable of surviving fairly high turbulence spectra formed at representative Kolmogorov length scale – wind speed conditions. This biophysical protection might be the result of cell size-facilitated entrainment within the micro-eddies formed during turbulent energy dissipation. The swimming speeds of 71 clones of dinoflagellates are compared and related to reported rates of vertical motion in coastal upwelling systems. There are slow and fast swimmers; many exhibit motility rates that can exceed representative in situ vertical and horizontal water mass movements.At least four dinoflagellates from upwelling systems form chains leading to increased swimming speeds, and may be an adaptation for growth in coastal upwelling habitats. Red tides are frequent and fundamental features of upwelling systems, particularly during intermittent upwelling relaxations, rather than dichotomous (sometimes catastrophic)  interruptions of the diatom blooms characteristically induced by upwelling. Successional sequences and the “red tide” zone may differ between upwelling and non-upwelling systems. In the latter, red tides diverge from the main sequence and are appropriately positioned in the Mandala’s ecological space of high nutrients and low turbulence. An amended Mandala based on Pingree’s S-kh model and the Smayda andReynolds life-form model is presented to accommodate the range of red tide development and their successional routing found in coastal upwelling systems. Ecophysiological data support the Pitcher and Boyd seeding mechanism model, which can lead to red tides in upwelling systems. Nutrients, phyto-stimulation and grazing pressure as triggering factors in upwelling-system red tides are considered. Some red tides may be stimulated by nutrients and growth promoting factors excreted by migrating shoals and “boils” of clupeoid stocks, with selective zooplanktongrazing contributory. Substantial collapses in grazing pressure may be essential in anoxic red tide events. The mass mortalities that accompany anoxia, common to the Benguela and Peru upwelling systems, may be a trophic control mechanism to maintain biogeochemical balance and regional homeostasis, which are vital to upwelling ecosystem dynamics. Some traditional concepts of phytoplankton ecology may not completelyapply to dinoflagellate bloom events in coastal upwelling systems

Population Dynamics and Pattern Formation in an Info-chemical Mediated Tri-trophic Plankton Model

In this thesis, we study a spatio–temporal prey–predator model of plankton. This model has spatial interaction terms which represent a plankton dynamics that includes info–chemical mediated trophic interactions. We consider both a simplified two species model which has been studied in the literature (mostly in biological terms) and an extended, four-species model. In the latter, the grazing pressure of microzooplankton (M) on phytoplankton (P) is controlled through external infochemical (C) mediated predation by copepods (Z). We undertake a stability analysis of both the two species model and the four species model and compare the system dynamics. In relation to this, the critical conditions for Turing instability are derived; these are necessary and sufficient. Furthermore, we consider the degenerated situation wherein Turing bifurcation and Hopf bifurcation occur simultaneously. We also consider under what conditions Turing patterns are exhibited and under what conditions spatiotemporal patterns are observed generally. The Transient Turing instability of spatial interactions –exhibited by the two species model–is introduced and investigated in a number of ways. We also study the effects of the paradox of enrichment. This paradox led to a loss of stability in the four species model after this was derived from the two species model by expansion and by the addition of resources. Further, a numerical continuation technique was used to determine the existence of multiple stationary patterns

Abstracts of manuscripts submitted in 1989 for publication

This volume contains the abstracts of manuscripts submitted for publication during calendar year 1989 by the staff and students of the Woods Hole Oceanographic Institution. We identify the journal of those manuscripts which are in press or have been published. The volume is intended to be informative, but not a bibliography. The abstracts are listed by title in the Table of Contents and are grouped into one of our five deparments, marine policy, or the student category. An author index is presented in the back to facilitate locating specific papers

Dinoflagellate blooms and physical systems in the Gulf of Maine

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution May 1990Numerous studies have shown dinoflagellate blooms to be closely related to density discontinuities and fronts in the ocean. The spatial and temporal patterns of the dinoflagellate population depend on the predominant mode of physical forcing, and its scales of variability. The present study combined field sampling of hydrographic and biological variables to examine the relationship of dinoflagellate population distributions to physical factors along the southwestern cost of the Gulf of Maine. A bloom of Ceratium longipes occurred along this coast during the month of June, 1987. A simple model which coupled along-isopycnal diffusion with the logistic growth equation suggested that the cells had a growth rate of about 0.1 d-1 , and had reached a steady horizontal across-shelf distribution within about 10 d. Fur~her variations in population density appeared to be related to fluctuations of light with periods of -10 d. To our knowledge, this was the first use of this simple diffusion model as a diagnostic tool for quantifying parameters describing the growth and movement of a specific phytoplankton population. Blooms of the toxic dinoflagellate, Alexandrium tamarense have been nearly annual features along the coasts of southern Maine, New Hampshire and Massachusetts since 1972; however the mechanisms controlling the distribution of cells and concomitant shellfish toxicity are relatively poorly understood. Analysis of field data gathered from April to September, 1987-1989, showed that in two years when toxicity was detected in the southern part of this region, A. tamarense cells were apparently transported into the study area between Portsmouth and Cape Ann, Massachusetts, in a coastally trapped buoyant plume. This plume appears to have been formed off Maine by the outflow from the Androscoggin and Kennebec Rivers. Flow rates of these rivers, hydrographic sections, and satellite images suggest that the plume had a duration of about a month, and extended alongshore for several hundred kilometers. The distribution of cells followed the position of the plume as it was influenced by wind and topography. Thus when winds were downwelling-favourable, cells were moved alongshore to the south, and were held to the coast; when winds were upwelling-favourable, the plume sometimes separated from the coast, advecting the cells offshore. The alongshore advection of toxic cells within a coastally trapped buoyant plume can explain the temporal and spatial patterns of shellfish toxicity along the coast. The general observation of a north-to-south temporal trend of toxicity is consistent with the southward advection of the plume. In 1987 when no plume was present, Alexandrium tamarense cells were scarce, and no toxicity was recorded at the southern stations. A hypothesis was formulated explaining the development and spread of toxic dinoflagellate blooms in this region. This plume-advection hypothesis included: source A. tamarense populations in the north, possibly associated with the Androscoggin and Kennebec estuaries; a relationship between toxicity patterns and river flow volume and timing of flow peaks; and a relationship between wind stresses and the distribution of low salinity water and cells. Predictions of the plume-advection hypothesis were tested with historical records of shellfish toxicity, wind speed and direction, and river flow. The predictions tested included the north-south progression of toxic outbreaks, the occurrence of a peak in river flow prior to the PSP events, the relationship of transit time of PSP toxicity along the coast with river flow volume, and the influence of surface wind stress on the timing and location of shellfish toxicity. All the predictions tested were supported by the historical records. In addition it was found that the plume-advection hypothesis explains many details of the timing and spread of shellfish toxicity, including the sporadic nature of toxic outbreaks south of Massachusetts Bay, and the apparently rare occurrence of toxicity well offshore on Nantucket Shoals and Georges Bank.This research was supported by ONR contract N00014-87-K-0007 and ONR grant N00014-89-J-111 to Donald M. Anderson, and NOAA Office of Sea Grant contract NA86AA-D-SG090

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