<p> Relative motion is an ecological mechanism with the power to change the stability and longevity of populations and predict large scale movement patterns in highly mobile species. This dissertation introduces relative motion as an ecological mechanism using simulations and experiments at varying levels of spatial complexity. Chapters 2 and 3 describe the interactions between population movement and one-dimensional habitat movement, while Chapters 4 and 5 focus on the interactions between individual movement and three-dimensional habitat movement. Chapters 2 and 4 lay out my model justification, model development, and simulation results, while the remaining two chapters describe case studies competing those models with data. In Chapter 2, I simulate populations chasing moving habitat using stochastic spatial spread models. Results from these simulations show that populations lose symmetry when the habitat begins to move and suggest that loss of symmetry increases extinction risk. Results also show that assisted migration can restore some of that lost symmetry, but the success of assisted migration is sensitive to the transplant location and habitat speed. In Chapter 3, I build on the simulations presented in Chapter 2 by investigating assisted migration as a method of restoring symmetry using <i> Tribolium</i> microcosm experiments. Experimental results show that assisted migration both restored symmetry to the moving populations under fast-moving habitat conditions and significantly reduced extinction risk compared to the controls. Chapter 4 describes a 3-dimensional Geographic Information System (GIS) to track multiple sources of relative motion in the environment at once, using rigid body mathematics to move individual components in their own direction. In Chapter 5, I apply this GIS to deconstruct the migratory paths of 22 Greater shearwater (<i>Puffinus gravis</i>) migrants and rank the relative contributions of solar, wind, temperature, humidity, and surface cues to the figure-8 shaped migratory paths observed in this species.</p>

Consists of papers previously published in various journals. / Includes bibliographical references. / 1 v. (various pagings) : / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (D.Sc.)--University of Adelaide, 1995

Modelling is a powerful method for understanding complex systems, which works by simplifying them to their most essential components. The choice of the components is driven by the aspects studied. The tool chosen to perform this task will determine what can be modelled, the maximum number of components which can be represented, as well as the analyses which can be performed on the system. Performance Evaluation Process Algebra (PEPA) was initially developed to tackle computer systems issues. Nevertheless, it possesses some interesting properties which could be exploited for the study of epidemiological systems. PEPA's main advantage resides in its capacity to change scale: the assumptions and parameter values describe the behaviour of a single individual, while the resulting model provides information on the population behaviour. Additionally, stochasticity and continuous time have already proven to be useful features in epidemiology. While each of these features is already available in other tools, to find all three combined in a single tool is novel, and PEPA is proposed as a useful addition to the epidemiologist's toolbox. Moreover, an algorithm has been developed which allows converting a PEPA model into a system of Ordinary Differential Equations (ODEs). This provides access to countless additional software and theoretical analysis methods which enable the epidemiologist to gain further insight into the model. Finally, most existing tools require a deep understanding of the logic they are based on and the resulting model can be difficult to read and modify. PEPA's grammar, on the other hand, is easy to understand since it is based on few, yet powerful concepts. This makes it a very accessible formalism for any epidemiologist. The objective of this thesis is to determine precisely PEPA's ability to describe epidemiological systems, as well as extend the formalism when required. This involved modelling two systems: the bubonic plague in prairie dogs, and measles in England and Wales. These models were chosen as they exhibit a good range of typical features, allowing to thoroughly test PEPA. All features required in each of these models have been analysed in detail, and a solution has been provided for representing each of these features. While some of them could be expressed in a straightforward manner, PEPA did not provide the tools to express others. In those cases, we determined methods to approach the desired behaviour, and the limitations of said methods were carefully analysed. In the case of models with a structured population, PEPA was extended to simplify their expression and facilitate the writing process of the PEPA model. The work also required the development of an algorithm to derive ODEs adapted to the type of models encountered. Finally, the PEPAdum software was developed to assist the modeller in the generation and analysis of PEPA models, by simplifying the process of writing a PEPA model with compartments, performing the average of stochastic simulations and deriving and explicitly providing the ODEs using the Stirling Amendment.

Biological invasions are devastating ecosystems and economies world-wide, while many native species' survival depends on their ability to track climate change. Characterising the spread of biological populations is therefore of utmost importance, and can be studied with spatially explicit, discrete-time integro-difference equations (IDEs), which reflect numerous species' processes of demography and dispersal. While spatial variation has often been ignored when implementing IDE models, real landscapes are rarely spatially uniform and environmental variation is crucial in determining biological spread. To address this, we use novel methods to characterise population spread in heterogeneous landscapes. Asymptotic analysis is used for highly fragmented landscapes, where habitat patches are isolated and smaller than the dispersal scale, and in landscapes with low environmental variation, where the ecological parameters vary by no more than a small factor from their mean values. We find that the choice of dispersal kernel determines the effect of landscape structure on spreading speed, indicating that accurately fitting a kernel to data is important in accurately predicting speed. For the low-variation case, the spreading speeds in the heterogeneous and homogeneous landscapes differ by &straightepsilon;², where &straightepsilon; governs the degree of variation, suggesting that in many cases, a simpler homogeneous model gives similar spread rates. For irregular landscapes, analytical methods become intractable and numerical simulation is needed to predict spread. Accurate simulation requires high spatial resolution, which, using existing techniques, requires prohibitive amounts of computational resources (RAM, CPU etc). We overcome this by developing and implementing a novel algorithm that uses adaptive mesh refinement. The approximations and simulation algorithm produce accurate results, with the adaptive algorithm providing large improvements in efficiency without significant losses of accuracy compared to non-adaptive simulations. Hence, the adaptive algorithm enables faster simulation at previously unfeasible scales and resolutions, permitting novel areas of scientific research in species spread modelling.

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Orientador: João Frederico da Costa Azevedo Meyer / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-16T01:39:24Z (GMT). No. of bitstreams: 1 Almeida_JoseRicardoFerreirade_M.pdf: 4553728 bytes, checksum: 624a425a2bcd810bbcf5f8306e5edca4 (MD5) Previous issue date: 2010 / Resumo: Este trabalho usa o modelo clássico de Difusão-Advccção-Reação para simular o comportamento evolutivo bidimensional de manchas de poluentes em um domínio aquático. Em função da ausência de possibilidade de solução analítica (primordialmente pelo tipo de domínio em que sit estuda o referido problema), recorre-se a um método de aproximação baseado em diferenças finitas centradas tanto para as variáveis espaciais quanto para a variável temporal (esta, via uso adequadamente explicitado do método de Crank-Nicolson). As condições de contorno são definidas com foco na situação real, considerando a absorção de poluentes nas margens em trechos determinados em função de seu comportamento. O trecho de rio considerado é o do rio Paraíba do Sul na região de Volta Redonda. RJ, que se caracteriza por ser um trecho reto do referido corpo aquático. Adota-se, como perfil de velocidades, a parábola devida a Poiseuille [11], o que afeta a montagem do sistema de diferenças finitas. Especial atenção é dedicada à precisão numérica resultante da estratégia de aproximação, bem como à possibilidade de visualizar qualitativamente os resultados, criando, assim, um recurso de software que podo ser usado em muitas outras situações minimamente semelhantes de contaminação hídrica sistemática ou emergência / Abstract: His work use the classical model of diffusiou-advection-reaction to simulate the evolutionary two-dimensional behavior of patch.es of pollutants in an aquatic domain. Because of the lack of possibility of analytical solution (primarily by the type of domain where you study the problem), it resorts to an approximation method based on finite differences centered for both spatial variables and for the time variable (this, via the use adequately explained of the Crank-Nicolson method). The boundary conditions are set to focus on the real situation, considering the absorption of pollutants into the bank in determined sections depending on their behavior. The considered stretch of river is this Paraíba do Sul river in region of Volta Redonda, RJ, which is characterized by a straight stretch of that body of water. It is adopted, such a velocity profile, the parabola due to Poiseuillc, which affects the mounting of the system of finite differences. Special attention is devoted to numerical accuracy resulting from the approximation strategy, and the ability to qualitatively visualize the results, thus creating a software feature that can be used in many other similar minimally situations of systematic water contamination or emergency / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

Orientador: João Frederico da Costa Azevedo Meyer / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T17:19:29Z (GMT). No. of bitstreams: 1 Krindges_Andre_D.pdf: 12331441 bytes, checksum: ca3fa7d1c704c02f04ba59043413e0f7 (MD5) Previous issue date: 2011 / Resumo: Um dos problemas enfrentados pelo grupo de Ecologia Matemática do IMECC da UNICAMP é o de trabalhar com difusão de uma pluma poluente com 3 variáveis espaciais, além da temporal. Esta tese não só aborda esta questão, propondo, inclusive um algoritmo computacional para esta situação, mas fá-lo resolvendo aproximadamente a Equação de Navier-Stokes num domínio irregular. A primeira parte consiste na formulação do modelo matemático para o estudo de um sistema que inclui o campo de velocidades e o comportamento evolutivo de um material poluente. Na segunda parte, é feita a formulação variacional, são constituídas aproximações via o método de Galerkin para Elementos Finitos no espaço e Crank-Nicolson no tempo para a equação de difusão-advecção, e o método da projeção para a equação de Navier-Stokes. Em seguida, faz-se a descrição do algoritmo, indicando dificuldades operacionais do ponto de vista de computação científica e apontando soluções. O domínio utilizado para o estudo de caso é o da represa do rio Manso, que, discretizada em três dimensões, foi tratado com o software livre GMSH. Finalmente, um código numérico em plataforma MATLAB foi executado e resultados são apresentados no texto. O programa e diversas considerações técnicas essenciais fazem parte dos anexos / Abstract: One of the challenges faced by the Mathematical Ecology group at the Mathematics Institute at Campinas State University is that of working with the diffusion of a pollutant plume in three spatial variables, besides time. This work not only addresses this issue by proposing an approximation strategy as well as a computer algorithm for this situation, but it also includes a three-dimensional numerical approximation for the Navier-Stokes equation in an irregular domain. The first part consists in formulating the mathematical model for the study of a system that includes the velocity field and the evolutionary behavior of a polluting material. The second part begins with the variational formulation of the Navier-Stiokes system, and approximations are undertaken via the Galerkin method for finite elements in space and Crank-Nicolson in time for both the advection-diffusion equation and the method of projection for the Navier-Stokes equations. The algorithm is described, indicating operational difficulties in terms of scientific computing as well as the way in which these aforementioned difficulties are solved. The domain used for the case study is the Manso River reservoir, which, discretized in three dimensions, was treated with the free software GMSH. Finally, a numeric code in MATLAB environment was completed and results are presented in the text. The program and various essential technical considerations are part of the annexes / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Orientador: João Frederico da Costa Azevedo Meyer / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T22:13:08Z (GMT). No. of bitstreams: 1 Miyaoka_TiagoYuzo_M.pdf: 9483350 bytes, checksum: 13a6ce526d2a0eca797c7b2c56f65600 (MD5) Previous issue date: 2015 / Resumo: Este trabalho trata da modelagem matemática e da simulação computacional de um problema de dinâmica populacional, mais precisamente a interação de um poluente tóxico a duas espécies que competem entre si por espaço e alimento. A modelagem é feita a partir de dispersão e advecção populacional juntamente com o modelo clássico de Lotka-Volterra e reprodução do tipo de Verhulst, mas com um termo inovador para a interação entre poluente e população. Este termo inovador visa a melhoria do modelo a médio e longo prazos, pois tem comportamento assintótico em relação ao tempo. Temos assim um sistema de equações diferenciais parciais não-linear, cuja solução analítica é impossível de ser obtida. Recorremos então a métodos numéricos e simulações computacionais para obter soluções aproximadas. Para isso, utilizamos os métodos de Elementos Finitos (com elementos triangulares de primeira ordem) nas variáveis espaciais e de Diferenças Finitas (mais especificamente, o método de Crank-Nicolson) na temporal, além do método preditor-corretor de Douglas e Dupont para tratar não linearidades, detalhando o procedimento de se obter um software capaz de gerar cenários qualitativamente realistas (os parâmetros utilizados foram estimados). Com o software obtido apresentamos gráficos das soluções aproximadas em cenários hipotéticos distintos, de forma a poder analisar possíveis impactos ambientais causados pela poluição despejada no meio ambiente / Abstract: This work treats the mathematical modeling and computational simulation of a populational dynamics problem, more precisely the interaction of a toxic pollutant in two species which compete with each other for space and food. The modeling is done from populational dispersion and advection together with the classical model of Lotka-Volterra and Verhulst type reproduction, but with a innovative term for the interaction of pollutant and population. This innovative term aims the improvement of the model in the medium and long time, because it has asymptotic behaviour in relation to time. Therefore we have a system of non linear partial differential equations, whose analytical solution is impossible to be obtained. We then appeal to numerical methods and computational simulations to obtain approximated solutions. For this, we use the Finite Elements method (with first order triangular elements) in spatial variables and Finite Differences method (more specifically the Crank-Nicolson method), in addition to the Douglas and Dupont predictor-corrector method to treat non linearities, detailing the process of obtaining a software capable of generating qualitatively realistic scenarios (the parameters used were estimated). With the obtained software we present plots of approximate solutions in different hypothetical scenarios, in order to analyze possible enviromental impacts caused by pollution released into the environment / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada