Thesis (Ph.D.)--Lehigh University, 2007. / Adviser: Eric P. Salathe.

The objective of this dissertation is to use modelling and statistical approaches to expand our knowledge of the immune responses against gastrointestinal nematode infections, to assess the impact of nematode infection, and to use our improved knowledge to examine novel means of selective breeding in farm animals (sheep) as a control strategy. To expand the knowledge of the host immune response against infection, Chapter 2 of this dissertation focuses on immunoglobulin A (IgA), an antibody that binds nematode molecules, and its transfer through the body from the abomasal mucus (i.e. site of infection, where it is produced) to the blood plasma, where it is typically measured. These findings have been published in Parasitology (Prada Jimenez de Cisneros et al., 2014a). The implications of low levels of infection in adult milking ewes, which are more resistant than lambs, were also studied. A relationship is generated between infection levels using parasitological data and production data. There were however limitations in the dataset, which are discussed at the end of Chapter 3. Parasite resistance in adults sheep at low levels of infection was also studied, especially since the most common parasitological marker of disease is the faecal egg count (i.e. number of nematode eggs in the animals faeces) which is subject to substantial measurement error, among other limitations. Chapter 4 analyses a dataset of adult animals with low infection levels using a zero inflated binomial model (ZINB) and extends the model by including other evidence of parasite resistance to discriminate between exposed and unexposed animals. To examine selective breeding, an individual-based data-driven immunogenetically explicit mathematical model was developed. One application of this model is to compare the efficacy of two selective breeding schemes, each based on a different marker for disease, namely faecal egg counts and plasma IgA. This work has been published in Journal of the Royal Society Interface (Prada Jimenez de Cisneros et al., 2014b). The model can be extended to create a distribution for the variation in larval intake that best fits the field data. This allows the partitioning of the variation in adult worm burden into different components. The purpose is to quantify the contribution of the immune response and larval intake to determine which of the two accounts for more of the variation in the level of infection. The model can be also extended to explore selection schemes in the two components of the immune response (i.e. namely the IgA mediated and IgE mediated immune response) and estimate animal size at the end of the grazing season.

This thesis consists of two parts, which deal with different topics in dynamical systems. Part I (DYNAMICS FROM GAMES) is the main scope of the work. There we study a family of flows which are often applied in studies of some game dynamics in animal competition and evolutionary biochemistry. These flows are the solutions, on simplexes, of cubic differential equations determined by "pay-off" matrices. The main result in this part is a proof for a classification of stable flows in this family, in dimension 2, first conjectured by Zeeman in 1979 (stability under small perturbations in the pay-off matrix). We add necessary and sufficient conditions for stability, which decide the exact class for each stable flow in the family. We also give as preliminary properties some simple expressions to calculate eigenvalues at fixed points and prove that hyperbolicity of these is necessary for stability, in all dimensions. In order to complete Zeeman's classification we had to adapt, in dimension 2, some techniques of structural stability for flows not satisfying the usually required transversality condition. We discuss some aspects and difficulties present when one attempts to study cases in dimension i3. One important three-dimensional example, involving a Hopf bifurcation, is discussed in detail. In the final chapter, we present some three-dimensional cases to which a discussion of stability is feasible. Part II (LIAPUNOVF UNCTIONSF OR DIFFEOMORPHISMSh) as as its purpose the construction of Liapunov functions for diffeomorphisms. A local construction is presented in neighbourhood of compact isolated invariant sets. A globalization is obtained for Axiom A diffeos with no cycles.

<p> Here we present the results of two distinct projects in the field of cellular mechanics. In the first project, we describe a non-monotonicity in the scaling of force production in actomyosin stress fibers. We develop a continuum mechanical model to explain that non-monotonicity and, using both analytical and numerical techniques, conclude that the scaling is due to an interaction between different physical lengthscales inherent in the actomyosin force-production system. Using singular perturbation methods, we study the model further to make predictions about the physical conditions under which a cell can break symmetry. In the second project, we explore how lipid flow in the plane of the plasma membrane contributes to membrane translocation during cell migration. By numerically solving the Stokes equations, we quantify the magnitude of the force necessary to generate this flow, and analyze how the presence of transmembrane protein obstacles influences the resulting front-to-rear membrane tension gradient. We make several analytic estimates of the mechanical importance of this membrane tension for cell motility.</p>

Symmetry breaking of the left-right body axis is a crucial step in development for many vertebrate species. In many this is initiated with a directional cilia-driven fluid flow in the organising structure. This work focuses on the mouse and the zebrafish organising structures, the node and Kupffer's vesicle, wherein cilia perform a tilted rotation producing an asymmetric flow. Using singularities of Stokes flow, slender body theory and the boundary integral equation, a computational model of flow in the mouse node for a range of cilia configurations simulating developmental stages is developed and run on the University of Birmingham's cluster, BlueBEAR. The results show the emergence of a directional flow as the cilia tilt increases. To model the Kupffer's vesicle the regularised boundary integral equation is used with a mesh representation of the entire domain to investigate potential cilia mechanisms that produce the observed flow as there is not a consensus. The results show that a combination of the experimental observations could be a sufficient mechanism. This model is expanded using observations of cilia with two rotation frequencies which are incorporated by allowing such cilia to ‘wobble’. This wobble accentuates the asymmetric flow in wildtype embryos and diminishes it in mutant embryos. All of these results agree well with experiment suggesting that vertebrates develop a combination of rotation mechanisms in their organising structures before an appropriate symmetry breaking flow is established.

The real world is a spatial world, and all living organisms live in a spatial environment. For mathematical biologists striving to understand the dynamical behaviour and evolution of interacting populations, this obvious fact has not been an easy one to accommodate. Space was considered a disposable complication to systems for which basic questions remained unanswered and early studies ignored it. But as understanding of non-spatial systems developed attention turned to methods of incorporating the effects of spatial structure. The essential problem is how to usefully manage the vast amounts of information that are implicit in a fully heterogeneous spatial environment. Various solutions have been proposed but there is no single best approach which covers all circumstances. High dimensional systems range from partial differential equations which model continuous population densities in space to the more recent individual-based systems which are simulated with the aid of computers. This thesis develops a relatively new type of model with which to explore the middle ground between spatially naive models and these fully complex systems. The key observation is to note the existence of correlations in real systems which may naturally arise as a consequence of their dynamical interaction amongst neighbouring individuals in a local spatial environment. Reflecting this fact - but ignoring other large scale spatial structure - the new models are developed as differential equations (pair models) which are based on these correlations. Effort is directed at a first-principles derivation from explicit assumptions with well stated approximations so the origin of the models is properly understood. The first step is consideration of simple direct neighbour correlations. This is then extended to cover larger local correlations and the implications of local spatial geometry. Some success is achieved in establishing the necessary framework and notation for future development. However, complexity quickly multiplies and on occasion conjectures necessarily replace rigorous derivations. Nevertheless, useful models result. Examples are taken from a range of simple and abstract ecological models, based on game theory, predator-prey systems and epidemiology. The motivation is always the illustration of possibilities rather than in depth investigation. Throughout the thesis, a dual interpretation of the models un-folds. Sometimes it can be helpful to view them as approximations to more complex spatial models. On the other hand, they stand as alternative descriptions of space in their own right. This second interpretation is found to be valuable and emphasis is placed upon it in the examples. For the game theory and predator-prey examples, the behaviour of the new models is not radically different from their non-spatial equivalents. Nevertheless, quantitative behavioural consequences of the spatial structure are discerned. Results of interest are obtained in the case of infection systems, where more realistic behaviour an improvement on non-spatial models is observed. Cautiously optimistic conclusions are reached that this, middle road of spatial modelling has an important contribution to make to the field.

No description available.

This thesis is an accumulation of work regarding the role of phosphorus (P) and water in soils in relation to crop growth and food production. We use a multiscale modelling approach to initially capture the interactions of soil and water on a single cylindrical root and further expand to a growing root structure. Moreover, we have a multi-physics problem involving fluid dynamics of water uptake in plants, and reactive solute transport in the soil for plant P uptake. We use detailed climate data and the super computer at the University of Southampton (Iridis 4) to parameterise our models. These facilities allow us to analyse the root structure as well as P and water in the soil in great detail. The collaboration of mathematics, biology and operational research makes it possible to complete this project. The analytical models recently developed within our group have shown to agree remarkably well with full 3D simulation models. These analytical models help provide the structure for the models used within this thesis and will for the first time enable us to start using optimisation techniques to find the optimal conditions for increasing plant P uptake efficiency. By using mathematical models to predict plant P and water uptake within the soil, we have addressed a number of questions surrounding the optimal plant root structure for P accumulation, and the survival of crops in a low P environment. In addition, we were able to predict the behaviour of water in the soil over the course of a full year. And finally, utilising all the above, we have outlined the optimal fertiliser and soil management strategy.

Antifouling coatings are crucial for protection of vessels’ hulls against marine biofouling. A range of technologies is available, although biocidal coatings - containing toxic or deterrent compounds – still represent a majority of the market. A long-term goal is the development of less environmentally harmful and persistent compounds; one of many potential avenues is that of synthetic analogues of natural products from marine organisms. The development of coatings using natural products has been hampered by poor performance in the field without sufficient work on their leach rates and behaviour. Furthermore, little work has been carried out on the leach rate of traditional organic biocides as used in modern coatings. Prediction of biocide diffusion is crucial to estimation of antifouling efficacy. However, diffusion in glassy polymers is a complex and oft-neglected topic; the chemically and physically changeable environment of the ocean and swelling of the polymer in such a ternary system also increase the complexity of models. A test matrix of antifouling paint coatings was composed, including polymethylmethacrylate (pMMA), an erodible rosin-based commercial binder and a novel trityl methacrylate/butylacrylate copolymer (pTrMA/BA) as binders. Copper (I) oxide and usnic acid, a natural product biocide of interest, were incorporated into the binders and the coatings were subjected to 10 months of natural immersion and 6 months of accelerated rotor immersion tests (17 knots, 25 °C). A novel application of fluorescence microscopy was developed, allowing quantification of the usnic acid content within the test coatings from both immersion schemes. This fluorescence technique and optical microscopy techniques were applied to these coatings before and after immersion, allowing quantification of the organic biocide and pigment distribution. Existing literature models for diffusion in glassy systems were adapted with a novel method for taking into account the presence of seawater as a diluent, to obtain effective diffusion coefficients for usnic acid. These have been integrated into mathematical models of diffusion to predict biocide lifetime. These data were compared with experimental data for biocide leaching from the long term immersions. The biocide leached completely from the p(TrMA/BA) binder during rotor testing, compared to 35% from the pMMA binder. For pontoon immersions, 61% of the additive was lost from the pMMA coating, and 53% from the rosin-based binder. An accelerated loss of usnic acid occurred in the surface of the rosin-based binder, due to rosin depletion. In all samples, release of the biocide was inhibited beyond the cuprous oxide front, which was congruent with the leached layer in samples where cuprous oxide release occurred. The erodible binder was the only one which demonstrated synchronous depletion of both additives, and it demonstrated a good resistance to fouling in immersion trials. Results of the mathematical modelling of the biocide diffusion were in good agreement with the observed data in the case of pMMA, highlighting in particular the importance of water uptake with respect to biocide diffusion. However, there was poor agreement in the case of p(TrMA/BA), for which the model under-predicted the release rate by about three orders of magnitude.

<p> Increasing individual ecological literacy levels may help citizens make informed choices about the environmental challenges facing society. The purpose of this study was to explore the impacts of an arboretum curriculum incorporating mobile technology and an urban greenspace on the ecological knowledge, environmental attitudes and beliefs, and environmental behaviors of undergraduate biology students and pre-service K-8 teachers during a summer course.</p><p> Using a convergent parallel mixed-methods design, both quantitative and qualitative data were collected, analyzed, and later merged to create an enhanced understanding of the impact of the curriculum on the environmental attitudes and beliefs of the participants. Quantitative results revealed a significant difference between pre- and post-survey scores for ecological knowledge, with no significant differences between pre- and post-scores for the other variables measured. However, no significant difference in scores was found between experimental and comparison groups for any of the three variables.</p><p> When the two data sets were compared, results from the quantitative and qualitative components were found to converge and diverge. Quantitative data indicated the environmental attitudes and beliefs of participants were unaffected by the arboretum curriculum. Similarly, qualitative data indicated participants&rsquo; perceived environmental attitudes and beliefs about the importance of nature remained unchanged throughout the course of the study. However, qualitative data supporting the theme <i>connecting with the curriculum</i> suggested experiences with the arboretum curriculum helped participants develop an appreciation for trees and nature and led them to believe they increased their knowledge about trees.</p><p>