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- All Subjects: Biology
- Creators: Kang, Yun
- Member of: ASU Electronic Theses and Dissertations
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
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
Description
Many studies over the past two decades examined the link between climate patterns and discharge, but few have attempted to study the effects of the El Niño Southern Oscillation (ENSO) on localized and watershed specific processes such as nutrient loading in the Southwestern United States. The Multivariate ENSO Index (MEI) is used to describe the state of the ENSO, with positive (negative) values referring to an El Niño condition (La Niña condition). This study examined the connection between the MEI and precipitation, discharge, and total nitrogen (TN) and total phosphorus (TP) concentrations in the Upper Salt River Watershed in Arizona. Unrestricted regression models (UMs) and restricted regression models (RMs) were used to investigate the relationship between the discharges in Tonto Creek and the Salt River as functions of the magnitude of the MEI, precipitation, and season (winter/summer). The results suggest that in addition to precipitation, the MEI/season relationship is an important factor for predicting discharge. Additionally, high discharge events were associated with high magnitude ENSO events, both El Niño and La Niña. An UM including discharge and season, and a RM (restricting the seasonal factor to zero), were applied to TN and TP concentrations in the Salt River. Discharge and seasonality were significant factors describing the variability in TN in the Salt River while discharge alone was the significant factor describing TP. TN and TP in Roosevelt Lake were evaluated as functions of both discharge and MEI. Some significant correlations were found but internal nutrient cycling as well as seasonal stratification of the water column of the lake likely masks the true relationships. Based on these results, the MEI is a useful predictor of discharge, as well as nutrient loading in the Salt River Watershed through the Salt River and Tonto Creek. A predictive model investigating the effect of ENSO on nutrient loading through discharge can illustrate the effects of large scale climate patterns on smaller systems.
ContributorsSversvold, Darren (Author) / Neuer, Susanne (Thesis advisor) / Elser, James (Committee member) / Fenichel, Eli (Committee member) / Arizona State University (Publisher)
Created2012
Description
Phosphorus (P), an essential nutrient for growth of all organisms, is often in limited biological supply for herbivore consumers compared to other elements, such as carbon (C). Ecological stoichiometry studies have assessed responses of filter-feeding zooplankton from the genus Daphnia to single and multi-species food resources that are P-limited, finding decreased growth as a result to changes in metabolic processes and feeding behavior. Conversely, recent laboratory studies have shown that P-rich algal food resources also result in decreased growth rates for Daphnia, though the possible mechanisms behind this maladaptive response is understudied. Moreover, no published study tests the existence of the “stoichiometric knife edge” hypothesis for low C:P under field conditions. To address this lack of information, I measured growth rate as well as respiration and ingestion rates for D. magna, D. pulicaria, and D. pulex that were fed natural lake seston experimentally enriched with different levels of PO43-. I found heterogeneous effects of high dietary P across Daphnia species. Growth rate responses for D. magna were strong and indicated a negative effect of high-P, most likely as a result to decreased ingestion rates that were observed. The seston treatments did not elicit significant growth rate responses for D. pulex and D. pulicaria, but significant responses to respiration rates were observed for all species. Consumer body stoichiometry, differences in seston C:P for each experiment, or differential assimilation by producer types may be driving these results. My study suggests that the stoichiometric knife edge documented in laboratory studies under low C:P conditions may not operate to the same degree when natural seston is the food source; diet diversity may be driving complex nuances for consumer performance that were previously overlooked.
ContributorsCurrier, Courtney M (Author) / Currier, James (Thesis advisor) / Harrison, Jon (Committee member) / Neuer, Susanne (Committee member) / Arizona State University (Publisher)
Created2015
Description
The most advanced social insects, the eusocial insects, form often large societies in which there is reproductive division of labor, queens and workers, have overlapping generations, and cooperative brood care where daughter workers remain in the nest with their queen mother and care for their siblings. The eusocial insects are composed of representative species of bees and wasps, and all species of ants and termites. Much is known about their organizational structure, but remains to be discovered.
The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
ContributorsRodríguez Messan, Marisabel (Author) / Kang, Yun (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Kuang, Yang (Committee member) / Page Jr., Robert E (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2018
Description
Why do many animals possess multiple classes of photoreceptors that vary in the wavelengths of light to which they are sensitive? Multiple spectral photoreceptor classes are a requirement for true color vision. However, animals may have unconventional vision, in which multiple spectral channels broaden the range of wavelengths that can be detected, or in which they use only a subset of receptors for specific behaviors. Branchiopod crustaceans are of interest for the study of unconventional color vision because they express multiple visual pigments in their compound eyes, have a simple repertoire of visually guided behavior, inhabit unique and highly variable light environments, and possess secondary neural simplifications. I first tested the behavioral responses of two representative species of branchiopods from separate orders, Streptocephalus mackini Anostracans (fairy shrimp), and Triops longicaudatus Notostracans (tadpole shrimp). I found that they maintain vertical position in the water column over a broad range of intensities and wavelengths, and respond behaviorally even at intensities below those of starlight. Accordingly, light intensities of their habitats at shallow depths tend to be dimmer than terrestrial habitats under starlight. Using models of how their compound eyes and the first neuropil of their optic lobe process visual cues, I infer that both orders of branchiopods use spatial summation from multiple compound eye ommatidia to respond at low intensities. Then, to understand if branchiopods use unconventional vision to guide these behaviors, I took electroretinographic recordings (ERGs) from their compound eyes and used models of spectral absorptance for a multimodel selection approach to make inferences about the number of photoreceptor classes in their eyes. I infer that both species have four spectral classes of photoreceptors that contribute to their ERGs, suggesting unconventional vision guides the described behavior. I extended the same modeling approach to other organisms, finding that the model inferences align with the empirically determined number of photoreceptor classes for this diverse set of organisms. This dissertation expands the conceptual framework of color vision research, indicating unconventional vision is more widespread than previously considered, and explains why some organisms have more spectral classes than would be expected from their behavioral repertoire.
ContributorsLessios, Nicolas (Author) / Rutowski, Ronald L (Thesis advisor) / Cohen, Jonathan H (Thesis advisor) / Harrison, John (Committee member) / Neuer, Susanne (Committee member) / McGraw, Kevin (Committee member) / Arizona State University (Publisher)
Created2016
Description
A key factor in the success of social animals is their organization of work. Mathematical models have been instrumental in unraveling how simple, individual-based rules can generate collective patterns via self-organization. However, existing models offer limited insights into how these patterns are shaped by behavioral differences within groups, in part because they focus on analyzing specific rules rather than general mechanisms that can explain behavior at the individual-level. My work argues for a more principled approach that focuses on the question of how individuals make decisions in costly environments.
In Chapters 2 and 3, I demonstrate how this approach provides novel insights into factors that shape the flexibility and robustness of task organization in harvester ant colonies (Pogonomyrmex barbatus). My results show that the degree to which colonies can respond to work in fluctuating environments depends on how individuals weigh the costs of activity and update their behavior in response to social information. In Chapter 4, I introduce a mathematical framework to study the emergence of collective organization in heterogenous groups. My approach, which is based on the theory of multi-agent systems, focuses on myopic agents whose behavior emerges out of an independent valuation of alternative choices in a given work environment. The product of this dynamic is an equilibrium organization in which agents perform different tasks (or abstain from work) with an analytically defined set of threshold probabilities. The framework is minimally developed, but can be extended to include other factors known to affect task decisions including individual experience and social facilitation. This research contributes a novel approach to developing (and analyzing) models of task organization that can be applied in a broader range of contexts where animals cooperate.
In Chapters 2 and 3, I demonstrate how this approach provides novel insights into factors that shape the flexibility and robustness of task organization in harvester ant colonies (Pogonomyrmex barbatus). My results show that the degree to which colonies can respond to work in fluctuating environments depends on how individuals weigh the costs of activity and update their behavior in response to social information. In Chapter 4, I introduce a mathematical framework to study the emergence of collective organization in heterogenous groups. My approach, which is based on the theory of multi-agent systems, focuses on myopic agents whose behavior emerges out of an independent valuation of alternative choices in a given work environment. The product of this dynamic is an equilibrium organization in which agents perform different tasks (or abstain from work) with an analytically defined set of threshold probabilities. The framework is minimally developed, but can be extended to include other factors known to affect task decisions including individual experience and social facilitation. This research contributes a novel approach to developing (and analyzing) models of task organization that can be applied in a broader range of contexts where animals cooperate.
ContributorsUdiani, Oyita (Author) / Kang, Yun (Thesis advisor) / Fewell, Jennifer H (Thesis advisor) / Janssen, Marcus A (Committee member) / Castillo-Chavez, Carlos (Committee member) / Arizona State University (Publisher)
Created2016
Description
Phytoplankton comprise the base of the marine food web, and, along with heterotrophic protists, they are key players in the biological pump that transports carbon from the surface to the deep ocean. In the world's subtropical oligotrophic gyres, plankton communities exhibit strong seasonality. Winter storms vent deep water into the euphotic zone, triggering a surge in primary productivity in the form of a spring phytoplankton bloom. Although the hydrographic trends of this "boom and bust" cycle have been well studied for decades, community composition and its seasonal and annual variability remains an integral subject of research. It is hypothesized here that proportions of different phytoplankton and protistan taxa vary dramatically between seasons and years, and that picoplankton represent an important component of this community and contributor to carbon in the surface ocean. Monthly samples from the Bermuda Atlantic Time-series Study (BATS) site were analyzed by epifluorescence microscopy, which permits classification by morphology, size, and trophic type. Epifluorescence counts were supplemented with flow cytometric quantification of Synechococcus, Prochlorococcus, and autotrophic pico- and nanoeukaryotes. Results from this study indicate Synechococcus and Prochlorococcus, prymnesiophytes, and hetero- and mixotrophic nano- and dinoflagellates were the major players in the BATS region plankton community. Ciliates, cryptophytes, diatoms, unidentified phototrophs, and other taxa represented rarer groups. Both flow cytometry and epifluorescence microscopy revealed Synechococcus to be most prevalent during the spring bloom. Prymnesiophytes likewise displayed distinct seasonality, with the highest concentrations again being noted during the bloom. Heterotrophic nano- and dinoflagellates, however, were most common in fall and winter. Mixotrophic dinoflagellates, while less abundant than their heterotrophic counterparts, displayed similar seasonality. A key finding of this study was the interannual variability revealed between the two years. While most taxa were more abundant in the first year, prymnesiophytes experienced much greater abundance in the second year bloom. Analyses of integrated carbon revealed further stark contrasts between the two years, both in terms of total carbon and the contributions of different groups. Total integrated carbon varied widely in the first study year but displayed less fluctuation after June 2009, and values were noticeably reduced in the second year.
ContributorsHansen, Amy (Author) / Neuer, Susanne (Thesis advisor) / Krajmalnik-Brown, Rosa (Committee member) / Sommerfeld, Milton (Committee member) / Arizona State University (Publisher)
Created2010
Description
Variation in living systems and how it cascades across organizational levels is central to biology. To understand the constraints and amplifications of variation in collective systems, I mathematically study how group-level differences emerge from individual variation in eusocial-insect colonies, which are inherently diverse and easily observable individually and collectively. Considering collective processes in three species where increasing degrees of heterogeneity are relevant, I address how individual variation scales to colony-level variation and to what degree it is adaptive. In Chapter 2, I introduce a Markov-chain decision model for stochastic individual quorum-based recruitment decisions of rock-ant workers during house hunting, and how they determine collective speed--accuracy balance. Differences in the average threshold-dependent response characteristics of workers between colonies cause collective differences in decision-making. Moreover, noisy behavior may prevent drastic collective cascading into poor nests. In Chapter 3, I develop an ordinary differential equation (ODE) model to study how cognitive diversity among honey-bee foragers influences collective attention allocation between novel and familiar resources. Results provide a mechanistic basis for changes in foraging activity and preference with group composition. Moreover, sensitivity analysis reveals that the main individual driver for foraging allocation shifts from recruitment (communication) to persistence (independent effort) as colony composition changes. This might favor specific degrees of heterogeneity that best amplify communication in wild colonies. Lastly, in Chapter 4, I consider diversity in size, age, and task for nest defense in stingless bees. To better understand how these dimensions of diversity interact to balance defensive demands with other colony needs, I study their effect on colony size and task allocation through a demographic Filippov ODE model. Along each dimension, variation is beneficial in a certain range, outside of which colony adaptation and survival are compromised. This work elucidates how variation in collective properties emerges from nonlinear interactions between varying components in eusocial insects, but it can be generalized to other biological systems with similar fundamental characteristics but less empirical tractability. Moreover, it has the potential of inspiring algorithms that capitalize on heterogeneity in engineered systems where simple components with limited information and no central control must solve complex tasks.
ContributorsNavas Zuloaga, Maria Gabriela (Author) / Kang, Yun (Thesis advisor) / Smith, Brian H (Thesis advisor) / Pavlic, Theodore P (Committee member) / Arizona State University (Publisher)
Created2022