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In this thesis we consider the N=1 super Yang-Mills theory on S5 with a single hypermultiplet in the adjoint representation. We argue that there is a critical value of the hypermultiplet mass M=3/2r, where r is the radius of S5, for which the free energy vanishes, and we study the model in the proximity of this value. For large N we provide analytical results for the free energy and the eigenvalue density in the weak and strong coupling limits, and in one case we solve the saddle point equation using a technique introduced by Hoppe. We present numerical results to show where each approximation is justified, and to explore the regimes where the model cannot be solved analytically. Based on the numerical results, we argue that in most cases the behaviour of the model is better understood in terms of an effective coupling constant λ'=λM. For small M the model simplifies to one whose kernel is non-singular. This simplified model shows a peculiar peak structure in the eigenvalue distribution, with the number of peaks growing as the effective coupling is increased. We interpret this as a series of phase transitions as M approaches 3/2r.

Motivated by models from evolutionary population dynamics, we study a general class of nonlinear difference equations called matrix models. Under the assumption that the projection matrix is non-negative and irreducible, we prove a theorem that establishes the global existence of a continuum with positive equilibria that bifurcates from an extinction equilibrium at a value of a model parameter at which the extinction equilibrium destabilizes. We give criteria for the global shape of the continuum, including local direction of bifurcation and its relationship to the local stability of the bifurcating positive equilibria. We discuss a relationship between backward bifurcations and Allee effects. Illustrative examples are given

We study a discrete time, structured population dynamic model that is motivated by recent field observations concerning certain life history strategies of colonial- nesting gulls, specifically the glaucouswinged gull ( Larus glaucescens). The model focuses on mechanisms hypothesized to play key roles in a population's response to degraded environment resources, namely, increased cannibalism and adjustments in reproductive timing. We explore the dynamic consequences of these mechanics using a juvenile- adult structure model. Mathematically, the model is unusual in that it involves a high co- dimension bifurcation at R0 = 1 which, in turn, leads to a dynamic dichotomy between equilibrium states and synchronized oscillatory states. We give diagnostic criteria that determine which dynamic is stable. We also explore strong Allee effects caused by positive feedback mechanisms in the model and the possible consequence that a cannibalistic population can survive when a non- cannibalistic population cannot.

Madagascar's freshwater crayfish, belonging to the endemic genus Astacoides, are harvested throughout their range in the eastern highlands of the country. They provide an important source of protein and revenue to local communities but there is concern that the harvest may be unsustainable. In this thesis I assess the sustainability of crayfish harvesting in and around Ranomafana National Park, an area well known for its reliance on crayfish harvesting. Six taxa (belonging to four described species) are found in the Ranomafana area. Most families in villages with access to forest carry out some harvesting for subsistence use. Due to variation in local taboos (fady) and in access to forest, commercial crayfish harvesting is very important in only three of the 27 villages I visited. However, in these villages crayfish revenue is very important, particularly to poorer households. One species, Astacoides granulimanus, dominates the harvest: more than 95% of crayfish caught in the harvesting village of Vohiparara are of this species. I used a mark-and-recapture study involving more than 26,000 A. granulimanus across 79 sites under a range of harvesting intensities to estimate demographic parameters (growth, fecundity and survival) and investigate density-dependent control of growth and fecundity. No evidence for density-dependent control of growth was found, but the density of large crayfish negatively influenced the proportion of females of a given size which reproduced. I investigated the sustainability of the harvest of A. granulimanus using two approaches: I) comparing population structure and density under varying harvesting intensity and II) using population models to investigate the forest area necessary to provide the observed annual harvest from one harvesting village and comparing that with the area available. The conclusions are encouraging as they suggest that the A. granulimanus harvest in the Ranomafana area may be sustainable under current conditions. Preliminary work suggests habitat loss may be a more immediate threat, so scarce conservation resources should perhaps be concentrated on reducing habitat loss rather than enforcing a ban on harvesting.

Population-level dynamics are affected by temporal variation in individual vital rates of survival and reproduction, which are in turn influenced by habitat-specific processes. Variation in habitat quality within a population’s range can drive movement of individuals between different areas, and so there may be a relationship between variation in vital rates and spatial heterogeneity in population growth (λ). I investigated this relationship for the feral horses (Equus ferus caballus) of Sable Island, Nova Scotia, Canada, from 2008−2010. The horses (n = 484 in September 2010) form a closed population that is free from human interference and predation. I analyzed annual population growth using age-structured projection matrix models parameterized with survival and fertility data collected from almost every female (98.7% of females). I found some evidence of temporal variation in growth during the two years I studied the population (λ2008−2009 = 1.065, λ2009−2010 = 1.117). Age structure appears to have converged to a stable age distribution, suggesting this growth rate has been sustained in the years leading up to the end of my study. Variation in vital rates of adult fertility and foal survival made the largest contribution to annual variation in population growth. Future growth is predicted to be most influenced by proportional changes in adult survival, which remained relatively unchanged between 2008 and 2010. The population can be stratified into three spatially distinct subunits found across a west−east longitudinal gradient of water resources (access to permanent ponds vs. ephemeral water sources and holes dug in sand). I assessed the existence of source-sink dynamics to determine if individual movements between subunits could explain spatial heterogeneity in population growth. I found that spatial heterogeneity in growth appears to be most influenced by immigration and emigration events between subunits. Evidence suggests that current growth of the overall Sable Island horse population is made possible by individual emigration from more productive into less productive subunits; in particular, a source presented in the west of the island where permanent water ponds are located.

Gauge theories are one of the corner stones of modern theoretical physics. They describe the nature of all fundamental interactions and have been applied in multiple branches of physics. The most challenging problem of gauge theories, which has not been solved yet, is their strong coupling dynamics. A class of gauge theories that admits simplifications allowing to deal with the strong coupling regime are supersymmetric ones. For example, recently proposed method of supersymmetric localization allows to reduce expectation values of supersymmetric observables, expressed through the path integral, to finite-dimensional matrix integral. The last one is usually easier to deal with compared to the original infinite-dimensional integral. This thesis deals with the matrix models obtained from the localization of different 5D gauge theories. The focus of our study is N=1 super Yang-Mills theory with different matter content as well as N=1 Chern-Simons-Matter theory with adjoint hypermultiplets. Both theories are considered on the five-spheres. We make use of the saddle-point approximation of the matrix integrals, obtained from localization, to evaluate expectation values of different observables in these theories. This approximation corresponds to the large-N limit of the localized gauge theory. We derive <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N%5E%7B3%7D" /> behavior for the free energy of 5D N=1* super Yang-Mills theory at strong coupling. This result is important in light of the relation between 5D theory and the world-volume theories of M5-branes, playing a significant role in string theory. We have also explored rich phase structure of 5D SU(N) N=1 super Yang-Mills theory coupled to massive matter in different representations of the gauge group. We have shown that in the case of the massive adjoint hypermultiplet theory undergoes infinite chain of the third order phase transitions while interpolating between weak and strong coupling in the decompactification limit. Finally, we obtain several interesting results for 5D Chern-Simons theory, suggesting existence of the holographic duals to this theory. In particular, we derive <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N%5E%7B5/2%7D" /> behavior of the free energy of this theory, which reproduces the behavior of the free energy for 5D theories with known  holographic duals.

Invasive plants have a significant detrimental effect on ecosystems globally, with impacts estimated at millions of dollars per invasive species each year. Biological control has long been used as a management tool for invasive plants, as it is considered a long–term cost–effective control strategy. Surprisingly, the impact of biological agents is rarely quantified. Any form of impact evaluation is generally conducted soon after agent release and establishment; with few studies examining the impact of the agents on the population dynamics of the invader, particularly once the agents have been established for a long time. The aim of the research in my thesis is to evaluate the biological control program of groundsel bush (Baccharis halimifolia L. Asteraceae) in Australia. The groundsel bush biological control agents were released up to 40 years ago and no quantitative assessment of agent impact has ever been conducted, despite the fact that the program has cost about $9.6 million. More specifically, the overall aim of this thesis is to investigate the impact of the released biological control agents on individual plants and populations of groundsel bush. In addition, my thesis aims to examine the impacts of climate as a potential confounding factor of the biological control program. My thesis provides a unique example of biological control evaluation by using a combination of observational damage studies, insect exclusion experiments, and statistical, population and climate modelling to assess, a posteriori, the effectiveness of biological control. This is the first time a long term biological control program has ever been evaluated. To assess the efficacy of the agents, I conducted a large field survey to examine whether the agents were distributed throughout the entire range of groundsel bush and if any biotic or abiotic factors influenced their effectiveness. In addition to this, I assessed the effect of the agents on the growth, survival and fecundity of individual plants under field conditions, and subsequently population growth rate. To do this, I used statistical models of observed effects of biological control agent damage and insect exclusion experiments on plant growth and fecundity to parameterise matrix population models. My results indicate that the groundsel bush biological control agents may be patchy in their effectiveness due to factors such as rainfall and plant size. At their current rate of damage, the groundsel bush biological control agents do not reduce plant growth or fecundity significantly. However, simulation models demonstrated that the agents have the potential to reduce individual plant and population growth when damage is at high levels. A reduction in an invader’s population growth rate, following the introduction of biological control agents, does not necessarily signify that the agents were responsible for the reduction. Factors such as land clearing, chemical and mechanical control, ecosystem health and climate may reduce populations of invasive plant species. With this in mind, I developed a series of climate models to examine how the favourability for growth of groundsel bush may change under different climate scenarios. The climate simulations demonstrated that the distribution and abundance of groundsel bush populations may have contracted in the past 50 years (post–biological control agent release) due to changing rainfall and temperature patterns. The results of the research in my thesis clearly show the need for thorough biological control evaluations, and for detailed data to be collected on the target plant’s demography and population sizes pre- and post-agent release. At a minimum, this should enable biological control practitioners to determine some level of agent impact and demonstrate support for further agent releases or integrative management strategies if necessary. Groundsel bush is a significant invader in Europe where biological control has not yet been carried out. Lessons from the evaluation of the Australian biological control program could be applied to new biological control programs elsewhere such as Europe. Overall, my research findings contribute to a better understanding of how to best evaluate a post-release biological control program, using groundsel bush as a case study. This is the first study to demonstrate an effective set of strategies and quantitative tools to evaluate a biological control program, which can be similarly applied to any biological control program and contributes significantly to an area of biological control which has only recently received significant attention.

Matrix population models are discrete in both time and state-space, where a matrix with density-dependent entries is used to project a population vector of a stage-structured population from one time to the next. Such models are useful for modeling populations with discrete categorizations (e.g. developmental cycles, communities of multiple species, differing sizes, etc.). We present a general matrix model of two interacting populations where one (the resident) has a stable cycle, and we analyze when the other population (the invader) can successfully invade. Specifically, we study the local bifurcations of coexistence cycles as the resident cycle destabilizes, where a cycle of length 1 corresponds to an equilibrium. We make no assumptions on the types of interactions between the populations or on the population structure of the resident; we consider when the invader's projection matrix is primitive or imprimitive and 2x2. The simplest biological scenarios for such structures are an iteroparous invader and a two-stage semelparous invader. When the invader has a primitive projection matrix, coexistence cycles (of the same period as the resident cycle) bifurcate from the resident-cycle. When the invader has an imprimitive two-stage projection matrix, two types of coexistence cycles bifurcate from the resident-cycle: cycles of the same period and cycles of double the period. In both the primitive and imprimitive cases, we provide diagnostic quantities to determine the direction of bifurcation and the stability of the bifurcating cycles. Because we only perform a local stability analysis, the only successful invasion provided by our results is through stable coexistence cycles. As we show in some simple examples, however, the invader may persist when the coexistence cycles are unstable through competitive exclusion where the branch of bifurcating cycles connects to a branch of invader attractors and creates a multi-attractor scenario known as a strong Allee effect.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19495号 / 理博第4155号 / 新制||理||1597(附属図書館) / 32531 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 福間 將文, 教授 川合 光, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM