Through the application of downhole logging techniques an innovative assessment of density dependent groundwater flow has been undertaken that highlights the limitations of water level measurements for assessing groundwater flow in coastal environments. The method utilises an EM39 bulk conductivity log to calculate fluid conductivity/fluid density that was then used to convert measured point water head to freshwater head/environmental head to improve the understanding of groundwater flow at the creek. This method of assessing density dependent flow is unique and has not previously been demonstrated. The converted water levels showed that interpretation of groundwater flow is critically dependent on a detailed knowledge of both head and density. An assessment of the potential error in the conversion process indicated that, for the low gradients at the study site, misinterpretation of flow could occur due to errors inherent in the process. As a result, it is recommended that pressure transducers and loggers be used to monitor pressure in variable density systems so that Darcy???s equation can be used directly to calculate groundwater flow and direction. The thesis also presents the results of high-resolution geophysical mapping of the distribution of saline groundwater beneath a tidal creek. The mapping was used to develop a detailed conceptual model of the salinity distribution at a tidal creek that included: the presence of saline intrusion beneath the creek; saline groundwater overlying fresh groundwater due to surface flooding in extreme tide events; concentrated discharge of groundwater (comprised of brackish water due to mixing in the aquifer) at the creek banks; and, significant changes in the distribution of saline groundwater according to rainfall events and only minor changes over a tidal cycle. The conceptual model, geophysical site assessment, water level analysis and numerical modelling represents a multi-disciplinary approach to the assessment of the interaction of saline and fresh groundwater that has not previously been undertaken. Significant anisotropy was inferred from geophysical observations that indicated vertical flow in the borehole annulus. This observation is particularly significant and implies that even relatively short (1.0 to 2.0 m) screened wells may not yield accurate fluid conductivity and head values in variable density systems.

No description available.

A population density, $u_{n}(x)$, is recursively defined by the formula egin{equation*} u_{n+1}(x)=int K(x-y)Big(1-ig(u_{n}(yig)Big)ig(u_{n} (yig)dy + ig(u_{n}(xig)ig(u_{n}(xig). end{equation*} Here, $K$ is a probability density function, $g(u)$ represents the fraction of the population that does not migrate, and $f$ is a monotonically decreasing function that behaves like the Beverton-Holt function. In this paper, I examine and modify the population genetics model found in cite{LV06} to include the case where a density-dependent fraction of the population does not migrate after the selection process.Using the expanded model, I developed a numerical application to simulate the spreading of a species and estimate the spreading speed of the population. The application is tested under various model conditions which include both density-dependent and density- independent dispersal rates. For the density-dependent case, I analyzed the fixed points of the model and their relationship to whether a given species will spread.

Spatial segregation among life cycle stages has been observed in many stage-structured species, including species of the flour beetle Tribolium. Patterns have been observed both in homogeneous and heterogeneous environments. We investigate density dependent dispersal of life cycle stages as a mechanism responsible for this separation. By means of mathematical analysis and numerical simulations, we explore this hypothesis using stage-structured, integrodifference equation (IDE) models that incorporate density dependent dispersal kernels.In Chapter 2 we develop a bifurcation theory approach to the existence and stability of (non-extinction) equilibria for a general class of structured integrodifference equation models on finite spatial domains with density dependent kernels. We show that a continuum of such equilibria bifurcates from the extinction equilibrium when it loses stability as the net reproductive number n increases through 1. We give several examples to illustrate the theory.In Chapter 3 we investigate mechanisms that can lead to spatial patterns in two dimensional Juvenile-Adult IDE models. The bifurcation theory shows that such patterns do not arise for n near 1. For larger values of n we show, via numerical simulation, that density dependent dispersal can lead to the segregation of life cycle stages in the sense that each stage peaks in a different spatial location.Finally, in Chapter 4, we construct spatial models to describe the population dynamics of T. castaneum, T. confusum and T. brevicornis and use them to assess density dependent dispersal mechanisms that are able to explain spatial patterns that have been observed in these species.

Small back-barrier sand islands are poorly known in terms of hydrogeology and have been overlooked in more extensive studies of coastal groundwater systems that include larger barrier island complexes. This study employs a three-fold sequential approach to aquifer characterisation in a back-barrier sand island. A three-dimensional stratigraphic model forms the foundation framework, being derived from a multidisciplinary approach to sedimentary analysis and the construction of a depositional chronology. A conceptual hydrostratigraphic model is formulated based on the translation of sedimentary facies to hydrofacies, combined with density dependent flow calculations and tidal oscillation measurements. Groundwater hydrochemical data and mineral geochemistry are integrated with the resulting hydrogeological model to examine water-rock interaction and solute transport mechanisms. The study area is Toorbul Island, a small back-barrier sand mass of ~5 km2 with a maximum surface elevation of ~3.5 m AHD, located in the Pumicestone Passage of Southeast Queensland. The island hosts a dual aquifer system consisting of an unconfined island freshwater lens, underlain by a semi-confined palaeovalley-fill aquifer. Groundwater in the semi-confined aquifer is hyper-saline, carrying high concentrations of dissolved metals, with iron, in particular, ranging from 40 to < 200 mg l-1. This is of significant interest for both human health and environmental management, because iron is an important nutrient source for toxic algal bacteria such as Lyngbya majuscula. Conceptual modelling demonstrates that iron oxides and hydroxides are the main source of iron in the semi-confined aquifer, with a contribution from ferruginous chlorite dissolution. Aqueous manganese and a proportion of the aqueous iron are derived from the dissolution of manganoan ilmenite. Ferric iron minerals also contribute a significant proportion of dissolved iron in the deeper regions of the unconfined aquifer. Aqueous iron in the shallow unconfined groundwater is limited by iron sulphides, which also regulate acidity and indirectly limit dissolved aluminium concentrations. Groundwater redox state governed by seasonal climatic fluxes is the most significant control on iron-bearing mineral phase stability. Transport of dissolved metals to the surrounding estuary and the adjacent barrier island groundwater system is limited by the rate of ion diffusion across transition zone boundaries. The overall conclusions derived from this research show that back-barrier islands should be evaluated as discrete hydrogeological entities. The stratigraphic complexity that may be apparent within these island landforms should not be underestimated and the model domain should not necessarily be treated as a homogeneous system. This complexity is exemplified by the relationship between the upper and lower aquifers on Toorbul Island and the associated distribution of groundwater compositional heterogeneity. The complex stratigraphy within the sedimentary pile is derived from the presence of a sub-surface palaeovalley and the sedimentary response to changing sea-level over time. Considering the current widespread distribution of estuarine systems, complex hydrogeology as exhibited by Toobul Island, may be common in many small back-barrier island groundwater systems. The aquifer characteristics and their influence on solute transport and delivery can have significant ramifications for the exploitation of the adjacent coastal plain and barrier island aquifers. The potential influence on the latter is of particular concern due to the pressure imposed on potable groundwater supplies by increasing population densities in coastal areas.

Since the first cases of HIV/AIDS disease were recognised in the early 1980s, a large number of mathematical models have been proposed. However, the mobility of people among regions, which has an obvious impact on the spread of the disease, has not been much considered in the modelling studies. One of the main reasons is that the models for the spread of the disease in multiple populations are very complex and, as a consequence, they can easily become intractable. In this thesis we provide various new results pertaining to the spread of the disease in mobile populations, including epidemic intervention in multiple populations. We first develop stochastic models for the spread of the disease in a single heterosexual population, considering both constant and varying population sizes. In particular, we consider a class of continuous-time Markov chains (CTMCs). We establish deterministic and Gaussian diffusion analogues of these stochastic processes by applying the theory of density dependent processes. A range of numerical experiments are provided to show how well the deterministic and Gaussian counterparts approximate the dynamic behaviour of the processes. We derive threshold parameters, known as basic reproduction numbers, for both cases above the threshold which the disease is uniformly persistent and below the threshold which disease-free equilibrium is locally attractive. We find that the threshold conditions for both constant and varying population sizes have the same form. In order to take into account the mobility of people among regions, we extend the stochastic models to multiple populations. Various stochastic models for multiple populations are formulated as CTMCs. The deterministic and Gaussian diffusion counterparts of the corresponding stochastic processes for the multiple populations are also established. Threshold parameters for the persistence of the disease in the multiple population models are derived by applying the concept of next generation matrices. The results of this study can serve as a basic framework how to formulate and analyse a more realistic stochastic model for the spread of HIV in mobile heterogeneous populations—classifying all individuals by age, risk, and level of infectivities, and at the same time considering different modes of the disease transmission. Assuming an accurate mathematical model for the spread of HIV/AIDS disease, another question that we address in this thesis is how to control the spread of the disease in a mobile population. Most previous studies for the spread of the disease focus on identifying the most significant parameters in a model. In contrast, we study these problems as optimal epidemic intervention problems. The study is mostly motivated by the fact that more and more local governments allocate budgets over a certain period of time to combat the disease in their areas. The question is how to allocate this limited budget to minimise the number of new HIV cases, say on a country level, over a finite time horizon as people move among regions. The mathematical models developed in the first part of this thesis are used as dynamic constraints of the optimal control problems. In this thesis, we also introduce a novel approach to solve quite general optimal control problems using the Cross-Entropy (CE) method. The effectiveness of the CE method is demonstrated through several illustrative examples in optimal control. The main application is the optimal epidemic intervention problems discussed above. These are highly non-linear and multidimensional problems. Many existing numerical techniques for solving such optimal control problems suffer from the curse of dimensionality. However, we find that the CE technique is very efficient in solving such problems. The numerical results of the optimal epidemic strategies obtained via the CE method suggest that the structure of the optimal trajectories are highly synchronised among patches but the trajectories do not depend much on the structure of the models. Instead, the parameters of the models (such as the time horizon, the amount of available budget, infection rates) much affect the form of the solution.

Since the first cases of HIV/AIDS disease were recognised in the early 1980s, a large number of mathematical models have been proposed. However, the mobility of people among regions, which has an obvious impact on the spread of the disease, has not been much considered in the modelling studies. One of the main reasons is that the models for the spread of the disease in multiple populations are very complex and, as a consequence, they can easily become intractable. In this thesis we provide various new results pertaining to the spread of the disease in mobile populations, including epidemic intervention in multiple populations. We first develop stochastic models for the spread of the disease in a single heterosexual population, considering both constant and varying population sizes. In particular, we consider a class of continuous-time Markov chains (CTMCs). We establish deterministic and Gaussian diffusion analogues of these stochastic processes by applying the theory of density dependent processes. A range of numerical experiments are provided to show how well the deterministic and Gaussian counterparts approximate the dynamic behaviour of the processes. We derive threshold parameters, known as basic reproduction numbers, for both cases above the threshold which the disease is uniformly persistent and below the threshold which disease-free equilibrium is locally attractive. We find that the threshold conditions for both constant and varying population sizes have the same form. In order to take into account the mobility of people among regions, we extend the stochastic models to multiple populations. Various stochastic models for multiple populations are formulated as CTMCs. The deterministic and Gaussian diffusion counterparts of the corresponding stochastic processes for the multiple populations are also established. Threshold parameters for the persistence of the disease in the multiple population models are derived by applying the concept of next generation matrices. The results of this study can serve as a basic framework how to formulate and analyse a more realistic stochastic model for the spread of HIV in mobile heterogeneous populations—classifying all individuals by age, risk, and level of infectivities, and at the same time considering different modes of the disease transmission. Assuming an accurate mathematical model for the spread of HIV/AIDS disease, another question that we address in this thesis is how to control the spread of the disease in a mobile population. Most previous studies for the spread of the disease focus on identifying the most significant parameters in a model. In contrast, we study these problems as optimal epidemic intervention problems. The study is mostly motivated by the fact that more and more local governments allocate budgets over a certain period of time to combat the disease in their areas. The question is how to allocate this limited budget to minimise the number of new HIV cases, say on a country level, over a finite time horizon as people move among regions. The mathematical models developed in the first part of this thesis are used as dynamic constraints of the optimal control problems. In this thesis, we also introduce a novel approach to solve quite general optimal control problems using the Cross-Entropy (CE) method. The effectiveness of the CE method is demonstrated through several illustrative examples in optimal control. The main application is the optimal epidemic intervention problems discussed above. These are highly non-linear and multidimensional problems. Many existing numerical techniques for solving such optimal control problems suffer from the curse of dimensionality. However, we find that the CE technique is very efficient in solving such problems. The numerical results of the optimal epidemic strategies obtained via the CE method suggest that the structure of the optimal trajectories are highly synchronised among patches but the trajectories do not depend much on the structure of the models. Instead, the parameters of the models (such as the time horizon, the amount of available budget, infection rates) much affect the form of the solution.

Dissertação(mestrado) - Universidade Federal do Rio Grande, Programa de Pós-Graduação em Oceanografia Biológica, Instituto de Oceanografia, 2011. / Submitted by Cristiane Gomides (cristiane_gomides@hotmail.com) on 2013-10-14T11:15:53Z No. of bitstreams: 1 Luis.pdf: 935570 bytes, checksum: 7d5daa83c8296317d26a8027f9980e53 (MD5) / Approved for entry into archive by Sabrina Andrade (sabrinabeatriz@ibest.com.br) on 2013-10-17T02:53:42Z (GMT) No. of bitstreams: 1 Luis.pdf: 935570 bytes, checksum: 7d5daa83c8296317d26a8027f9980e53 (MD5) / Made available in DSpace on 2013-10-17T02:53:42Z (GMT). No. of bitstreams: 1 Luis.pdf: 935570 bytes, checksum: 7d5daa83c8296317d26a8027f9980e53 (MD5) Previous issue date: 2011 / O cienídeo demersal costeiro Macrodon atricauda (Günther, 1880), anteriormente M. ancylodon (Bloch & Schneider, 1801) foi amostrado para determinação de idades em quatro períodos (1976-79, 1884-86, 1995-97 e 2006-09) a partir da pesca comercial e de cruzeiros científicos ao longo do Sul do Brazil (Lat. 30°S e 34°40’S). A análise de incrementos marginais em seções finas de otólitos validou a determinação de idades e mostrou que bandas opacas e translúcidas são depositadas em todas as idades a cada primavera-verão e outono-inverno, respectivamente. A determinação de idades em M. atricauda em seções de otólitos é altamente recomendável, pois comparações com leituras feitas em otólitos inteiros mostraram que as últimas superestimaram as idades em um ou mais anos em 56,5% dos espécimes que tiveram suas idades determinadas. O crescimento de M. atricauda aumentou nas últimas quatro décadas, mais notavelmente em machos adultos acima de 2 anos e fêmeas adultas acima de 3 anos. Um decréscimo de três vezes na sua densidade e da comunidade de peixes demersais como um todo é a causa mais provável do aumento no crescimento. / The coastal demersal sciaenid Macrodon atricauda (Günther, 1880), formerly M. ancylodon (Bloch and Shneider, 1801) was sampled for ageing in four periods (1976-79, 1984-86, 1995-97 and 2006-09) from commercial fishing and scientific surveys along Southern Brazil (Lat. 30°S to 34°40’S). Maximum observed age was seven but no fish older than five years was sampled in the last period. Marginal increment analysis on thin sections validated ageing and showed that opaque and translucent bands were laid down at all ages in spring-summer and autumn-winter, respectively. Ageing M. atricauda on sectioned otoliths is highly recommended because comparisons with readings on whole otoliths showed that the last overestimated in one or more years in 56.5% of the aged specimens. The growth of M. atricauda increased in the last four decades, most noticeably for adult males over 2 years old and females over 3 years old. A three fold decrease in its density and the demersal fish community as a whole are the likely cause of the growth increase.

Abstract Although the present day management of semi-domesticated reindeer (Rangifer t. tarandus L.) and its operational environment have changed from the past, knowledge of the ecological mechanisms typical of traditional herding is still important. The main objective of this study was to examine factors related to stock productivity and carrying capacity of pastures in the Finnish semi-domesticated reindeer management area during 1960-1990's in order to clarify the basis of the present management strategies in Finland. In the Oraniemi district, before 1987, calf production was more affected by the snow conditions of the previous winter, than the weather conditions of the previous summer. Slaughtering mass of calves was more affected by the weather and precipitation in spring and summer than the snow conditions of the previous winter. Thick snow cover and unfrozen soil in early winter also probably affect the quality of natural winter food of reindeer by favouring the growth of certain micro fungi on pastures. Before the mid-1990's in the northern part of the management area, calf production decreased and its variability increased between the districts when reindeer densities on forest and heath land increased, amount of lichen (Cladonia spp.) pastures per reindeer decreased and condition of these pastures deteriorated. Variability in calf production increased especially when the amount of arboreal lichen (Alectoria, Bryoria spp.) pastures per reindeer decreased. The slaughtering mass of reindeer decreased when reindeer densities on all pastures increased. Intensive calf slaughtering increased reindeer stock productivity although it was density dependent. Because of intensified feeding, reindeer densities on winter pastures did not affect stock productivity in the whole management area between 1993 and 1999. Stock productivity could be increased markedly by feeding. Still, slaughtering mass and meat production per reindeer decreased when reindeer densities on summer pastures increased. In the Finnish grazing system, reindeer densities should have remained well below 10 reindeer/km2 lichen range for maintaining lichen ranges in a good condition. The average lichen biomass of lichen ranges in the management area in the mid-1990's was 13% of the lichen biomass at the maximum production. Lichen ranges should have been ungrazed for an average 18 years to recover to the maximum production. The time needed for the lichen ranges to recover to a good condition, would have been 7 years. This study showed that the amount and condition of pastures had a fundamental part in the productivity of Finnish reindeer stock. Calf slaughtering and feeding were effective ways to increase and stabilize stock productivity in the situation where the economic carrying capacity of winter ranges has obvuously been exceeded due to overgrazing and the effects caused by the other land use. This has made reindeer management more and more dependent on feeding. Improvements of the state and condition of winter ranges would only be possible during a long period by regulating reindeer stock size, developing pasture rotation and protecting reindeer pastures from the other land use.

By investigating the scope of future wind turbine projects in north Swedish coastal regions and Lapland inland, identification of especially sensitive areas and the effect of wind farm location for the white- tailed sea eagles (WSE) Haliaeetus albicilla at these sites were evaluated. Since the 1980s the WSE the population growth has been stable and intensified in the last two decades, the upgoing trend is evident especially at coastal areas of the Bothnian Sea and Lapland inland, these regions are also considered suitable for wind farm projects. The scope of this analysis consists of an investigation of the density-dependent effect and interference regarding WSE population for each concerned wind farm by using an option with 4 MW wind turbines and a 6 MW alternative. The purpose with this comparison was to identify where wind turbines impact is most critical for WSEs and to which extent wind farms affected land area usage as well as the carrying capacity levels.One of the key findings was in Norrbotten where the 6 MW wind turbines reduced land area usage by 37,59%. In Västerbotten the highest concentration of WSEs was found and where the interference was most severe, in one of the wind farms three WSEs were observed inside the WF area which was the highest number noticed for this category in the study.Based on the low occurrence of WSEs and the accessible land area in the north-east part of Sweden (Pajala), it was considered the least critical area in terms of risk mitigation for WSE interference. A similar scenario was noticed in the southern part of Gävleborg, however in this case it was mainly a slowdown of population growth related to issues with habitat preference that enabled further possibilities for wind power investments.