Plankton modeling at multiple scales
- Author(s): Birch, Daniel A.;
- et al.
This dissertation consists of three separate investigations of plankton models at different scales. In the first investigation the master equation for an individual-based model with pair interactions is formulated. Special cases of the master equation are used to explain the differences in behavior of the individual- based model and its mean-field approximation. In the second investigation constraints on the biomass and productivity of a continuum model for plankton are found using the large-scale properties of the model. The third investigation quantifies the hypothesis that thin layers of plankton and other passive tracers are created by vertically-sheared horizontal currents acting on horizontal property gradients. Chapter II contains the development of a master equation for a spatial population model for reproducing and interacting individuals. Additionally, Monte Carlo simulations demonstrate that the mean-field approximation to the individual-based model can grossly under- or over-estimate the population of the individual-based model, depending on the ratio of diffusive to reproductive time scales and the ratio of the growth rate to the interaction strength. The failure of the mean-field model is explained by applying the master equation to the special cases of no interactions and infinite-range interactions between individuals. Chapter III describes a continuum model for plankton growing, diffusing, and being stirred in an inhomogeneous environment. Bounds on the biomass and productivity are developed which allow the estimation of the plankton abundance without knowing the details of the flow or the spatially (and temporally) varying growth rate. Furthermore, a constrain is found that may forbid extinction, even when the average growth rate is negative. Chapter IV examines the situation of an initial patch of a passive tracer (such as plankton) being sheared into a thin vertical layer by a vertically-sheared horizontal current. The importance of initial conditions is emphasized and the time to minimum layer thickness, minimum layer thickness, layer intensity, and layer lifetime are all estimated. For oceanic parameters layers approximately 1 m thick are found to form in about 1 day and have a lifetime of the same order of the formation time