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Much is still unknown about dominance hierarchies. Many different species form dominance hierarchies and each species have very different ways of forming these hierarchies. Some engage in various different dominance interactions to establish a dominant position. This experiment aims to use the ant species, Harpegnathos saltator, as a model to explore what sets dominant individuals, or gamergates in this case, apart from non-dominant individuals, or non-gamergates. H. saltator ants perform various different behaviors such as dueling, which is a mutually beneficial behavior, dominance biting, which is an aggressive behavior, and policing which is used to bring down those who are dominant. These behaviors can be used to study the importance of initiation and aggression in hierarchy formation. This experiment will explore how aggression through dominance biting, duel initiation, group size, and time period affect the formation of gamergates. To do so, socially unstable colonies of 15, 30, and 60 ants were video recorded for days until gamergates were established. Then, from the recordings, a period of high activity was selected and observed for dueling, duel initiation, dominance biting, dominance bite downs, and policing. The results showed that gamergates tended to perform dominance biting and dominance bite downs far more than non-gamergates during the period of high activity, but not as clearly with duelling and duel initiations. It was inconclusive whether or not the combination of both dueling and dominance biting was what set gamergates apart from non gamergates as different groups showed different results. Gamergates performed visibly more dominance bite downs than non-gamergates, so aggression may be important in setting gamergates apart from non-gamergates. In terms of group size, the smallest group had the least number of gamergates and the least activity, and the medium and large group had a similar number of gamergates and activity.
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.
Chapter 2 focuses sorely on time where the escape of a generic cancer out of immune control is described by stochastic delayed differential equations (SDDEs). Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and stochasticity in the tumor proliferation rate are studied by including delay and noise in the model. Stability, persistence and extinction of the tumor are analyzed. The result shows that both time delay and noise can induce the transition from low tumor burden equilibrium to high tumor equilibrium. The aforementioned work has been published (Han et al., 2019b).
In Chapter 3, Glioblastoma multiforme (GBM) is studied using a partial differential equation (PDE) model. GBM is an aggressive brain cancer with a grim prognosis. A mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. A novel method is developed to approximate key characteristics of the wave profile, which can be compared with MRI data. Several test cases of MRI data of GBM patients are used to yield personalized parameterizations of the model. The aforementioned work has been published (Han et al., 2019a).
Chapter 4 presents an innovative way of forecasting spatial cancer invasion. Most mathematical models, including the ones described in previous chapters, are formulated based on strong assumptions, which are hard, if not impossible, to verify due to complexity of biological processes and lack of quality data. Instead, a nonparametric forecasting method using Gaussian processes is proposed. By exploiting the local nature of the spatio-temporal process, sparse (in terms of time) data is sufficient for forecasting. Desirable properties of Gaussian processes facilitate selection of the size of the local neighborhood and computationally efficient propagation of uncertainty. The method is tested on synthetic data and demonstrates promising results.
changes in the diffusion, growth, and death parameters was performed, in order to find a set of parameter values that accurately model observed tumor growth for a given patient. Additional changes were made to the diffusion parameters to account for the arrangement of nerve tracts in the brain, resulting in varying rates of diffusion. In general, small changes in the growth rates had a large impact on the outcome of the simulations, and for each patient there exists a set of parameters that allow the model to simulate a tumor that matches observed tumor growth in the patient over a period of two or three months. Furthermore, these results are more accurate with anisotropic diffusion, rather than isotropic diffusion. However, these parameters lead to inaccurate results for patients with tumors that undergo no observable growth over the given time interval. While it is possible to simulate long-term tumor growth, the simulation requires multiple comparisons to available MRI scans in order to find a set of parameters that provide an accurate prognosis.