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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

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
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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

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
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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 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.
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
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Description
Social insect colonies exhibit striking diversity in social organization. Included in this overwhelming variation in structure are differences in colony queen number. The number of queens per colony varies both intra- and interspecifically and has major impacts on the social dynamics of a colony and the fitness of its members.

Social insect colonies exhibit striking diversity in social organization. Included in this overwhelming variation in structure are differences in colony queen number. The number of queens per colony varies both intra- and interspecifically and has major impacts on the social dynamics of a colony and the fitness of its members. To understand the evolutionary transition from single to multi-queen colonies, I examined a species which exhibits variation both in mode of colony founding and in the queen number of mature colonies. The California harvester ant Pogonomyrmex californicus exhibits both variation in the number of queens that begin a colony (metrosis) and in the number of queens in adult colonies (gyny). Throughout most of its range, colonies begin with one queen (haplometrosis) but in some populations multiple queens cooperate to initiate colonies (pleometrosis). I present results that confirm co-foundresses are unrelated. I also map the geographic occurrence of pleometrotic populations and show that the phenomenon appears to be localized in southern California and Northern Baja California. Additionally, I provide genetic evidence that pleometrosis leads to primary polygyny (polygyny developing from pleometrosis) a phenomenon which has received little attention and is poorly understood. Phylogenetic and haplotype analyses utilizing mitochondrial markers reveal that populations of both behavioral types in California are closely related and have low mitochondrial diversity. Nuclear markers however, indicate strong barriers to gene flow between focal populations. I also show that intrinsic differences in queen behavior lead to the two types of populations observed. Even though populations exhibit strong tendencies on average toward haplo- or pleometrosis, within population variation exists among queens for behaviors relevant to metrosis and gyny. These results are important in understanding the dynamics and evolutionary history of a distinct form of cooperation among unrelated social insects. They also help to understand the dynamics of intraspecific variation and the conflicting forces of local adaptation and gene flow.
ContributorsOverson, Rick P (Author) / Gadau, Jürgen (Thesis advisor) / Fewell, Jennifer H (Committee member) / Hölldobler, Bert (Committee member) / Johnson, Robert A. (Committee member) / Liebig, Jürgen (Committee member) / Arizona State University (Publisher)
Created2011
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Description
Division of labor, whereby different group members perform different functions, is a fundamental attribute of sociality. It appears across social systems, from simple cooperative groups to complex eusocial colonies. A core challenge in sociobiology is to explain how patterns of collective organization are generated. Theoretical models propose that division of

Division of labor, whereby different group members perform different functions, is a fundamental attribute of sociality. It appears across social systems, from simple cooperative groups to complex eusocial colonies. A core challenge in sociobiology is to explain how patterns of collective organization are generated. Theoretical models propose that division of labor self-organizes, or emerges, from interactions among group members and the environment; division of labor is also predicted to scale positively with group size. I empirically investigated the emergence and scaling of division of labor in evolutionarily incipient groups of sweat bees and in eusocial colonies of harvester ants. To test whether division of labor is an emergent property of group living during early social evolution, I created de novo communal groups of the normally solitary sweat bee Lasioglossum (Ctenonomia) NDA-1. A division of labor repeatedly arose between nest excavation and guarding tasks; results were consistent with hypothesized effects of spatial organization and intrinsic behavioral variability. Moreover, an experimental increase in group size spontaneously promoted higher task specialization and division of labor. Next, I examined the influence of colony size on division of labor in larger, more integrated colonies of the harvester ant Pogonomyrmex californicus. Division of labor scaled positively with colony size in two contexts: during early colony ontogeny, as colonies grew from tens to hundreds of workers, and among same-aged colonies that varied naturally in size. However, manipulation of colony size did not elicit a short-term response, suggesting that the scaling of division of labor in P. californicus colonies is a product of functional integration and underlying developmental processes, rather than a purely emergent epiphenomenon. This research provides novel insights into the organization of work in insect societies, and raises broader questions about the role of size in sociobiology.
ContributorsHolbrook, Carter Tate (Author) / Fewell, Jennifer H (Thesis advisor) / Gadau, Jürgen (Committee member) / Harrison, Jon F. (Committee member) / Hölldobler, Berthold (Committee member) / Johnson, Robert A. (Committee member) / Arizona State University (Publisher)
Created2011
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Description
For interspecific mutualisms, the behavior of one partner can influence the fitness of the other, especially in the case of symbiotic mutualisms where partners live in close physical association for much of their lives. Behavioral effects on fitness may be particularly important if either species in these long-term relationships displays

For interspecific mutualisms, the behavior of one partner can influence the fitness of the other, especially in the case of symbiotic mutualisms where partners live in close physical association for much of their lives. Behavioral effects on fitness may be particularly important if either species in these long-term relationships displays personality. Animal personality is defined as repeatable individual differences in behavior, and how correlations among these consistent traits are structured is termed behavioral syndromes. Animal personality has been broadly documented across the animal kingdom but is poorly understood in the context of mutualisms. My dissertation focuses on the structure, causes, and consequences of collective personality in Azteca constructor colonies that live in Cecropia trees, one of the most successful and prominent mutualisms of the neotropics. These pioneer plants provide hollow internodes for nesting and nutrient-rich food bodies; in return, the ants provide protection from herbivores and encroaching vines. I first explored the structure of the behavioral syndrome by testing the consistency and correlation of colony-level behavioral traits under natural conditions in the field. Traits were both consistent within colonies and correlated among colonies revealing a behavioral syndrome along a docile-aggressive axis. Host plants of more active, aggressive colonies had less leaf damage, suggesting a link between a colony personality and host plant health. I then studied how aspects of colony sociometry are intertwined with their host plants by assessing the relationship among plant growth, colony growth, colony structure, ant morphology, and colony personality. Colony personality was independent of host plant measures like tree size, age, volume. Finally, I tested how colony personality influenced by soil nutrients by assessing personality in the field and transferring colonies to plants the greenhouse under different soil nutrient treatments. Personality was correlated with soil nutrients in the field but was not influenced by soil nutrient treatment in the greenhouse. This suggests that soil nutrients interact with other factors in the environment to structure personality. This dissertation demonstrates that colony personality is an ecologically relevant phenomenon and an important consideration for mutualism dynamics.
ContributorsMarting, Peter (Author) / Pratt, Stephen C (Thesis advisor) / Wcislo, William T (Committee member) / Hoelldobler, Bert (Committee member) / Fewell, Jennifer H (Committee member) / Gadau, Juergen (Committee member) / Arizona State University (Publisher)
Created2018
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Description
An important component of insect social structure is the number of queens that cohabitate in a colony. Queen number is highly variable between and within species. It can begin at colony initiation when often unrelated queens form cooperative social groups, a strategy known as primary polygyny. The non-kin cooperative groups

An important component of insect social structure is the number of queens that cohabitate in a colony. Queen number is highly variable between and within species. It can begin at colony initiation when often unrelated queens form cooperative social groups, a strategy known as primary polygyny. The non-kin cooperative groups formed by primary polygyny have profound effects on the social dynamics and inclusive fitness benefits within a colony. Despite this, the evolution of non-kin queen cooperation has been relatively overlooked in considerations of the evolution of cooperative sociality. To date, studies examining the costs and benefits of primary polygyny have focused primarily on the advantages of multiple queens during colony founding and early growth, but the impact of their presence extends to colony maturity and reproduction.

In this dissertation, I evaluate the ecological drivers and fitness consequences of non-kin queen cooperation, by comparing the reproduction of mature single-queen versus polygynous harvester ant (Pogonomyrmex californicus) colonies in the field. I captured and quantified the total number and biomass of reproductives across multiple mating seasons, comparing between populations that vary in the proportion of single queen versus polygynous colonies, to assess the fitness outcomes of queen cooperation. Colonies in a mainly polygynous site had lower reproductive investment than those in sites with predominantly single-queen colonies. The site dominated by polygyny had higher colony density and displayed evidence of resource limitation, pressures that may drive the evolution of queen cooperation.

I also used microsatellite markers to examine how polygynous queens share worker and reproductive production with nest-mate queens. The majority of queens fairly contribute to worker production and equally share reproductive output. However, there is a low frequency of queens that under-produce workers and over-produce reproductive offspring. This suggests that cheating by reproducing queens is possible, but uncommon. Competitive pressure from neighboring colonies could reduce the success of colonies that contain cheaters and maintain a low frequency of this phenotype in the population.
ContributorsHaney, Brian R (Author) / Fewell, Jennifer H (Thesis advisor) / Cole, Blaine J. (Committee member) / Gadau, Juergen (Committee member) / Hoelldobler, Bert (Committee member) / Rutowski, Ron L (Committee member) / Arizona State University (Publisher)
Created2017
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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

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.
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
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Description
Bee communities form the keystone of many ecosystems through their pollination services. They are dynamic and often subject to significant changes due to several different factors such as climate, urban development, and other anthropogenic disturbances. As a result, the world has been experiencing a decline in bee diversity and abundance,

Bee communities form the keystone of many ecosystems through their pollination services. They are dynamic and often subject to significant changes due to several different factors such as climate, urban development, and other anthropogenic disturbances. As a result, the world has been experiencing a decline in bee diversity and abundance, which can have detrimental effects in the ecosystems they inhabit. One of the largest factors that impacts bees in today's world is the rapid urbanization of our planet, and it impacts the bee community in mixed ways. Not very much is understood about the bee communities that exist in urban habitats, but as urbanization is inevitably going to continue, knowledge on bee communities will need to strengthen. This study aims to determine the levels of variance in bee communities, considering multiple variables that bee communities can differ in. The following three questions are posed: do bee communities that are spatially separated differ significantly? Do bee communities that are separated by seasons differ significantly? Do bee communities that are separated temporally (by year, interannually) differ significantly? The procedure to conduct this experiment consists of netting and trapping bees at two sites at various times using the same methods. The data is then statistically analyzed for differences in abundance, richness, diversity, and species composition. After performing the various statistical analyses, it has been discovered that bee communities that are spatially separated, seasonally separated, or interannually separated do not differ significantly when it comes to abundance and richness. Spatially separated bee communities and interannually separated bee communities show a moderate level of dissimilarity in their species composition, while seasonally separated bee communities show a greater level of dissimilarity in species composition. Finally, seasonally separated bee communities demonstrate the greatest disparity of bee diversity, while interannually separated bee communities show the least disparity of bee diversity. This study was conducted over the time span of two years, and while the levels of variance of an urban area between these variables were determined, further variance studies of greater length or larger areas should be conducted to increase the currently limited knowledge of bee communities in urban areas. Additional studies on precipitation amounts and their effects on bee communities should be conducted, and studies from other regions should be taken into consideration while attempting to understand what is likely the most environmentally significant group of insects.
ContributorsPhan, James Thien (Author) / Sweat, Ken (Thesis director) / Foltz-Sweat, Jennifer (Committee member) / School of Music (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
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For colonies of ponerine ant species, sterility regulation after a founding queen's death is not totally achieved in the worker caste, and the possibility of sexual reproduction is opened to workers. The persisting survival of these colonies is dependent on capturing the optimal reproductive ratio; yet, an informational gap bounds

For colonies of ponerine ant species, sterility regulation after a founding queen's death is not totally achieved in the worker caste, and the possibility of sexual reproduction is opened to workers. The persisting survival of these colonies is dependent on capturing the optimal reproductive ratio; yet, an informational gap bounds the mechanisms detailing the selection of new reproductives and the suppression of ovarian development in rejected reproductives. We investigated the mechanisms of worker policing, one of the primary methods of ovarian suppression, through continuous video observation for a period of five days at the start of colony instability. Observations suggest policing in H. saltator is performed by a majority of a colony, including potential reproductives, and requires multiple events to fully discourage ovarian growth.
ContributorsChien, Jeffrey (Co-author) / Barat Ali, Fatima (Co-author) / Kang, Yun (Thesis director) / Liebig, Juergen (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12