An overcrowding problem of nyala, and lately also of impala in the Ndumo Game Reserve, South Africa, has been detrimental to other species and vegetation structures over a period of two decades. In the present study a deterministic model for three competing species (where two species tend to be overpopulated while the third faces probable localized extinction) is constructed, while future trends coupled with their coexistence are projected. On a mathematical basis, we seek reasons for the failure of the cropping strategies implemented by management over the last two decades, and suggest alternative, scientifical-based approaches to the calculation of cropping quotas to ensure the future coexistence of all three species. A system of three first-order nonlinear differential equations is used, with parameter values based on field data and opinions of specialist ecologists. The effect of various cropping strategies, and the introduction of a fourth species (man as a predator) to the system, is investigated mathematically. This model was implemented as a harvesting strategy in 2002, and is being continuously tested. Final assessment can only be done over a 10–15-year period, but so far indications are promising.

Time-rate analysis and time-rate-pressure analysis methods are available to estimate reserves and study flow performance of wells in unconventional gas reservoirs. However, these tools are often incorrectly used or the analysis can become difficult because of the complex nature of the reservoir system. Conventional methods (e.g., Arps' time-rate relations) are often used incorrectly to estimate reserves from such reservoirs. It was only recently that a serious study was conducted to outline the limitations of these relations and to set guidelines for their correct application. New time-rate relations, particularly the Duong and logistic growth model, were introduced to estimate reserves and forecast production from unconventional reservoirs. These new models are being used with limited understanding of their characteristics and limitations. Moreover, well performance analyses using analytical/semi-analytical solutions (time-rate-pressure) are often complicated from non-uniqueness that arises when estimating well/formation properties. In this work, we present a detailed study of the Duong model and logistic growth model to investigate the behaviors and limitations of these models when analyzing production data from unconventional reservoirs. We consider production data generated from numerical simulation cases and data obtained from unconventional gas reservoirs to study the quality of match to specific flow regimes and compare accuracy of the reserve estimates. We use the power-law exponential model (PLE), which has been shown to model transient, transition and boundary-dominated flow regimes reliably, as a benchmark to study performance of Duong and logistic growth models. Moreover, we use the "continuous EUR" approach to compare these models during reserve estimation. Finally, we develop four new time-rate relations, based on characteristics of the time-rate data on diagnostic plots. Using diagnostic plots we show that the new time-rate relations provide a quality match to the production data across all flow regimes, leading to a reliable reserve estimate. In a preliminary study, we integrated time-rate model parameters with fundamental reservoir properties (i.e., fracture conductivity (Fc) and 30 year EUR (EUR30yr)), by studying 15 numerical simulation cases to yield parametric correlations. We have demonstrated a methodology to integrate time-rate model parameters and reservoir properties. This method avoids the non-uniqueness issues often associated with model-based production data analysis. This study provides theoretical basis for further demonstration of the methodology using field cases.

Current models used to forecast production in unconventional oil and gas formations are often not producing valid results. When traditional decline curve analysis models are used in shale formations, Arps b-values greater than 1 are commonly obtained, and these values yield infinite cumulative production, which is non-physical.. Additional methods have been developed to prevent the unrealistic values produced, like truncating hyperbolic declines with exponential declines when a minimum production rate is reached. Truncating a hyperbolic decline with an exponential decline solves some of the problems associated with decline curve analysis, but it is not an ideal solution. The exponential decline rate used is arbitrary, and the value picked greatly effects the results of the forecast. A new empirical model has been developed and used as an alternative to traditional decline curve analysis with the Arps equation. The new model is based on the concept of logistic growth models. Logistic growth models were originally developed in the 1830s by Belgian mathematician, Pierre Verhulst, to model population growth. The new logistic model for production forecasting in ultra-tight reservoirs uses the concept of a carrying capacity. The carrying capacity provides the maximum recoverable oil or gas from a single well, and it causes all forecasts produced with this model to be within a reasonable range of known volumetrically available oil. Additionally the carrying capacity causes the production rate forecast to eventually terminate as the cumulative production approaches the carrying capacity. The new model provides a more realistic method for forecasting reserves in unconventional formations than the traditional Arps model. The typical problems encountered when using conventional decline curve analysis are not present when using the logistic model. Predictions of the future are always difficult and often subject to factors such as operating conditions, which can never be predicted. The logistic growth model is well established, robust, and flexible. It provides a method to forecast reserves, which has been shown to accurately trend to existing production data and provide a realistic forecast based on known hydrocarbon volumes. / text

Namaqualand is world renowned for its mass displays of annual wildflowers occurring in highly disturbed areas. Leysera gnaphalodes is a short-lived perennial shrub that encroaches into this wildflower display, lessening the aesthetic appeal. For this reason populations of L. gnaphalodes need to be kept as small as possible. This is usually achieved by tilling the area regularly, but a less disruptive method would be preferable. Alternatives to this approach are explored. The effect of many interacting factors needed to be examined over long periods of time so that alternative management strategies could be evaluated. Ecological modelling was used as it is ideally suited to this purpose. A review of modelling and its application in ecology is given, which includes a description of the modelling process and a discussion of different types of models and their applications. It was hypothesised that grazing and low rainfall, in addition to tilling, could control the population size of L. gnaphalodes. Data was used from an eight-year study conducted to determine the effects of tilling, grazing and environmental factors on the seedbank and population size of L. gnaphalodes. A rule-based mechanistic mathematical model based on the logistic growth curve was constructed to describe the population dynamics of this species. The model-fit was evaluated using Pearson’s correlation coefficients and graphs, and it proved to be a good model. Tilling and low rainfall were both found to be effective in reducing populations of L. gnaphalodes but grazing had no reducing effect. Simulations based on the model were run to test three different basic management strategies under stochastic rainfall conditions. The management strategy, which most effectively controlled the population was to till the lands whenever the population of L. gnaphalodes reaches of exceeds a relative frequency of 45%. Multivariate statistical models were constructed to determine the effects of all of these factors on the population of L. gnaphalodes. Tilling was confirmed to be effective in reducing the population, but grazing was found to have no effect. Low rainfall was also effective in controlling the population but has the disadvantages of being out of management control and also affecting the desirable wildflowers. / Dissertation (MSc (Botany))--University of Pretoria, 2005. / Plant Science / unrestricted

Neste trabalho de tese, estudamos o modelo de crescimento logístico de populações biológicas utilizando a abordagem de espaço de estados. Os estados não observados são as biomassas anuais, a equação de observação é linear e a equação de estado é não linear. As distribuições de probabilidade utilizadas para os termos de erro de observação aditivos são: Normal, t-student, Skew-normal e Skew-t. As distribuições Log-normal, Log-t, Log-skew-normal e Log-skew-t são consideradas para os erros de observação multiplicativos. A inferência nos modelos é realizada considerando-se métodos Bayesianos e as distribuições a posterior de interesse são aproximadas utilizando-se algoritmos MCMC e a aproximação de Laplace. Apresentamos duas aplicações, a primeira referente a pesca de camarão marinho na costa do Chile, na qual a variável observável é o rendimento médio anual de pesca (captura por unidade de esforço média). Na segunda é considerada a pesca de lagostim vermelho na costa de Chile, na qual além do rendimento médio anual da pesca, observa-se as estimativas anuais de biomassa vulnerável, obtidas através de estudos de área varrida. Para o primeiro conjunto de dados, os modelos com erros de observação multiplicativos têm melhor performance, particularmente os modelos Log-skew-normal e Log-skew-t. Considerando estes resultados, no segundo caso utilizamos somente erros multiplicativos e a distribuição a posteriori preditiva mostra que cada variável observável parece ter sua própria família de distribuição de probabilidades. Além disso, os resultados também revelam uma crescente complexidade do modelo ao incorporar a classe mais geral de distribuições assimétricas. / We study the logistic population growth model using a state-space approach. The non observable states are the annual biomass of the population with a linear observation equation and a non-linear state equation. The probability distribution used for the additives observation error terms are Normal, Student-t, Skew-normal and Skew-t, and Log-normal, Log-t, Log-skew-normal and Log-skew-t for multiplicative observation errors terms. The inference about the parameters of the models is performed using Bayesian methods, with MCMC algorithms and Laplace approximations. We present two applications to real data sets. The first in marine shrimp population off the coast of Chile, where observable variable is the average annual fishing yield. The second application is for the population of the red squat lobster off Chile, where in addition to the average annual fishing yield, a second observable variable was included. In the first case, the multiplicative observational errors models presented the best results. Particularly the Log-skew-normal and Log-skew-t models has the better performances. Considering these results, in the second application we use only multiplicative observation errors models.

Neste trabalho de tese, estudamos o modelo de crescimento logístico de populações biológicas utilizando a abordagem de espaço de estados. Os estados não observados são as biomassas anuais, a equação de observação é linear e a equação de estado é não linear. As distribuições de probabilidade utilizadas para os termos de erro de observação aditivos são: Normal, t-student, Skew-normal e Skew-t. As distribuições Log-normal, Log-t, Log-skew-normal e Log-skew-t são consideradas para os erros de observação multiplicativos. A inferência nos modelos é realizada considerando-se métodos Bayesianos e as distribuições a posterior de interesse são aproximadas utilizando-se algoritmos MCMC e a aproximação de Laplace. Apresentamos duas aplicações, a primeira referente a pesca de camarão marinho na costa do Chile, na qual a variável observável é o rendimento médio anual de pesca (captura por unidade de esforço média). Na segunda é considerada a pesca de lagostim vermelho na costa de Chile, na qual além do rendimento médio anual da pesca, observa-se as estimativas anuais de biomassa vulnerável, obtidas através de estudos de área varrida. Para o primeiro conjunto de dados, os modelos com erros de observação multiplicativos têm melhor performance, particularmente os modelos Log-skew-normal e Log-skew-t. Considerando estes resultados, no segundo caso utilizamos somente erros multiplicativos e a distribuição a posteriori preditiva mostra que cada variável observável parece ter sua própria família de distribuição de probabilidades. Além disso, os resultados também revelam uma crescente complexidade do modelo ao incorporar a classe mais geral de distribuições assimétricas. / We study the logistic population growth model using a state-space approach. The non observable states are the annual biomass of the population with a linear observation equation and a non-linear state equation. The probability distribution used for the additives observation error terms are Normal, Student-t, Skew-normal and Skew-t, and Log-normal, Log-t, Log-skew-normal and Log-skew-t for multiplicative observation errors terms. The inference about the parameters of the models is performed using Bayesian methods, with MCMC algorithms and Laplace approximations. We present two applications to real data sets. The first in marine shrimp population off the coast of Chile, where observable variable is the average annual fishing yield. The second application is for the population of the red squat lobster off Chile, where in addition to the average annual fishing yield, a second observable variable was included. In the first case, the multiplicative observational errors models presented the best results. Particularly the Log-skew-normal and Log-skew-t models has the better performances. Considering these results, in the second application we use only multiplicative observation errors models.

Veterinarians often perform controlled experiments in which they inoculate animals with infectious diseases. They then monitor the transmission process in infected animals. The aim of such experiments can be to assess vaccine effects. The fitting of individual-level models (ILMs) to the infectious disease data, typically achieved by means of Markov Chain Monte Carlo (MCMC) methods, can be computationally burdensome. Here, we want to see if a vaccination effect can be identified using simpler regression-type models rather than the complex infectious disease models. We examine the use of various logistic growth curve models, via a series of simulated experiments in which the underlying true model is a mechanistic model of infectious disease spread. We want to investigate whether a vaccination effect can be identified when only partial epidemic curves are observed, and to assess the performance of these models when experiments are run with various sets of observational times.

This study compares four recently developed decline curve methods and the traditional Arps or Fetkovich approach. The four methods which are empirically formulated for shale and tight gas wells are: 1. Power Law Exponential Decline (PLE). 2. Stretched Exponential Decline (SEPD). 3. Duong Method. 4. Logistic Growth Model (LGM). Each method has different tuning parameters and equation forms. The main objective of this work is to determine the best method(s) in terms of Estimated Ultimate Recovery (EUR) accuracy, goodness of fit, and ease of matching. In addition, these methods are compared against each other at different production times in order to understand the effect of production time on forecasts. As a part of validation process, all methods are benchmarked against simulation. This study compares the decline methods to four simulation cases which represent the common shale declines observed in the field. Shale wells, which are completed with horizontal wells and multiple traverse highly-conductive hydraulic fractures, exhibit long transient linear flow. Based on certain models, linear flow is preceded by bilinear flow if natural fractures are present. In addition to this, linear flow is succeeded by Boundary Dominated Flow (BDF) decline when pressure wave reaches boundary. This means four declines are possible, hence four simulation cases are required for comparison. To facilitate automatic data fitting, a non-linear regression program was developed using excel VBA. The program optimizes the Least-Square (LS) objective function to find the best fit. The used optimization algorithm is the Levenberg-Marquardt Algorithm (LMA) and it is used because of its robustness and ease of use. This work shows that all methods forecast different EURs and some fit certain simulation cases better than others. In addition, no method can forecast EUR accurately without reaching BDF. Using this work, engineers can choose the best method to forecast EUR after identifying the simulation case that is most analogous to their field wells. The VBA program and the matching procedure presented here can help engineers automate these methods into their forecasting sheets.

Este trabalho investiga os processos de crescimento e evolução das localizações comerciais no espaço urbano. A formação e o desenvolvimento de múltiplos núcleos comerciais é parte do cenário urbano contemporâneo, criando padrões espaciais e temporais heterogêneos, que desafiam a compreensão de teóricos e planejadores. O estudo desses processos requer abordagens dinâmicas, compatíveis com a escala e a velocidade das mudanças. Nesse contexto, recorta-se como problema de pesquisa a modelagem do crescimento das localizações comerciais em setores urbanos, ao longo do tempo. O trabalho propõe a representação da dinâmica de crescimento quantitativo do comércio no espaço urbano através da distribuição logística, um modelo dinâmico e não-linear, capaz de descrever tipos de crescimento com capacidade limitada. O modelo adotado pressupõe um processo descentralizado de tomada de decisões individuais de localização por parte dos agentes - os lojistas - condicionados pelas decisões dos demais. Tais decisões dependem da interação com um ambiente que está em transformação, portanto as respostas também variam. Nesta concepção, forças de aceleração e desaceleração do crescimento das localizações comerciais, que emanam do processo de estruturação espacial urbana, são filtradas através de um processo de leitura e percepção por parte dos agentes. O modelo proposto é validado em quatro setores na cidade de Porto Alegre: Centro, Azenha, Menino Deus e Iguatemi, considerando dados de número de estabelecimentos varejistas ao longo de uma série temporal de 23 anos, de 1983 a 2006. Nesta pesquisa, o modelo logístico também foi explorado como instrumento de descrição e análise de dois problemas relacionados ao crescimento das localizações comerciais em setores urbanos. O primeiro diz respeito aos fatores envolvidos em tal crescimento. A hipótese adotada é que diferenças no processo de estruturação espacial urbana teriam capacidade de produzir uma especificidade no processo de crescimento do comércio em cada área considerada. Diferentes indicadores da estrutura espacial urbana são relacionados à dinâmica de crescimento em cada área, visando identificar os fatores mais relevantes a atuar nesse processo. O segundo problema envolve a aplicação do modelo logístico para o caso da implantação de um grande equipamento comercial, do tipo shopping center, avaliando como este afeta o crescimento do comércio no seu entorno. A investigação demonstra que o modelo proposto descreve o crescimento das localizações comerciais com alto grau de correlação com os dados empíricos em todas as áreas estudadas. O trabalho evidencia também que o modelo possibilita associar os fatores da estrutura espacial urbana ao crescimento do comércio. O modelo também se mostrou um instrumento válido para a análise do impacto da implantação de grandes equipamentos comerciais sobre o processo de crescimento do comércio no seu entorno. / This thesis investigates growth and evolution in retail location. The presence of multiple retail centers is an essential part of the contemporary urban scene, leading to heterogeneous spatial and temporal patterns, whose comprehension defies scholars and planners. Dynamic approaches are required for studying those processes of urban change, considering the scale and speed of change. In this context, this study focuses on modeling the growth of retail location in urban areas through time. To represent quantitative growth of retail location, the work proposes the use of logistic model, a non-linear model designed to describe a specific capacitated growing dynamics. The model assumes a decentralized process of individual location decisions taken by agents – the retailers – constrained by others decisions. Such decisions interact on a changing environment, thus, the answers also change. In this sense, accelerating and deterring forces for retail location growing, emanating from urban spatial structure, pass through a sort of filtering process: the way agents perceive and interpret the environment. Proposed model is validated in four areas in the city of Porto Alegre, Brazil: Centro, Azenha, Menino Deus and Iguatemi, considering data on number of retail establishment through a temporal data set of 23 years, from 1983 to 2006. In this study, logistic model has also been applied to describe and analyze two problems regarding retail location growth. The first problem refers to the causal factors involved in such growth process. The hypothesis adopted is that differences in spatial structuration process are able to produce a specific pattern of temporal growth. Different urban spatial structure indicators are then related to dynamics of growth in each area, trying to identify the most relevant aspects affecting this process. The second problem involves the use of logistic model referring to the case of large retail formats – such as regional shopping centers - aiming to understand the impact of such planned centers on quantitative retail growth. The investigation demonstrates that proposed model describes the growing of retail location with high levels of correlation to empirical data in all studied areas. It also shows that is possible to relate urban spatial structure factors to retail location growth. The model also performs as a valid instrument of impact analysis of large retail formats on the retail growth process at its neighborhood.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Atualmente observa-se uma expressiva perda de biodiversidade global resultante de atividades antrópicas, sendo a introdução de espécies exóticas uma das mais impactantes. A jaqueira Artocarpus heterophyllus é uma espécie exótica introduzida no Brasil durante o período colonial, sendo considerada invasora em diversas localidades. Na Mata Atlântica invade áreas de mata aberta e de borda, habitualmente associadas a ambientes antrópicos. Na Ilha Grande é encontrada em grande abundância em decorrência do histórico de ocupação humana. Para compreender como a mastofauna responde a presença da jaqueira, o Laboratório de Ecologia de Mamíferos da Universidade do Estado do Rio de Janeiro (UERJ) vem desenvolvendo um estudo ao longo de seis anos nos arredores da Vila Dois Rios, localizada na face oceânica da Ilha Grande. A partir dos resultados prévios iniciou-se uma segunda etapa do estudo no mesmo local que buscou avaliar diferentes métodos de controle das jaqueiras. O presente estudo é uma continuação direta desses dois trabalhos anteriores e teve como objetivo acompanhar as respostas da comunidade de pequenos mamíferos no período imediatamente posterior ao controle. Durante 18 meses foram amostradas bimestralmente 18 grades, 10 aonde foi efetuado o controle das jaqueiras e 8 aonde não foi constatada a presença desta árvore. Em cada grade foram colocadas 11 armadilhas de captura viva sendo banana a isca utilizada. Os mamíferos capturados foram medidos e suas fezes coletadas. A quantidade de jacas em cada área também foi anotada bimensalmente. As fezes foram analisadas em laboratório e as sementes encontradas identificadas. Os resultados obtidos indicam que a influência de A. heterophyllus sobre a estrutura da comunidade de pequenos mamíferos foi menor após o tratamento de controle. A única espécie que parece ainda responder a abundância de jaqueiras é o roedor Trinomys dimidiatus, que apresentou densidades mais elevadas nas áreas em tratamento, porém mais próximas a resultados obtidos para espécies congêneres em áreas pouco antropizadas. Utilizando uma abordagem de redes complexas observamos que, embora T. dimidiatus seja a espécie mais abundante em termos de número de indivíduos, o gambá Didelphis aurita parece ser a espécie de mamífero mais importante para dispersão de sementes nativas, aparecendo como espécie com maior número de conexões com espécies de sementes nas redes contruídas para as áreas sem jaqueiras e com jaqueiras antes e após o tratamento. Finalmente, a partir dos dados obtidos criamos um modelo matemático para a população de T. dimidiatus dos arredores da Vila Dois Rios, baseado em um crescimento logístico. Os resultados do modelo proposto se mostraram correlacionados com os dados de abundância reais, de modo que ele parece ser um simulador adequado da população local. / Currently, the world is experiencing a severe loss of biodiversity as consequence of human activities. Of these, the introduction of exotic species is one of the most harmful. The jackfruit tree, Artocarpus heterophyllus, is considered an exotic species in Brazil, where it was introduced during colonial times. In the Brazilian Atlantic Rainforest, A. heterophyllus colonizes open canopy and edge areas, mostly associated with anthropic environments. In Ilha Grande it can be found in high densities as a result of the historical process of human occupation of the island. To better understand if and how the small mammalian fauna responded to the presence of A. heterophyllus, the Laboratory of Mammal Ecology of Universidade do Estado do Rio de Janeiro (UERJ) has been developing a study in the course of the last six years in the surroundings of Vila Dois Rios, located in the oceanic front of Ilha Grande. Based on previous results, a second phase of the study was implemented in the same local. This second study aimed to evaluate the best control method for the jackfruit trees (Moura 2011). The present study is a direct continuation of both studies, its main objective being to accompany the responses of mammalian community in the period immediately after the treatment of the jackfruit trees. During the course of 18 months 18 grids were sampled in a bimonthly basis, 10 where the jackfruit trees were treated and 8 where jackfruit trees were absent. In each grid 11 live traps were opened, and the bait was banana. The captured mammals were ear-tagged and measured and their feces collected. The number of jackfruits was also counted in each area bimonthly. The feces were analyzed in laboratory and the found seeds identified. Our results indicate that the community structure is being less influenced by A. heterophyllus abundances after the control treatment. The only species that still presented a response to the presence of A. heterophyllus was the spiny rat Trinomys dimidiatus. Even so, although the density of T. dimidiatus was high, it was lower than the density found previously, being more similar to results obtained for congeneric species in less anthropized sites. By using complex network analysis we observed that, although T. dimidiatus is the most abundant species in the study area, the opossum Didelphis aurita seems to be the most important species in terms of seed dispersal. D. aurita was the species with most connections in all built networks for areas without jackfruit trees and with jackfruit trees before and after the treatment. Finally, based on the obtained results we created a mathematical model for T. dimidiatus population of the surroundings of Vila Dois Rios, based on the logistic growth equation. The results of the proposed model were statistically correlated with our actual data, and so may be considered an adequate simulator for this particular population.