D.Phil. / Despite a sharp decline in the birthrate, recent projections show that the population groups in the RSA are still expected to grow rapidly in the future. Since its inception in 1974, the National Family Planning Programme has been very successful, and by 1980 more than a million women from all population groups were practising contraception. Although the programme planners set as their goal an annual increase in this figure, it was not clear what the effect of a given increase would be on population growth in the RSA. In this study recent population projections for the RSA were used as the point of departure, and it was established what the increased family planning input would have to be if the prospect of reduced population sizes were held out. Furthermore, it was assumed in the models used that changes would take place over a period of time in respect of the average period of use of contraceptives, and that there would be a shift to more effective methods. The TABRAP and PROJTARG models used for these analyses were extremely suitable for experimentation so that an in-depth study of the family planning situation of Asians, Coloureds and Blacks could be made. There are certain shortcomings in these models, however, and a new model incorporating characteristics from both models was developed to conduct projections up to the year 2010.

No description available.

Ever since Maynard-Smith and Price first introduced the concept of an evolutionary stable strategy (ESS) in 1973, there has been a growing amount of work in and around this field. Many new concepts have been introduced, quite often several times over, with different acronyms by different authors. This led to other authors trying to collect and collate the various terms (for example Lessard, 1990 & Eshel, 1996) in order to promote better understanding ofthe topic. It has been noticed that dynamic selection did not always lead to the establishment of an ESS. This led to the development ofthe concept ofa continuously stable strategy (CSS), and the claim that dynamic selection leads to the establishment of an ESSif it is a CSS. It has since been proved that this is not always the case, as a CSS may not be able to displace its near neighbours in pairwise ecological competitions. The concept of a neighbourhood invader strategy (NIS) was introduced, and when used in conjunction with the concept of an ESS, produced the evolutionary stable neighbourhood invader strategy (ESNIS) which is an unbeatable strategy. This work has tried to extend what has already been done in this field by investigating the dynamics of coexisting species, concentrating on systems whose dynamics are governed by Lotka-Volterra competition models. It is proved that an ESNIS coalition is an optimal strategy which will displace any size and composition of incumbent populations, and which will be immune to invasions by any other mutant populations, because the ESNIS coalition, when it exists, is unique. It has also been shown that an ESNIS coalition cannot exist in an ecologically stable state with any finite number of strategies in its neighbourhood. The equilibrium population when the ESNIS coalition is the only population present is globally stable in a n-dimensional system (for finite n), where the ESNIS coalition interacts with n - 2 other strategies in its neighbourhood. The dynamical behaviour of coexisting species was examined when the incumbent species interacted with various invading species. The different behaviour ofthe incumbent population when invaded by a coalition using either an ESNIS or an NIS phenotype underlines the difference in the various strategies. Similar simulations were intended for invaders who were using an ESS phenotype, but unfortunately the ESS coalition could not be found. If the invading coalition use NIS phenotypes then the outcome is not certain. Some, but not all of the incumbents might become extinct, and the degree to which the invaders flourish is very dependent on the nature ofthe incumbents. However, if the invading species form an ESNIS coalition, one is certain of the outcome. The invaders will eliminate the incumbents, and stabilise at their equilibrium populations. This will occur regardless of the composition and number of incumbent species, as the ESNIS coalition forms a globally stable equilibrium point when it is at its equilibrium populations, with no other species present. The only unknown fact about the outcome in this case is the number ofgenerations that will pass before the system reaches the globally stable equilibrium consisting ofjust the ESNIS. For systems whose dynamics are not given by Lotka-Volterra equations, the existence ofa unique, globally stable ESNIS coalition has not been proved. Moreover, simulations of a non Lotka-Volterra system designed to determine the applicability ofthe proof were inconclusive, due to the ESS coalition not having unique population sizes. Whether or not the proof presented in this work can be extended to non Lotka-Volterra systems remains to be determined. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 2000.

No description available.

CAPES / O presente trabalho evidencia alguns aspectos das equações de diferenças lineares com coeficientes constantes, algumas de suas aplicações e algumas formas de resolução das mesmas. As equações de diferenças não lineares foram analisadas de forma qualitativa, ou seja, através de seus pontos de equilíbrio e a análise da estabilidade desses pontos. As equações de diferenças são úteis quando se pretende trabalhar com sistemas dinâmicos discretos, ou seja, em situações onde as grandezas mudam a cada intervalo de tempo. Uma de suas aplicações consiste no estudo de crescimento populacional e aqui, em especial, veremos os modelos desenvolvidos por Malthus (crescimento geométrico) e Verhulst (crescimento logístico). Uma análise comparativa será realizada com o intuito de verificar se o modelo de Verhulst se adequa aos dados oficiais e o quanto ele é capaz de acompanhar as projeções oficiais. / The present work aims to show some aspects of linear differences equations with constant coefficients, some of their applications and some ways of solving them. The nonlinear differences equations were analyzed in a qualitative way, through their equilibrium points and stability analysis of these points. The difference equations are useful when working with discrete dynamic systems, in situations where the quantities change within each time interval. One of its applications is the study of population growth, and here, in particular, we will see the models developed by Malthus (geometric growth) and Verhulst (logistic growth). A comparative analysis will be carried out to verify if the Verhulst model fits the official data and how much it is able to follow the official projections.

Population estimation in inter-censual years has many important applications. In this research, high-resolution pan-sharpened IKONOS image, LiDAR data, and parcel data are used to estimate small-area population in the eastern part of the city of Denton, Texas. Residential buildings are extracted through object-based classification techniques supported by shape indices and spectral signatures. Three population indicators -building count, building volume and building area at block level are derived using spatial joining and zonal statistics in GIS. Linear regression and geographically weighted regression (GWR) models generated using the three variables and the census data are used to estimate population at the census block level. The maximum total estimation accuracy that can be attained by the models is 94.21%. Accuracy assessments suggest that the GWR models outperformed linear regression models due to their better handling of spatial heterogeneity. Models generated from building volume and area gave better results. The models have lower accuracy in both densely populated census blocks and sparsely populated census blocks, which could be partly attributed to the lower accuracy of the LiDAR data used.

The first two official AIDS cases were diagnosed in South Africa in 1982. During the same period of the 1980s, the black/African population was experiencing an accelerated fertility decline, following a period of accelerated mortality decline. Demographers invoked the demographic transition theory to explain the observed mortality and fertility decline. According to the demographic transition theory, mortality and fertility rates would continue declining to low, post transitional levels with increasing modernization. The relatively higher prevalence of HIV/AIDS estimated among black/African South Africans is expected to alter their demographic transition. This research investigated the impact of HIV/AIDS on the demographic transition of black/Africans by 2021.

The first two official AIDS cases were diagnosed in South Africa in 1982. During the same period of the 1980s, the black/African population was experiencing an accelerated fertility decline, following a period of accelerated mortality decline. Demographers invoked the demographic transition theory to explain the observed mortality and fertility decline. According to the demographic transition theory, mortality and fertility rates would continue declining to low, post transitional levels with increasing modernization. The relatively higher prevalence of HIV/AIDS estimated among black/African South Africans is expected to alter their demographic transition. This research investigated the impact of HIV/AIDS on the demographic transition of black/Africans by 2021.