Matching Items (4)

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Stoichiometric producer-grazer models, incorporating the effects of excess food-nutrient content on grazer dynamics

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There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be

There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.

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Date Created
  • 2014

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Population ecology and stoichiometry of the western black widow spider: from solitary desert predator to urban pest

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Human-induced rapid environmental change (HIREC) influences nearly all of Earth's ecosystems through processes such as urbanization. Previous studies have found that urbanization influences biodiversity patterns, often yielding an increase in

Human-induced rapid environmental change (HIREC) influences nearly all of Earth's ecosystems through processes such as urbanization. Previous studies have found that urbanization influences biodiversity patterns, often yielding an increase in the abundance of a few urban-adapted taxa at the expense of native species diversity. The western black widow spider, Latrodectus hesperus, is a medically-important pest species that often forms dense urban subpopulations (i.e., infestations) relative to the low-density subpopulations found throughout undisturbed, desert habitat. Here, I employ field and laboratory studies to examine the population ecology and stoichiometry of this urban pest to increase our understanding of the mechanisms underlying its success. The population ecology of ten black widow subpopulations spread across metropolitan Phoenix, AZ was examined during the peak breeding season (June-August). This study revealed that arthropod prey abundance, female mass and population density of females showed significant spatial variation across the ten subpopulations. Additionally, prey abundance and foraging success, measured as the number of carcasses found in webs, were a strong determinant of female mass and population density within each subpopulation. To test the mechanisms that drive black widow infestations, I used ecological stoichiometry to examine the nutrient (nitrogen and phosphorus) composition of spiders and arthropod prey from urban habitat, desert habitat and a laboratory diet regime. These studies revealed that (1) spiders are more nutrient rich than cricket prey in the field, (2) spider subpopulations exhibit significant spatial variation in their nitrogen composition, (3) nutrient composition of urban spider subpopulations does not differ significantly from Sonoran desert subpopulations, (4) laboratory-reared spiders fed a diet of only laboratory-reared crickets are more nitrogen and phosphorus limited than field-captured spiders, and (5) cannibalism by laboratory-reared spiders alleviated phosphorus limitation, but not nitrogen limitation, when compared to field-captured spiders. This work highlights the need to examine the population ecology of species relationships, such as predator-prey dynamics, to fully understand the fecundity and population growth of urban pest species. Moreover, the integration of population ecology and stoichiometry illustrates the need to address mechanisms like nutrient limitation that may explain why urban pest populations thrive and native species diversity suffers following HIREC.

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Date Created
  • 2012

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Cell quota based population models and their applications

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In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth

In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth is directly dependent on intracellular nutrient concentration is useful for understanding the dynamics in many ecological systems. The cell quota in particular lends itself to ecological stoichiometry, which is a powerful framework for mathematical ecology. Three models are developed based on the cell quota principal in order to demonstrate its applications beyond chemostat culture.

First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.

Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.

Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.

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Date Created
  • 2014

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Computational Methods for Kinetic Reaction Systems

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This work is concerned with the study and numerical solution of large reaction diffusion systems with applications to the simulation of degradation effects in solar cells. A discussion of the

This work is concerned with the study and numerical solution of large reaction diffusion systems with applications to the simulation of degradation effects in solar cells. A discussion of the basics of solar cells including the function of solar cells, the degradation of energy efficiency that happens over time, defects that affect solar cell efficiency and specific defects that can be modeled with a reaction diffusion system are included. Also included is a simple model equation of a solar cell. The basics of stoichiometry theory, how it applies to kinetic reaction systems, and some conservation properties are introduced. A model that considers the migration of defects in addition to the reaction processes is considered. A discussion of asymptotics and how it relates to the numerical simulation of the lifetime of solar cells is included. A reduced solution is considered and a presentation of a numerical comparison of the reduced solution with the full solution on a simple test problem is included. Operator splitting techniques are introduced and discussed. Asymptotically preserving schemes combine asymptotics and operator splitting to use reasonable time steps. A presentation of a realistic example of this study applied to solar cells follows.

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Date Created
  • 2020