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In this thesis we study the matter of hypersensitivity to model structure in the Rosenzweig- MacArthur predator-prey model, and in particular whether the introduction of stochasticity reduces the sensitivity of the !-limit sets to small changes in the underlying vector field. To do this, we study the steady-state probability distributions of stochastic differential equations driven by a compound Poisson process on a bounded subset of Rn, as steady-state distributions are analogous to !-limit sets for stochastic differential equations. We take a primarily analytic approach, showing that the steady-state distributions are equivalent to weak measure-valued solutions to a certain partial differential equation. We then analyze perturbations of the underlying vector field using tools from the theory of compact operators. Finally, we numerically simulate and compare solutions to both the deterministic and stochastic versions of the Rosenzweig-MacArthur model. / Thesis / Master of Science (MSc)

Defining how closely related a pair or a group of organisms are, is necessary both for the construction of phylogenetic trees, which constitutes the academic science of systematics, and for making practical conservation management decisions, as for example, whether it would result in deleterous genetic consequences (decreased fitness on reproductive capability) if two closely related animals e.g. blesbok, Damaliscus dorcas phillipsi, and bontebok, Damaliscus dorcas dorcas, were allowed to interbreed, in which case active steps would be required to manage the animals in an appropriate way. Reliance on traditional morphological characters to answer such questions are difficult because morphological characters change at a rate which is very poorly correlated with time, whereas the genetic differences which affect management decisions change at a progressive and generally linear rate with time (Wilson et al., 1977). In order, therefore, to try and measure such genetic differences in a more quantitative way, biologists turned to biochemical methods (two to three decades ago) and initially studied differences in protein allozymes, with considerable success (reviewed in Chapter 1). Over the last few years attention has switched to use of differences at the level of DNA, since this is the most direct biochemical measure of genetic variation, being the material of which genes are made (Wilson et al., 1977). Organelle DNA from mitochondria in animals has been widely used since it has a number of advantages compared to nuclear DNA, and is the DNA used in the studies reported here. Mitochondrial DNA accumulates single base point mutations with time, at a rate about 5 to 10 times faster than in nuclear DNA (Brown et al., 1979), which renders it the DNA of choice for comparisons between sub-species, species or genera. This project set out to establish modern biochemical methods of comparative DNA analysis and to apply these to local animal groups and so obtain objective data of both academic interest and of practical value to nature conservation problems. The major academic results are the construction of a molecular phylogeny for a major proportion of the Southern African Bovidae (Chapter 3). The family Bovidae has been one of the most difficult mammalian families to classify and there is no general agreement concerning its classification (Ansell, 1971b). Mt DNA restriction analyses were performed on 14 Southern African bovids and restriction maps constructed independently for all 14 species. Phylogenetic trees were constructed by using both distance and cladistic methods. Cladograms supported a sister status of the impala relative to the Alcelaphini and Connochaetini. Four members of the Tragelaphini remained an unresolved quadrichotomy and this would be consistent with inclusion of the eland within Tragelaphus. Distance dendograms would be consistent with a major radiation at the tribal level at the end of the Miocene. Answers to questions of specific conservation interest have been obtained with respect to several animals where conservation management requires knowledge as to how closely related certain pairs or groups of animals are. The answers relate to: ( 1) bontebok, Damaliscus dorcas dorcas vs blesbok, Damaliscus dorcas phillipsi ( Chapter 4); ( 2) African wild cat, Felis lybica vs domestic cat, Felis catus (Chapter 5) and (3) Kruger vs Addo elephant (Chapter 6). A specific request of Nature conservation authorities was to define the genetic relationship between the bontebok and the blesbok, which has conservation management relevance. The sequence divergence between the blesbok and bontebok confirmed that there is no justification in terms of genetic distance alone for applying separate specific status to the bontebok and the blesbok, but would be an appropriate value consistent with maintaining their present subspecific designation. Another request of Nature conservation authorities was to define the genetic relationship between the African wild cat and the domestic cat, since interbreeding between the two takes place where the range of the African wild cat border on those areas inhabited by man, which might effectively cause the disappearance of F.lybica (Smithers, 1983). Mt DNA restriction maps were constructed for the domestic cat, African wild cat and the European wild cat, Felis sylvestris, which was also included in our analysis. The domestic cat and African wild cat were found to have identical restriction maps emphasizing their close relationship. The domestic cat and African wild cat are therefore likely to have no preferences against inbreeding and the chances of the wild cat phenotype therefore being lost by dilution into the domestic cat is high. The sequence divergence between the African wild cat and European wild cat on the other hand, suggests that the common ancestral mt DNA of these cats existed about 650 000 years ago, indicating a more recent descent than was previously thought. A further request from conservation managers was to show the genetic difference, if any, between the Knysna and Kruger elephant herds. Mt DNA fragment size comparisons were performed on 9 elephants from the Kruger National Park and 5 elephants from the Addo Elephant National Park. All the restriction patterns found in the Addo population could be found in the Kruger population. The Addo population's results was extrapolated to the Knysna population. Therefore, genetically the Knysna population would represent a subset of the larger Kruger population. There is therefore no support from the mitochondrial studies for the Knysna and the Kruger elephant populations to be considered as different subspecies.

New cyclic 1,3-diazaphospholidine-2,4,5-triones were synthesised and their solvolytic behaviour was studied. Methanolysis of 2-methylamino (24) and 2-dimethylamino (25) derivatives showed evidence of cleavage of both imide P-N bonds. This indicates that the ring opening in these derivatives is much slower than the second P-N cleavage in the ring-opened intermediate (30, scheme 11). On the other hand, methanolysis of 1,3-dimethyl-2-phenoxy-1,3,2-diazaphospholidine-2,4,5-trione (22) yielded the product of the cleavage of only one P-N bond. This product (26, scheme 9) was relatively stable towards further solvolysis. This was taken by Mulliez8 as evidence for the addition-elimination mechanism of solvolysis, since in such a case 22 would experience the usual rate accelerating effect upon the formation of the pv intermediate with trigonal bipyramidal structure. The crystal structures of 24 and 25 were determined in order to investigate the low reactivity of 24 and 25 to solvolysis. This low reactivity correlates with the small size (92.3 and 91.9° respectively) of their endocyclic N-P-N angle. In the case of these two compounds, this suggests that the driving force towards the formation of the pv trigonal bipyramidal intermediate is reduced. Aminolysis of 22 with ammonia and p-anisidine resulted in products which indicate that nucleophilic attack takes place exclusively at the phosphorus atom. In the aminolysis with p-anisidine, both P-0 bond cleavage (displacement of phenol, 43) and ring P-N bond cleavage (44) products were obtained. This can be explained in terms of pseudorotation of the initially formed pv intermediate (22A, scheme 23). The aminolysis of 22 with ammonia yielded exclusively the ring-retained P-OPh bond cleavage product (23). This indicates that pseudorotation of the initially formed pv intermediate (22A, scheme 20) is much faster than endocyclic P-N bond cleavage. Finally,amminolysis of 22 with benzylamine was performed.As reported by Mulliez8, this reaction yielded the product (45) of the initial C-N cleavage, followed by ring closure Acidolysis studies were carried out in anhydrous TFA. These studies indicated that the low reactivity towards nucleophilic attack of 2-amino (23), 2-methylamino (24),2-dimethylamino (25) and 2- p-anisidino (43) derivatives may also be accounted for by the lowered electrophilicity of their phosphorus atom. Finally, within the cyclic 1,3-diazaphospholidine-2,4,5-trione series the reactivity of the various compounds was found to be vastly different, depending on which substituents were present on the exocyclic N atom. Part of the work reported in this thesis has been published; viz.; Phosphoric Carboxylic lmides. Part 6. Structure and Reactivity of 1 ,3,2-diazaphospholidine4,5-diones; Crystal Structure of 1,3-Dimethyl-2-methylamino-1,3,2-diazaphospholidine-2,4,5- trione,Alan T. Hutton, Tomasz A. Modro, Margaret L. Niven, and Sonia Scaillet, J. Chem. Soc. Perkin Trans. II, 17 (1986).

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Sequence Analysis Tool (SAT) is an X-window (OPEN LOOK version) based interactive system developed for sequence analysis. In this first version, it provides a friendly graphical user interface and convenient functions for performing various tasks required in sequence alignment. In particular, space-efficient algorithms for pairwise alignment and 3-star alignment are implemented as functionalities, which can be used to serve most sequence alignment tasks and therefore provide a basis for further improvement of this tool. SAT is also targeted at providing a testing platform for performance analysis of various alignment-related algorithms. A set of procedures is developed to provide an application programming interface with which other related programs can be easily connected to SAT. SAT is programmed in C/Xlib/OLIT. The object-oriented style makes further maintenance and improvement easy. / Thesis / Master of Science (MSc)