<p> A model of two predators competing for the same prey also involving predation interaction between the two predators is considered. Coexistence in forms of equilibria and periodic orbits is obtained by using bifurcation and dynamical systems theory. Global dynamics is obtained by studying the survival functions and persistence is obtained by using a theorem of Freedman and Waltman. Finally, numerical results for a specific example demonstrate the above. A Hopf bifurcation at the interior equilibrium and its unstable periodic orbit are observed.</p> / Thesis / Master of Science (MSc)

The ecological niche of a population is dynamic and will be affected by changes in the ecosystem and as a population migrates. An ontogenetic niche shift can also occur as organisms grow and can include changes in morphology, habitat, and feeding behaviour. Although they are the two most abundant salmon species, and are further augmented through hatchery stocking, it is unclear the degree to which the niches of juvenile pink salmon (Oncorhynchus gorbuscha) and chum salmon (O. keta) overlap. Furthermore, juvenile pink salmon and chum salmon undergo a period of rapid growth during their first summer at sea and it is unclear how their ecological niche changes with their ontogeny. Understanding the foodweb dynamics of juvenile salmon in the coastal marine environment is important because a large proportion of the overall mortality of salmon is thought to occur during their first summer at sea. The purpose of this study is to determine the degree to which the niches of juvenile pink salmon and chum salmon overlap, how their trophic position and food source changes as they grow into a new ontogenetic niche, and how these processes are affected by ocean conditions. I expected that years of poorer feeding conditions and increased competition would result in reduced trophic position and greater overlap of the niches of juvenile pink salmon and chum salmon. I hypothesized that juvenile salmon would shift their diet to a more offshore-based foodweb as they grew and that their trophic position would increase with size, but that the shift would be stronger when feeding conditions were improved. Statistical analysis showed evidence that the overlap of the niches of pink salmon and chum salmon increased when the abundance of salmon was high. Contrary to expectations, the trophic position of salmon appeared to decrease under favourable conditions. The trophic position of both pink salmon and chum salmon was higher in the southern portion of the study area, and increased when juvenile abundance was high. I suggest that the higher trophic position among juvenile salmon when there is more competition might result from increased reliance on gelatinous zooplankton, which are carnivorous, but a nutritionally poor food choice compared to other common prey items. The ontogenetic shift from summer to fall among juvenile salmon included a shift to a more offshore-based diet and a higher trophic position. In the northern portion of the study area, which was comprised of the southern reaches of the Alaska Coastal Current (ACC), the shift to an offshore-based food source was more pronounced than the trophic shift. In the southern portion of the study area, which included the Transition Domain (TD) between the ACC and the California Current System (CCS), the shift to a higher trophic position was more pronounced than the shift in food source. The results of this study suggest that if climate change leads to poorer feeding conditions, the niches of pink salmon and chum salmon may increasingly overlap when the abundance of these species is high. Hatchery stocking of these species may also contribute to this trend if it leads to a greater abundance of juvenile salmon in the coastal marine environment. There is evidence that the structure of the food web and the nature of the ontogenetic niche shift are very different in the ACC and the TD, and climate change and hatchery stocking will most likely affect these regions differently. / Graduate

<p>This thesis presents models applicable for aquatic ecosystems. Geographical Information Systems (GIS) form an important part of the thesis. The dynamic mass balance models focus on nutrient fluxes, biotic/abiotic interactions and operate on different temporal and spatial scales (site, local, regional and international). The relevance and role of scale in mass balance modelling is a focal point of the thesis.</p><p>A mesocosm experiment was used to construct a model to estimate the nutrient load of phosphorus and nitrogen from net cage fish farming (i.e., the site scale). The model was used to estimate what feeding conditions that are required for a sustainable aquaculture scenario, i.e., a zero nutrient load situation (a linkage between the site scale and the regional scale). </p><p>A dynamic model was constructed for suspended particulate matter (SPM) and sedimentation in coastal areas (i.e., the local scale) with different morphometric characteristics and distances to the Sea. The results demonstrate that the conditions in the Sea (the regional and international scale) are of fundamental importance, also for the most enclosed coastal areas.</p><p>A foodweb model for lakes was transformed and recalibrated for Baltic Sea conditions (i.e., the international scale). The model also includes a mass balance model for phosphorus and accounts for key environmental factors that regulate the presuppositions for production and biomasses of key functional groups of organisms. The potential use of the new model for setting fish quotas of cod was examined.</p><p>For the intermittent (i.e., regional) scale, topographically complex areas can be difficult to define and model. Therefore, an attempt was made to construct a waterscape subbasin identification program (WASUBI). The method was tested for the Finnish Archipelago Sea and the Okavango Delta in Botswana. A comparison to results from a semi-random delineation method showed that more enclosed basins was created with the WASUBI method.</p>

This thesis presents models applicable for aquatic ecosystems. Geographical Information Systems (GIS) form an important part of the thesis. The dynamic mass balance models focus on nutrient fluxes, biotic/abiotic interactions and operate on different temporal and spatial scales (site, local, regional and international). The relevance and role of scale in mass balance modelling is a focal point of the thesis. A mesocosm experiment was used to construct a model to estimate the nutrient load of phosphorus and nitrogen from net cage fish farming (i.e., the site scale). The model was used to estimate what feeding conditions that are required for a sustainable aquaculture scenario, i.e., a zero nutrient load situation (a linkage between the site scale and the regional scale). A dynamic model was constructed for suspended particulate matter (SPM) and sedimentation in coastal areas (i.e., the local scale) with different morphometric characteristics and distances to the Sea. The results demonstrate that the conditions in the Sea (the regional and international scale) are of fundamental importance, also for the most enclosed coastal areas. A foodweb model for lakes was transformed and recalibrated for Baltic Sea conditions (i.e., the international scale). The model also includes a mass balance model for phosphorus and accounts for key environmental factors that regulate the presuppositions for production and biomasses of key functional groups of organisms. The potential use of the new model for setting fish quotas of cod was examined. For the intermittent (i.e., regional) scale, topographically complex areas can be difficult to define and model. Therefore, an attempt was made to construct a waterscape subbasin identification program (WASUBI). The method was tested for the Finnish Archipelago Sea and the Okavango Delta in Botswana. A comparison to results from a semi-random delineation method showed that more enclosed basins was created with the WASUBI method.

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