The thesis describes various modifications of the predator-prey model. The modifications are considering several harvesting methods. At the beginning a solution and a sensitivity analysis of the basic model are provided. The first modification is the percentage harvesting model, which could be easily converted to the basic model. Secondly a constant harvesting including a linearization is derived. A significant part is devoted to regulation models with special a focus on environmental applications and the stability of the system. Optimization algorithms for one and both species harvesting are derived and back-tested. One species harvesting is based on econometrical tools; the core of two species harvesting is the modified Newton's method. The economic applications of the model in macroeconomics and oligopoly theory are expanded using the methods derived in the thesis.

Orientadores: João Vasconcellos Neto, Marcelo de Oliveira Gonzaga / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Biologia / Made available in DSpace on 2018-08-24T05:04:24Z (GMT). No. of bitstreams: 1 Souza_HebertdaSilva_M.pdf: 4147716 bytes, checksum: 886fc92941a725beb4f3c73d25b6a031 (MD5) Previous issue date: 2013 / Resumo: O grupo das aranhas é extremamente diverso e está distribuído em praticamente todos os habitats terrestres. No entanto, a ocorrência de grande parte das espécies é condicionada por fatores abióticos e bióticos bem definidos. Dessa forma, elementos como altitude, intensidade luminosa, temperatura, umidade, bem como as interações existentes com outros organismos, como a relação entre presas e predadores, podem influenciar o padrão de distribuição e os ajustes populacionais de aranhas ao longo do tempo. A vegetação é um fator determinante para a biologia de aranhas orbitelas, pois além de providenciar condições microclimáticas adequadas, fornece abrigo e pontos de apoio para a construção de teia... Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital / Abstract: The Group of spiders is extremely diverse and is distributed in practically all terrestrial habitats. However, the occurrence of most species is conditioned by abiotic and biotic factors. Thus, elements such as altitude, light intensity, temperature, humidity, as well as existing interactions with other organisms, such as the relationship between prey and predators, may influence the distribution pattern and population adjustments of spiders over time. The vegetation is a determining factor for the biology of Orb-Weavers spiders, because, in addition to providing adequate microclimatic conditions, it provides shelter and support spots for construction of webs. Eustala taquara (Araneidae) inhabits herbaceous plants and shrubs, and are difficult to be seen by blending with the dry vegetation where they lie... Note: The complete abstract is avaiable with the full electronic document / Mestrado / Biodiversidade Animal / Mestre em Biologia Animal

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

Cette thèse est dédiée à l’étude des propriétés de propagation de systèmes de réaction – diffusion issus de la dynamique des populations. Dans la première partie, on étudie la limite de forte compétition de systèmes à deux espèces. À l’aide de la ségrégation spatiale, on détermine le signe de la vitesse de l’onde progressive bistable. La généralisation aux ondes pulsatoires bistables en milieu spatialement périodique est ensuite envisagée afin d’étudier le rôle de l’hétérogénéité spatiale. Après avoir donné une condition suffisante pour l’existence de telles ondes ainsi qu’une condition suffisante pour l’existence d’états stationnaires stables susceptibles au contraire de bloquer l’invasion, on suppose qu’une famille d’ondes pulsatoires existe et on prouve un résultat semblable à celui obtenu en milieu homogène. Dans la seconde partie, des systèmes de type KPP à un nombre arbitraire d’espèces sont considérés. On étudie l’existence d’états stationnaires et d’ondes progressives, les propriétés qualitatives de ces solutions ainsi que la vitesse asymptotique de propagation de certaines solutions du problème de Cauchy. Cela résout des questions ouvertes sur les systèmes de mutation – compétition – diffusion, qui constituent le prototype de système de type KPP. Dans la troisième partie, on revient aux systèmes à deux espèces. Considérant cette fois-ci le cas monostable, on étudie les vitesses asymptotiques de propagation de certaines solutions du problème de Cauchy et, ce faisant, on montre l’existence de solutions décrivant l’invasion d’un territoire inhabité par un compétiteur faible mais rapide suivie de l’invasion de ce territoire par un compétiteur fort mais lent. / This thesis is dedicated to the study of propagation properties of various reaction–diffusion systems coming from population dynamics. In the first part, we study the strong competition limit of competition–diffusion systems with two species. Thanks to the spatial segregation, we determine the sign of the speed of the bistable traveling wave. The generalization to bistable pulsating fronts in spatially periodic media is then considered in order to study the role of spatial heterogeneity. We find a condition sufficient for the existence of such fronts as well as a condition sufficient for the existence of stable steady states which might on the contrary block the propagation. Then we show that whenever a family of strongly competing pulsating fronts exists, we can establish a result very similar to the one obtained in homogeneous media. In the second part, systems of KPP type with any number of species are considered. We study the existence of steady states and traveling waves, the qualitative properties of these solutions as well as the asymptotic speed of spreading of certain solutions of the Cauchy problem. This settles several open questions on the prototypical KPP systems that are mutation–competition–diffusion systems. In the third part, we go back to competition–diffusion systems with two species. Considering this time the monostable case, we study the asymptotic speeds of spreading of certain solutions of the Cauchy problem. By so doing, we show the existence of propagating terraces describing the invasion of an uninhabited territory by a weak but fast competitor followed by the invasion by a strong but slow competitor.

MSc (Botany) / Department of Botany

The implementation of the National Curriculum Statement in 2006 saw the name of the subject known as Biology change to Life Sciences accompanied by changes in subject content. The curriculum committee excluded systematics as a separate unit from the new outcomes-based Life Sciences curriculum for grades 10 to 12 that was implemented in 2006. Educators had to include aspects of systematics in teaching these concepts without guidance from the curriculum. This posed the question whether mastery of population dynamics and biodiversity is dependent on content of systematics in the context of the new curriculum. The New Content Framework for Life Sciences implemented in 2009 reintroduced systematics as a single unit. This raised the question why systematics has been reintroduced in the Life Sciences curriculum. This study aims to determine the influence the exclusion of systematics as a separate unit from the Life Sciences curriculum, implemented in 2006, had on the teaching of population studies and biodiversity. Data was gathered by evaluating and analysing the relevant curriculum statements, work schedules and content frameworks. Semi-structured interviews were conducted, first in 2008 when systematics was excluded from the curriculum and then in 2009 after the reintroduction. The first interviews dealt with the exclusion of systematics and the second interviews queried the reintroduction of systematics in the New Content Framework. Interviews were conducted with grade 11 Life Sciences educators at two secondary schools and two curriculum developers involved in compiling the Life Sciences curriculum. An expert in systematics and another in ecology were interviewed about the exclusion of systematics. The workbooks of some grade 11 learners were studied. Classroom observations were conducted when the relevant topics were being covered in class. A number of reasons for the exclusion of systematics from the NCS were advanced. These included: there was no population dynamics expert in the curriculum development team, emphasis was placed on outcomes and not content, the academic background of the members of the curriculum team and the difficulty of teaching systematics, perceived to be uninteresting. There was disagreement whether systematics is essential for understanding population dynamics but there is consensus that the study of systematics influences biodiversity and its exclusion left a regrettable void. However, systematics should be taught in a more interesting way. Prior knowledge is important for understanding of certain processes and concepts as well as for the application of practical skills like problem-solving and scientific inquiry. The curriculum does not provide detailed guidance on the content and practical activities to be covered and educators are encouraged to develop their own curriculum and activities. Experienced educators with strong academic backgrounds in animal and plant sciences referred to or used knowledge of systematics in some lessons. In 2009, systematics was reintroduced in the Life Sciences curriculum to ensure that learners understand biodiversity and evolution through natural selection. It provides learners a better foundation to understand similarities and differences in the structure and function of different organisms and body plans and ensures that they use higher-order thinking skills when doing problem-solving and scientific inquiry activities. / Dissertation (MEd)--University of Pretoria, 2010. / Curriculum Studies / unrestricted

The population size of the horned grebe, Podiceps auritus, is declining in most of the world due to loss of wetlands, deteriorating water quality and establishment of predatory fish such as pike, Esox lucius, in former fish free wetlands. The horned grebe is now globally classified as vulnerable. In this study, data on population dynamics of the horned grebe in six created wetlands in Linköpings kommun was examined together with field work carried out in three of the wetlands. The results indicate that the number of pairs and juveniles of horned grebe crash six to eight years after the wetland is created and does not recover if there is fish present. The pairs and juveniles of horned grebe decreased significantly with the increasing age of the wetland if there was pike present in the wetland. Reduction fishing and drainage of the water in two of the wetlands inhabited pike showed a small improvement in population size of the horned grebe, but the numbers ultimately declined after a few years. Reduction fishing of common roach in one wetland showed a continuing improvement in the population size of horned grebe. Other factors that affected the horned grebe negatively, was an abundance of macrophytes such as Canadian pondweed, Elodea canadensis, that makes foraging harder.

<p>  </p> <p>Tar spot is a new foliar disease of corn in the United States. Tar spot was first detected in 2015 and is now among the most important corn diseases in the Midwest. Tar spot is caused by the obligate biotrophic fungus, <em>Phyllachora maydis</em> Maubl, from the genus, <em>Phyllachora </em>which consist of over 1,200 species of host-specific fungi. Due to the recent emergence, studies relating to <em>P. maydis</em> population dynamics in the U.S. are limited. How much genetic diversity, variation, and level of gene flow are occurring within and among these populations? Knowledge of the population dynamics is imperative for understanding the pathogen’s biology, ecology, epidemiology, and management. Currently, no corn hybrid is fully resistant to tar spot. Foliar fungicides are currently the most effective option for disease management, but best practices for fungicide management remain unknown. Better information is needed on fungicide efficacy and fungicide application timing to reduce tar spot severity, protect yield, and increase profitability for Indiana corn growers. </p> <p>This research dissertation presents four chapters to answers those questions and bridge the gaps between the knowns and unknows of this novel corn-<em>Phyllachora maydis</em> pathosystem. <strong>Chapter 1</strong> presents a literature review on tar spot of corn, its economic impact, the causal pathogen, its host, lifecycle, distribution, and known management strategies as a resource for understanding the pathosystem in the U.S. <strong>Chapter 2</strong> examines the genetic population structure, diversity, geneflow and mode of reproduction in Midwest U.S. by employing microsatellite (SSR) markers. <strong>Chapter 3</strong> presents results from multi-year, multi-location, small-plot field trials on the net return of foliar fungicides and fungicide timing on tar spot management in Indiana. Lastly, <strong>Chapter 4</strong> concludes by evaluating of an integrated management strategy for tar spot by examining the integration of tillage, corn hybrids and fungicide application in reducing tar spot severity while protecting yields.</p> <p>Results provided in this research dissertation will be used to guide future studies and provide stakeholders such as researchers, corn growers, extension personnel in academia and industry with valuable information needed to guide effective disease management decisions. </p>

Insular fauna face disproportionate risks of extinction owing to direct human perturbation and intrinsic factors that are enhanced at small population sizes. Currently, our understanding of the processes that promote long-term persistence of naturally small populations and the cryptic processes that may contribute to accelerating their decline is limited by lack of empirical investigations across the range of natural conditions. Implementing effective protections for rare and understudied taxa requires the identification and examination of factors that limit recruitment at critical life stages. Predicting population health outcomes of future perturbations further necessitates an understanding a taxon’s behavioral ecology. Finally, cryptic threats to viability, such as inbreeding depression, must be investigated with an appreciation for taxon-specific life history, as these attributes can alter the context in which severe fitness reductions are expressed. In this project I enlist integrative and cross-disciplinary approaches to study the behavioral ecology and conservation genetics of a critically endangered West Indian Rock Iguana, Cyclura nubila caymanensis, on Little Cayman Island. I demonstrate how coastal communal nesting areas, a critical limiting resource on the island, serve a diverse population demographic and contribute to significantly enhanced nesting outcomes. These data emphasize the importance of expanding protections for major sites, as aggregative nesting appears to be perpetuated by both habitat suitability and adaptive fitness benefits. I next evaluate the possibility of evolved inbreeding avoidance strategies, including natal dispersal, non-assortative mate choice, and genetic bet-hedging. I conclude that the contribution of pre-reproductive dispersal to inbreeding avoidance likely outweighs that of active mate choice. Importantly, observed patterns of siring success imply constrained female choice and sexual conflict over genetic mating outcomes – a pattern that may extend to many territorial, male-driven mating systems and therefore should be an important consideration in genetic management. Finally, I investigate age-dependent inbreeding effects and the degree to which inbreeding depression may limit recruitment to the breeding population. I fail to reveal significant correlations of multi-locus heterozygosity with hatchling fitness; however, negative effects of parental inbreeding on fecundity and hatching success imply fitness consequences of inbreeding depression could be felt at other life stages.

[pt] É comum observar na natureza a emergência de comportamentos coletivos em populações biológicas, como formação de padrão. Neste trabalho, estamos interessados em caracterizar a distribuição de uma população de espécie única (como alguns tipos de bactérias ou de vegetação), a partir de modelos matemáticos que descrevem a evolução espaço-temporal, governados por processos elementares como: dispersão, crescimento e competição não-local por recursos. Primeiramente, utilizando uma generalização da equação de FKPP, analisamos numérica e analiticamente, o impacto de mecanismos de regulação dependentes da densidade, tanto na difusão quanto no crescimento. Tais mecanismos representam processos internos de retroalimentação, que modelam a resposta do sistema à superlotação ou rarefação da população. Mostramos que, dependendo do tipo de resposta em ação, os indivíduos podem se auto-organizar em subpopulações desconectadas (fragmentação), mesmo na ausência de restrições externas, ou seja, em uma paisagem homogênea. Discutimos o papel crucial que a dependência com a densidade tem na forma dos padrões, particularmente na fragmentação, o que pode trazer consequências importantes para processos de contato como disseminação de epidemias. Tendo compreendido esse fenômeno em um meio homogêneo, estudamos o papel que um ambiente heterogêneo tem na organização espacial de uma população, que representamos através de uma taxa de crescimento que varia com a posição. Investigamos as estruturas que emergem próximo a fronteira de um meio para o outro. Descobrimos que, dependendo da forma de interação nãolocal e de outros parâmetros do modelo, três perfis diferentes podem emergir a partir da interface: (i) oscilações não-atenuadas (ou padrões espaciais, sem decaimento da amplitude); (ii) oscilações atenuadas (com amplitude decaindo a partir da interface); (iii) decaimento exponencial (sem oscilações) a um perfil homogêneo. Relacionamos o comprimento de onda e a taxa de decaimento das oscilações com os parâmetros das interações (comprimento característico e forma de decaimento com a distância). Discutimos como as heterogeneidades do ambiente permitem acessar informações (ocultas no caso homogêneo) sobre os fenômenos biológicos do sistema, tais como os que mediam interações competitivas. / [en] It is common to observe in nature the emergence of collective behavior in biological populations, such as pattern formation. In this work, we are interested in characterizing the distribution of a single-species population (such as some bacteria or vegetation), based on mathematical models that describe the spatio-temporal evolution, and governed by elementary processes, such as: dispersion, growth, and nonlocal competition by resources. First, using a generalization of the FKPP equation, we analyze numerically and analytically the impact of density-dependent regulatory mechanisms, both on diffusion and growth. Such mechanisms represent processes of internal feedback, which shape the system s response to population overcrowding or rarefaction. We show that, depending on the type of the response in action, some individuals can organize themselves in disconnected sub-populations (fragmentation), even in the absence of external restrictions, that is in a homogeneous landscape. We discuss the crucial role that density-dependence has in the form of patterns, particularly in fragmentation, which can have important consequences for contact processes, such as the spread of epidemics. After understanding this phenomenon in a homogeneous environment, we study the role that a heterogeneous environment has in the spatial organization of a population, which was presented as a growth rate that varies with position. We investigate the structures that emerge near the border from one environment to the other. We found that, depending on the shape of nonlocal interaction and other model parameters, three different profiles can emerge from the interface: (i) sustained oscillations (or spatial patterns, without amplitude decay); (ii) attenuated oscillations (with amplitude decreasing from the interface); (iii) exponential decay (without oscillations) to a homogeneous profile. We related the wavelength and the rate of decay of oscillations with the parameters of the interaction (characteristic length and form of decay with distance). We discussed how the heterogeneities of the environment allow access to information (hidden in the homogeneous case) about the biological phenomena of the system, such as those that mediate competitive interactions.