Dynamical systems theory and bifurcation are used to analyze some simple models of nutrient limited phytoplankton growth. The models are restricted to batch culture type conditions allowing the use of a mass balance constraint. Two popular models from the literature, the Michaelis-Menton-Monod or M³ model, and the Droop internal nutrient model are analyzed and found to yield unreasonable predictions for certain ambient environmental conditions. The M³ model predicts that the population size becomes unbounded at equilibrium for certain values of the parameters. The Droop model predicts that the amount of nutrient left over during a nutrient uptake experiment would be very small, regardless of how large the initial external nutrient concentration is. Numerical comparisons of data with the predictions from both models demonstrate that the conditions for unreasonable behavior could occur both in cultures and in natural aquatic ecosystems. In the predicted nutrient concentration at uptake equilibrium is several orders of magnitude off. Two specific enzyme mechanisms for nutrient transport are proposed as alternatives to current models. The models differ in the assumptions made about how the backflow reaction with the enzymes responsible for transport proceeds. A nutrient uptake equation for each model is derived directly from the enzyme kinetics, while the equation for growth in population size is taken from the Droop model. The dynamics of both models are analyzed, treating the nutrient uptake equations with the singular perturbation assumption. The simple model predicts that the external nutrient concentration at uptake equilibrium should be a constant percentage of the internal concentration, while in the inhibition uptake model, the population size could exhibit relaxation type oscillations during the batch culture steady state. Qualitative evidence supporting both models is discussed. Applications of these models to water quality simulation and implications for theoretical ecology are discussed.

In marine environments, the open system (OS) theory, whereby populations are assumed to be well connected through large-scale dispersal, is currently being challenged by studies demonstrating limited dispersal. Using a novel metapopulation framework featuring nonequilibrium within-site disturbance cycles and limited dispersal, I investigate the large-scale response of marine mussel populations to changes in oceanographic productivity. By altering the fecundity parameter, I am able to shift from open to dynamically-coupled systems (DCS), thereby generating predictions that can be used to test the connectivity of marine populations. Within-site disturbance cycles scale-up and drive regional dynamics in both OS and DCS. Fast disturbance cycles induce synchronized oscillations that promote regional extinction risk in response to changes in oceanographic productivity for DCS but not OS. Slow disturbance cycles maintain spatial variability and temporal stability in both OS and DCS. These predictions can be used to test the applicability of OS theories to natural coastal ecosystems.

No description available.

The SELECT model (Frost, 1982) is analyzed, criticized, and extended to embrace new information about the feeding behaviour of copepods and the structure of the planktonic food web in a series of alternative models. Diel variations in photosynthesis, grazing, and predation on copepods (temporal structure) and patchiness of zooplankton and their predators (spatial structure) are modelled in other variants. It is observed that the vertical, temporal, and (horizontal) spatial structure of the planktonic ecosystem are important components of ecosystem models that can not safely be ignored. It is further observed that a convincing mechanism for the termination of diatom blooms is lacking and should be a subject of intensive research, and that the status of chlorophyll-containing microflagellates as phototrophs is questionable and should be reconsidered. / Science, Faculty of / Zoology, Department of / Graduate

This thesis presents a quantitative model of interactions among phytoplankton, nutrients, bacteria and grazers in an enclosed marine ecosystem. The enclosed system was a 23 m deep, 9.6 m diameter column of surface water in Saanich Inlet, British Columbia. Dynamics of large- and small-celled diatoms and flagellates in response to observed irradiance and zooplankton numbers and observed or simulated nitrogen and silicon concentrations were modelled over a simulated 76-day period between July 12 and September 26. The model's predictions poorly matched the observed events in Controlled Experimental Ecosystem 2 (CEE2), but nevertheless provided some important insights into system behavior. Ciliate grazing probably prevented small-celled phytoplankton from increasing to large concentrations in CEE2. By virtue of their tremendous numbers, colourless flagellates were potentially the most important grazers on bacteria, much more important than larvaceans or metazoan larvae. Whereas small-celled phytoplankton were limited by grazers, large phytoplankton dynamics were not markedly affected by grazing. The average observed rate of 14C fixation in the surface 8 m was roughly consistent with an interpretation in which artificial additions of nitrogen contributed 62% of inferred net uptake of nitrogen by phytoplankton, mixing from subsurface water contributed 18%, bacterial remineralization 12%, and zooplankton excretion 9%. However, independent observations of rapid activity by microheterotrophs (presumably bacteria) suggested that 1*C fixation considerably underestimated net primary production. This yielded an alternative interpretation in which nutrient additions contributed 46% of inferred net uptake of nitrogen in the surface layer, mixing 13%, bacteria 35%, and zooplankton 7%. Dissolution of silica was responsible for the observed accumulation of silicic acid below 8 m depth in CEE2, but the importance of silica dissolution as a source of Si for diatom growth in the surface 8 m is uncertain. The model's major failing was its assumption of unchanging maximum growth rates of phytoplankton, and unchanging rates of exudation, sinking, and respiration. Physiological parameter values which accounted for the huge bloom of Stephanopyxis in CEE2 could not account for the ensuing collapse. Traditional modelling assumptions of slowly changing internal physiology, although adequate for marine systems dominated by physical factors such as seasonality or water movement, cannot capture the behavior of biologically dominated systems like the enclosed system considered here. / Science, Faculty of / Zoology, Department of / Graduate

We study problems in the stability of nonlinear ecological models and in the theory of collective motion in physical systems. We first establish criteria for global stability in deterministic nonlinear population models, including the most general criteria so far available for the Lotka-Volterra model. Next we study conditions for coexistence under periodic perturbations in population models and establish criteria for the appearance of dynamic equilibrium states. The third study in ecological stability establishes that a measure of the stability of population models in the presence of white noise is given by a Liapunov function for the nonlinear deterministic model, and the implications of the result are examined. We consider next the use of kinetic equations to study physical systems, and prove that the use of higher order derivatives in the Mori formalism leads to results formally identical with Mori's continued fraction theory. We then apply the method of using higher derivatives to develop a physical picture of collective mode dynamics in the linear Heisenberg chain. The collective modes and their time scales are isolated and studied.

No description available.

Bibliography: leaves 132-153. / viii, 153 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Spatially explicit models and computer intensive analysis were employed to explore how processes acting at the individual level scale up to population dynamics when processes are variable in space as well as the consequences of sampling spatially complex variability for drawing conclusions from limited ecological data. Dispersal and variation in marsupial mortality and development in relation to habitat selection and quality were studied, while evaluating spatially explicit models. The study of dynamics models of tick populations on sleepy lizards considered the effect of spatial and temporal variability, and demonstrated that counting ticks is a poor indicator of tick abundance. The "virtual ecologist" model is a useful method for linking the output of spatially explicit population models to reality, and will be a valuable approach for improving the design of ecological field research on spatially complex landscapes. / Thesis (Ph.D.)--University of Adelaide, Dept. of Environmental Science and Management, 1999?

Bibliography: leaves 132-153. Spatially explicit models and computer intensive analysis were employed to explore how processes acting at the individual level scale up to population dynamics when processes are variable in space as well as the consequences of sampling spatially complex variability for drawing conclusions from limited ecological data. Dispersal and variation in marsupial mortality and development in relation to habitat selection and quality were studied, while evaluating spatially explicit models. The study of dynamics models of tick populations on sleepy lizards considered the effect of spatial and temporal variability, and demonstrated that counting ticks is a poor indicator of tick abundance. The "virtual ecologist" model is a useful method for linking the output of spatially explicit population models to reality, and will be a valuable approach for improving the design of ecological field research on spatially complex landscapes.

Bibliography: leaves 132-153. / viii, 153 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Spatially explicit models and computer intensive analysis were employed to explore how processes acting at the individual level scale up to population dynamics when processes are variable in space as well as the consequences of sampling spatially complex variability for drawing conclusions from limited ecological data. Dispersal and variation in marsupial mortality and development in relation to habitat selection and quality were studied, while evaluating spatially explicit models. The study of dynamics models of tick populations on sleepy lizards considered the effect of spatial and temporal variability, and demonstrated that counting ticks is a poor indicator of tick abundance. The "virtual ecologist" model is a useful method for linking the output of spatially explicit population models to reality, and will be a valuable approach for improving the design of ecological field research on spatially complex landscapes. / Thesis (Ph.D.)--University of Adelaide, Dept. of Environmental Science and Management, 1999?