Les travaux portent sur l’estimation de la variance dans le cas d’une non- réponse partielle traitée par une procédure d’imputation. Traiter les valeurs imputées comme si elles avaient été observées peut mener à une sous-estimation substantielle de la variance des estimateurs ponctuels. Les estimateurs de variance usuels reposent sur la disponibilité des probabilités d’inclusion d’ordre deux, qui sont parfois difficiles (voire impossibles) à calculer. Nous proposons d’examiner les propriétés d’estimateurs de variance obtenus au moyen d’approximations des probabilités d’inclusion d’ordre deux. Ces approximations s’expriment comme une fonction des probabilités d’inclusion d’ordre un et sont généralement valides pour des plans à grande entropie. Les résultats d’une étude de simulation, évaluant les propriétés des estimateurs de variance proposés en termes de biais et d’erreur quadratique moyenne, seront présentés. / Variance estimation in the case of item nonresponse treated by imputation is the main topic of this work. Treating the imputed values as if they were observed may lead to substantial under-estimation of the variance of point estimators. Classical variance estimators rely on the availability of the second-order inclusion probabilities, which may be difficult (even impossible) to calculate. We propose to study the properties of variance estimators obtained by approximating the second-order inclusion probabilities. These approximations are expressed in terms of first-order inclusion probabilities and are usually valid for high entropy sampling designs. The results of a simulation study evaluating the properties of the proposed variance estimators in terms of bias and mean squared error will be presented.

Woody invasion into grasslands has been reported world-wide and has affected both the magnitude and spatial heterogeneity of soil carbon (C) and nitrogen (N). Since grasslands cover a large portion of the Earth's land surface, invasion of woody plants could have impacts on regional and global biogeochemistry. To understand large-scale ecological and policy implications of woody invasion, it is critical to understand the spatial pattern and uncertainty of soil C and N and their relationship with vegetation and soil attributes, as well as develop effective approaches to estimate soil C and N over large landscapes and regions. The goal of this study was to improve our understanding of the spatial pattern of soil organic carbon (SOC) and total nitrogen (TN) and their controlling factors in savanna landscapes and develop efficient sampling strategies for evaluating the effects of woody invasion. Specific objectives of this study were to: (1) Quantify the spatial pattern and uncertainty associated with SOC and develop efficient sampling strategies to estimate SOC storage; (2) Assess the influence of soil and vegetation factors on spatial distribution of SOC and TN; and (3) Determine the influence of physical variables related to landscape position and soil on woody vegetation structure. Conditional sequential indicator simulations indicated that woody encroachment into grassland increased both spatial heterogeneity and uncertainty of SOC, which increased errors in estimating SOC storage. Stratified random sampling with higher density in woody patches, plus structured sampling in cluster with strong spatial pattern, substantially increased estimation accuracy. Efficient sampling strategies for estimating SOC storage were developed based on these findings. Direct and spatial correlation and scaling analyses showed that SOC and TN were strongly correlated with litter and root biomass. Invaded woody vegetation has the most impact on spatial distribution of SOC and TN. Canonical correspondence analysis showed that variables related to landscape position were the primary factors determining the spatial distribution of woody species. These new insights will facilitate the estimation of soil C and N pools at landscape and regional scales, and will help evaluate the potential impacts of woody plant encroachment on the biogeochemistry of C and N.

Woody invasion into grasslands has been reported world-wide and has affected both the magnitude and spatial heterogeneity of soil carbon (C) and nitrogen (N). Since grasslands cover a large portion of the Earth's land surface, invasion of woody plants could have impacts on regional and global biogeochemistry. To understand large-scale ecological and policy implications of woody invasion, it is critical to understand the spatial pattern and uncertainty of soil C and N and their relationship with vegetation and soil attributes, as well as develop effective approaches to estimate soil C and N over large landscapes and regions. The goal of this study was to improve our understanding of the spatial pattern of soil organic carbon (SOC) and total nitrogen (TN) and their controlling factors in savanna landscapes and develop efficient sampling strategies for evaluating the effects of woody invasion. Specific objectives of this study were to: (1) Quantify the spatial pattern and uncertainty associated with SOC and develop efficient sampling strategies to estimate SOC storage; (2) Assess the influence of soil and vegetation factors on spatial distribution of SOC and TN; and (3) Determine the influence of physical variables related to landscape position and soil on woody vegetation structure. Conditional sequential indicator simulations indicated that woody encroachment into grassland increased both spatial heterogeneity and uncertainty of SOC, which increased errors in estimating SOC storage. Stratified random sampling with higher density in woody patches, plus structured sampling in cluster with strong spatial pattern, substantially increased estimation accuracy. Efficient sampling strategies for estimating SOC storage were developed based on these findings. Direct and spatial correlation and scaling analyses showed that SOC and TN were strongly correlated with litter and root biomass. Invaded woody vegetation has the most impact on spatial distribution of SOC and TN. Canonical correspondence analysis showed that variables related to landscape position were the primary factors determining the spatial distribution of woody species. These new insights will facilitate the estimation of soil C and N pools at landscape and regional scales, and will help evaluate the potential impacts of woody plant encroachment on the biogeochemistry of C and N.

Šiame magistro diplominiame darbe, naudojant skirtingas atstumo funkcijas ir kalibravimo lygtis, išvedami Horvico ir Tompsono įvertinio dispersijos įvertinių svoriai. Tokiu būdu, sukonstruojami aštuoni nauji Horvico ir Tompsono įvertinio dispersijos įvertiniai. Naudojant Teiloro ištiesinimo metodą pateikiamos sukonstruotų įvertinių apytikslės dispersijos ir pasiūlyti šių dispersijų įvertiniai. Be to, darbe atliekamas matematinis modeliavimas, kurio eksperimentai atlikti naudojant darbo autorės sukurtas MATLAB programas. Matematinio modeliavimo tikslas - naujus įvertinius palyginti tarpusavyje ir su standartiniu įvertiniu. Tiriama, kaip įvertinių tikslumas priklauso nuo pasirinkto imties plano. / In this master's graduation work, the weights of estimators of Horvitz & Thompson estimator of variance are defined by using some different distance function and calibration equations. In such a way, the new eight estimators of Horvitz & Thompson estimator of variance were constructed. Using the Taylor linearization method the approximate variances of the constructed estimators were derived. The estimators of the variances of these estimators are proposed as well. Also we perform here a mathematical modeling using MATLAB program. The aim of this mathematical modeling is to compare the new estimators with each other and with a standard one. We analyze also how the accuracy of estimators depends of selected sampling design.

Yellow perch (Perca flavescens) in Lake Erie support valuable commercial and recreational fisheries critical to the local economy and society. The study of yellow perch's temporal and spatial population dynamics is important for both stock assessment and fisheries management. I explore the spatial and temporal variation of the yellow perch population by analyzing the fishery-independent surveys in Lake Erie. Model-based approaches were developed to estimate the relative abundance index, which reflected the temporal variation of the population. I also used design-based approaches to deal with the situation in which population density varied both spatially and temporally. I first used model-based approaches to explore the spatial and temporal variation of the yellow perch population and to develop the relative abundance index needed. Generalized linear models (GLM), spatial generalized linear models (s-GLM), and generalized additive models (GAM) were compared by examining the goodness-of-fit, reduction of spatial autocorrelation, and prediction errors from cross-validation. The relationship between yellow perch density distribution and spatial and environmental factors was also studied. I found that GAM showed the best goodness-of-fit shown as AIC and lowest prediction errors but s-GLM resulted in the best reduction of spatial autocorrelation. Both performed better than GLM for yellow perch relative abundance index estimation. I then applied design-based approaches to study the spatial and temporal population dynamics of yellow perch through both practical data analysis and simulation. The currently used approach in Lake Erie is stratified random sampling (StRS). Traditional sampling designs (simple random sampling (SRS) and StRS) and adaptive sampling designs (adaptive two-phase sampling (ATS), adaptive cluster sampling (ACS), and adaptive two-stage sequential sampling (ATSS)) for fishery-independent surveys were compared. From accuracy and precision aspect, ATS performed better than the SRS, StRS, ACS and ATSS for yellow perch fishery-independent survey data in Lake Erie. Model-based approaches were further studied by including geostatistical models. The performance of the GLM and GAM models and geostatistical models (spatial interpolation) were compared when they are used to analyze the temporal and spatial variation of the yellow perch population through a simulation study. This is the first time that these two types of model- based approaches have been compared in fisheries. I found that arithmetic mean (AM) method was only preferred when neither environment factors nor spatial information of sampling locations were available. If the survey can not cover the distribution area of the population due to biased design or lack of sampling locations, GLMs and GAMs are preferable to spatial interpolation (SI). Otherwise, SI is a good alternative model to estimate relative abundance index. SI has rarely been realized in fisheries. Different models may be recommended for different species/fisheries when we estimate their spatial-temporal dynamics, and also the most appropriate survey designs may be different for different species. However, the criteria and approaches for the comparison of both model-based and design-based approaches will be applied for different species or fisheries. / Ph. D.

Depuis de nombreuses années, les évaluations de la faune circulante au sein de l’estuaire de la Gironde s’appuient sur plusieurs dispositifs de suivis ichtyologiques, chroniques de pêches scientifiques et professionnelles. Cependant, ces approches conventionnelles nécessitent souvent un échantillonnage conséquent, restent ponctuelles dans le temps, spatialement limitées et destructrices. Tester la mise en œuvre d’un suivi acoustique prend ainsi toute son sens et son intérêt. Plus largement appliqué en milieux marin et lacustre, cette approche reste encore rarement utilisée en estuaires. En raison de l’extrême variabilité intrinsèque de ce type d’écosystème, la mise en œuvre de cet outil est un réel défi. En s’appuyant sur la connaissance préalablement acquise, une réflexion méthodologique approfondie a été menée pour définir des stratégies d’échantillonnage acoustiques afin d’optimiser la récolte de ce type de données. Plusieurs stratégies acoustiques ont d’abord été testées en tenant compte de la complexité et de la taille importante de l’écosystème étudié. La pertinence de ces données recueillies a ensuite été confrontée aux données des pêches scientifiques. Enfin, l’hydroacoustique a été mis à profit pour répondre à des questions sur la dynamique ichtyologique à des échelles spatiales et temporelles plus fines notamment pour étudier les influences tidales et nycthémérales. Ce travail démontre qu’il est possible de mettre en place un suivi acoustique des peuplements ichtyologiques pour un estuaire comme la Gironde. Comme outil complémentaire aux approches traditionnelles, l’hydroacoustique ouvre un large champ de possibilités pour appréhender la biocénose piscicole pour les milieux estuariens. / For many years, assessments of fish densities within the Gironde estuary have been based on a number of different fish monitoring techniques, as well as professional and scientific surveys. However, these approaches are often destructive. They require substantial sampling, and are limited from the points of view of both time and space. With this in mind, the benefits of non-invasive acoustic monitoring are clear. While such methods are often used in lakes and other marine environments, they have yet to be widely applied to shallow-water areas, in particular estuaries. Applying an acoustic approach to this kind of intrinsically changeable environment represents a real challenge. In this research project, an in-depth methodological study was carried out to determine the optimum way of applying acoustic sampling. Several acoustic monitoring strategies were then tested, keeping in mind the size and complexity of the ecosystem under investigation. The results of these tests were then checked for relevance against data from scientific fisheries. Finally, hydroacoustics was used to examine fish dynamics at finer spatial and temporal scales, notably in the study of diurnal and tidal influences. The results of this study show that it is possible to use acoustic monitoring to complement traditional methods of estimating fish populations in estuarine areas, and that the use of such a combination opens up a broad range of new possibilities.

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Vegetative species diversity is under threat from environmental pressures, particularly climate change. As the impacts of climate change vary from place to place, response of vegetative species diversity to a changing climate also vary depending on geographical location. The response of vegetative species diversity under dry conditions in Zimbabwe is not well known. This study assessed the impact of climate change on vegetative species diversity under semiarid conditions of Masvingo province in Zimbabwe. This was achieved by determining climate change trends over a period of forty years (1974-2014), and examining the relationship between vegetative species diversity and spatially interpolated climate data. The absence of historical diversity data prompted the use of remote sensing to enable the assessment of spatial and temporal changes. Thus, the Normalised difference vegetation index (NDVI) was used to assess vegetative species diversity changes after establishing a positive relationship between species diversity and NDVI. The mixed methods research design was used as the strategy of inquiry. The non-aligned block sampling design was used as the sampling framework from which 198 sampling points were identified. Meteorological data obtained from Zimbabwe Meteorological Services Department (ZMSD) and the National Climate Data Centre (NCDC) were used for climate change analysis. Data collected through image analysis, direct observations, questionnaire surveys and interviews were used to assess the impact of climate change on vegetative species diversity. Results indicate that all temperature and precipitation variables have significant (p<0.05) trends over the period under study. However, the trend for seasonal total precipitation was not significant but declining. The significant trends indicate that climate change occurred over the period under study. 93% of the respondents confirmed having experienced the climate change phenomenon. Results also show a significant relationship between climate elements (precipitation and temperature) and vegetative species diversity represented by Shannon Weaver Index (H). More so, there is a positive relationship between NDVI and H. Vegetative species diversity represented by NDVI decreased over the period under review. The results indicate that climate change has contributed to the decrease of vegetative species diversity in Masvingo province, thus it is a force behind many other factors contributing to biodiversity loss. / College of Agriculture and Environmental Sciences / Ph. D. (Environmental Sciences)

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