Matching Items (70)
Description
The Cave Creek Complex fires of June and July of 2005 north of Phoenix, Arizona, U.S.A. burned 248,310 acres of Sonoran desert, primarily on the Tonto National Forest, USFS. The fires consumed multiple stands of the keystone species Carnegiea gigantea, the saguaro cactus. Restoration efforts in late spring 2007 involved the monitoring of 200 transplanted saguaro cacti over a two year period for overall establishment and success. Observation of local saguaro distribution suggests that soil factors might influence saguaro growth. Therefore, soil samples were collected from each transplant location and analyzed for percentage coarse fragments, texture, pH and electrical conductivity as soil collection and analysis of these variables are relatively inexpensive and expedient. Regression analysis was used to determine which, if any of these soil characteristics significantly correlated with plant growth. The results of this study found significant correlation between saguaro transplant growth and the soil variables of clay content and pH, but no correlation between saguaro growth and coarse fragment percentages or electrical conductivity.
ContributorsElliott, Todd (Author) / Green, Douglas (Thesis advisor) / Steele, Kelly (Committee member) / Alford, Eddie (Committee member) / Arizona State University (Publisher)
Created2013
Description
Parallel Monte Carlo applications require the pseudorandom numbers used on each processor to be independent in a probabilistic sense. The TestU01 software package is the standard testing suite for detecting stream dependence and other properties that make certain pseudorandom generators ineffective in parallel (as well as serial) settings. TestU01 employs two basic schemes for testing parallel generated streams. The first applies serial tests to the individual streams and then tests the resulting P-values for uniformity. The second turns all the parallel generated streams into one long vector and then applies serial tests to the resulting concatenated stream. Various forms of stream dependence can be missed by each approach because neither one fully addresses the multivariate nature of the accumulated data when generators are run in parallel. This dissertation identifies these potential faults in the parallel testing methodologies of TestU01 and investigates two different methods to better detect inter-stream dependencies: correlation motivated multivariate tests and vector time series based tests. These methods have been implemented in an extension to TestU01 built in C++ and the unique aspects of this extension are discussed. A variety of different generation scenarios are then examined using the TestU01 suite in concert with the extension. This enhanced software package is found to better detect certain forms of inter-stream dependencies than the original TestU01 suites of tests.
ContributorsIsmay, Chester (Author) / Eubank, Randall (Thesis advisor) / Young, Dennis (Committee member) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2013
Description
Livestock-grazing, in particular cattle grazing, is a common use of public and private lands in western North America. As a result, the effects of grazing on both plants and animals are widely studied. Few studies, however, look directly at the long-term effects that cattle grazing may have on a particular species. The goal of this experiment was to continue research begun in 1988, to determine if the effects of cattle grazing are still seen in the age structure of two populations of saguaros (Carnegiea gigantea [Engelm.] Britton & Rose) at Saguaro National Park - Rincon Mountain District (SNP-RMD). The null hypothesis stated that enough time has elapsed since the cessation of grazing, and there is no difference in the age distribution of the saguaros of the two populations. The study area was comprised of a former fence line where grazing ceased on the western side of the fence in 1958 and the eastern side in 1978. Belt transects were laid on each side of the fence line and height was measured for each saguaro encountered in a transect. Approximate age of the individual was then calculated using an age-height correlation for SNP-RMD. Individuals were then placed into age classes of 10 year increments and a Log-Likelihood test was performed. The resulting calculated P value of 0.12 meant the null hypothesis was not rejected and there was no statistical difference between the age structure of the two populations. After 34 and 54 years rest from grazing, the negative effects of cattle grazing on the retention and recruitment of saguaro seedlings have ended, and replenishment of the populations is now dependent upon factors such as temperature and precipitation. Other factors such as climate change, increasing fire frequency, encroachment by invasive species, and poaching are sources of concern and increased mortality for these and other saguaros.
ContributorsKrone, Elizabeth AnnMarie Stewart (Author) / Alford, Eddie (Thesis advisor) / Brady, Ward (Committee member) / Green, Douglas (Committee member) / Arizona State University (Publisher)
Created2013
Description
Mycorrhizal fungi form symbiotic relationships with plant roots, increasing nutrient and water availability to plants and improving soil stability. Mechanical disturbance of soil has been found to reduce mycorrhizal inoculum in soils, but findings have been inconsistent. To examine the impact of restoration practices on riparian mycorrhizal inoculum potential, soil samples were collected at the Tres Rios Ecosystem Restoration and Flood Control Project located at the confluence of the Salt, Gila, and Agua Fria rivers in central Arizona. The project involved the mechanical removal of invasive Tamarix spp.( tamarisk, salt cedar) and grading prior to revegetation. Soil samples were collected from three stages of restoration: pre-restoration, soil banks with chipped vegetation, and in areas that had been graded in preparation for revegetation. Bioassay plants were grown in the soil samples and roots analyzed for arbuscular mycorrhizal (AM) and ectomycorrhizal (EM) infection percentages. Vegetations measurements were also taken for woody vegetation at the site. The mean number of AM and EM fungal propagules did not differ between the three treatment area, but inoculum levels did differ between AM and EM fungi with AM fungal propagules detected at moderate levels and EM fungi at very low levels. These differences may have been related to availability of host plants since AM fungi form associations with a variety of desert riparian forbs and grasses and EM fungi only form associations with Populus spp. and Salix spp. which were present at the site but at low density and canopy cover. Prior studies have also found that EM fungi may be more affected by tamarisk invasions than AM fungi. Our results were similar to other restoration projects for AM fungi suggesting that it may not be necessary to add AM fungi to soil prior to planting native vegetation because of the moderate presence of AM fungi even in soils dominated by tamarisk and exposed to soil disturbance during the restoration process. In contrast when planting trees that form EM associations, it may be beneficial to augment soil with EM fungi collected from riparian areas or to pre-inoculate plants prior to planting.
ContributorsArnold, Susanne (Author) / Stutz, Jean (Thesis advisor) / Alford, Eddie (Committee member) / Green, Douglas (Committee member) / Arizona State University (Publisher)
Created2012
Description
Mathematical modeling of infectious diseases can help public health officials to make decisions related to the mitigation of epidemic outbreaks. However, over or under estimations of the morbidity of any infectious disease can be problematic. Therefore, public health officials can always make use of better models to study the potential implication of their decisions and strategies prior to their implementation. Previous work focuses on the mechanisms underlying the different epidemic waves observed in Mexico during the novel swine origin influenza H1N1 pandemic of 2009 and showed extensions of classical models in epidemiology by adding temporal variations in different parameters that are likely to change during the time course of an epidemic, such as, the influence of media, social distancing, school closures, and how vaccination policies may affect different aspects of the dynamics of an epidemic. This current work further examines the influence of different factors considering the randomness of events by adding stochastic processes to meta-population models. I present three different approaches to compare different stochastic methods by considering discrete and continuous time. For the continuous time stochastic modeling approach I consider the continuous-time Markov chain process using forward Kolmogorov equations, for the discrete time stochastic modeling I consider stochastic differential equations using Wiener's increment and Poisson point increments, and also I consider the discrete-time Markov chain process. These first two stochastic modeling approaches will be presented in a one city and two city epidemic models using, as a base, our deterministic model. The last one will be discussed briefly on a one city SIS and SIR-type model.
ContributorsCruz-Aponte, Maytee (Author) / Wirkus, Stephen A. (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Camacho, Erika T. (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
Rabies disease remains enzootic among raccoons, skunks, foxes and bats in the United States. It is of primary concern for public-health agencies to control spatial spread of rabies in wildlife and its potential spillover infection of domestic animals and humans. Rabies is invariably fatal in wildlife if untreated, with a non-negligible incubation period. Understanding how this latency affects spatial spread of rabies in wildlife is the concern of chapter 2 and 3. Chapter 1 deals with the background of mathematical models for rabies and lists main objectives. In chapter 2, a reaction-diffusion susceptible-exposed-infected (SEI) model and a delayed diffusive susceptible-infected (SI) model are constructed to describe the same epidemic process -- rabies spread in foxes. For the delayed diffusive model a non-local infection term with delay is resulted from modeling the dispersal during incubation stage. Comparison is made regarding minimum traveling wave speeds of the two models, which are verified using numerical experiments. In chapter 3, starting with two Kermack and McKendrick's models where infectivity, death rate and diffusion rate of infected individuals can depend on the age of infection, the asymptotic speed of spread $c^\ast$ for the cumulated force of infection can be analyzed. For the special case of fixed incubation period, the asymptotic speed of spread is governed by the same integral equation for both models. Although explicit solutions for $c^\ast$ are difficult to obtain, assuming that diffusion coefficient of incubating animals is small, $c^\ast$ can be estimated in terms of model parameter values. Chapter 4 considers the implementation of realistic landscape in simulation of rabies spread in skunks and bats in northeast Texas. The Finite Element Method (FEM) is adopted because the irregular shapes of realistic landscape naturally lead to unstructured grids in the spatial domain. This implementation leads to a more accurate description of skunk rabies cases distributions.
ContributorsLiu, Hao (Author) / Kuang, Yang (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Lanchier, Nicolas (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2013
Description
Grassland habitat restoration activities are occurring within the semi-arid grasslands of the Agua Fria National Monument located 65 km north of Phoenix, AZ. The goal of these restoration activities is to reduce woody species encroachment, remove lignified plant materials and recycle nutrients within the ecosystem thus improving range conditions for both wildlife species and livestock. Broadcast burning, juniper thinning and slash pile burns are the principle tools used to accomplish resource objectives. Line cover, belt transect, densities, heights and biomass of vegetation data were collected to determine the response of the vegetative community to habitat restoration activities. Principal Component Analysis (PCA) was used to reduce data analysis to the more influential factors. Regression analysis was conducted for statistically significant response variables. Quadratic regression analysis found low predictive values. In broadcast burn treatment units, all important factors as identified by PCA had low predictive factors but significantly differed (R2 <0.01, p<0.05) between unburned and the years post treatment. Regression analysis found significant, albeit weak, relationships between time since treatment and independent variables. In pile burn treatment units, data reduction by PCA was not possible in a biologically meaningful way due to the high variability within treatment units. This suggests the effect of juniper encroachment on grassland vegetation persists long after junipers have been cut and burned. This study concluded that broadcast burning of the central Arizona grasslands does significantly alter many components of the vegetative community. Fuels treatments generally initially reduced both perennial woody species and grasses in number and height for two year post fire. However, palatable shrubs, in particular shrubby buckwheat, were not significantly different in broadcast burn treatment areas. The vegetative community characteristics of juniper encroached woodlands of central Arizona are unaffected by the removal and burning of junipers aside from the removal of hiding cover for predators for multiple years. It is recommended that habitat restoration activities continue provided the needs of wildlife are considered, especially pronghorn, with the incorporation of state and transition models specific to each of the respective ecological site descriptions and with the consideration of the effects of fire to pronghorn fawning habitat.
ContributorsSitzmann, Paul Roman (Author) / Miller, William (Thesis advisor) / Alford, Eddie (Committee member) / Green, Douglas (Committee member) / Arizona State University (Publisher)
Created2014
Description
In the field of infectious disease epidemiology, the assessment of model robustness outcomes plays a significant role in the identification, reformulation, and evaluation of preparedness strategies aimed at limiting the impact of catastrophic events (pandemics or the deliberate release of biological agents) or used in the management of disease prevention strategies, or employed in the identification and evaluation of control or mitigation measures. The research work in this dissertation focuses on: The comparison and assessment of the role of exponentially distributed waiting times versus the use of generalized non-exponential parametric distributed waiting times of infectious periods on the quantitative and qualitative outcomes generated by Susceptible-Infectious-Removed (SIR) models. Specifically, Gamma distributed infectious periods are considered in the three research projects developed following the applications found in (Bailey 1964, Anderson 1980, Wearing 2005, Feng 2007, Feng 2007, Yan 2008, lloyd 2009, Vergu 2010). i) The first project focuses on the influence of input model parameters, such as the transmission rate, mean and variance of Gamma distributed infectious periods, on disease prevalence, the peak epidemic size and its timing, final epidemic size, epidemic duration and basic reproduction number. Global uncertainty and sensitivity analyses are carried out using a deterministic Susceptible-Infectious-Recovered (SIR) model. The quantitative effect and qualitative relation between input model parameters and outcome variables are established using Latin Hypercube Sampling (LHS) and Partial rank correlation coefficient (PRCC) and Spearman rank correlation coefficient (RCC) sensitivity indices. We learnt that: For relatively low (R0 close to one) to high (mean of R0 equals 15) transmissibility, the variance of the Gamma distribution for the infectious period, input parameter of the deterministic age-of-infection SIR model, is key (statistically significant) on the predictability of the epidemiological variables such as the epidemic duration and the peak size and timing of the prevalence of infectious individuals and therefore, for the predictability these variables, it is preferable to utilize a nonlinear system of Volterra integral equations, rather than a nonlinear system of ordinary differential equations. The predictability of epidemiological variables such as the final epidemic size and the basic reproduction number are unaffected by (or independent of) the variance of the Gamma distribution for the infectious period and therefore for the choice on which type of nonlinear system for the description of the SIR model (VIE's or ODE's) is irrelevant. Although, for practical proposes, with the aim of lowering the complexity and number operations in the numerical methods, a nonlinear system of ordinary differential equations is preferred. The main contribution lies in the development of a model based decision-tool that helps determine when SIR models given in terms of Volterra integral equations are equivalent or better suited than SIR models that only consider exponentially distributed infectious periods. ii) The second project addresses the question of whether or not there is sufficient evidence to conclude that two empirical distributions for a single epidemiological outcome, one generated using a stochastic SIR model under exponentially distributed infectious periods and the other under the non-exponentially distributed infectious period, are statistically dissimilar. The stochastic formulations are modeled via a continuous time Markov chain model. The statistical hypothesis test is conducted using the non-parametric Kolmogorov-Smirnov test. We found evidence that shows that for low to moderate transmissibility, all empirical distribution pairs (generated from exponential and non-exponential distributions) for each of the epidemiological quantities considered are statistically dissimilar. The research in this project helps determine whether the weakening exponential distribution assumption must be considered in the estimation of probability of events defined from the empirical distribution of specific random variables. iii) The third project involves the assessment of the effect of exponentially distributed infectious periods on estimates of input parameter and the associated outcome variable predictions. Quantities unaffected by the use of exponentially distributed infectious period within low transmissibility scenarios include, the prevalence peak time, final epidemic size, epidemic duration and basic reproduction number and for high transmissibility scenarios only the prevalence peak time and final epidemic size. An application designed to determine from incidence data whether there is sufficient statistical evidence to conclude that the infectious period distribution should not be modeled by an exponential distribution is developed. A method for estimating explicitly specified non-exponential parametric probability density functions for the infectious period from epidemiological data is developed. The methodologies presented in this dissertation may be applicable to models where waiting times are used to model transitions between stages, a process that is common in the study of life-history dynamics of many ecological systems.
ContributorsMorales Butler, Emmanuel J (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Aparicio, Juan P (Thesis advisor) / Camacho, Erika T (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
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.
ContributorsPeace, Angela (Author) / Kuang, Yang (Thesis advisor) / Elser, James J (Committee member) / Baer, Steven (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
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.
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.
ContributorsPacker, Aaron (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014