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Research Publications (Systems Science)

Permanent URI for this collectionhttp://ir-dev.dut.ac.za/handle/10321/842

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Author: search.filters.author.Duffy, Kevin JanHas files: No

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    Consumption threshold used to investigate stability and ecological dominance in consumer-resource dynamics
    (Elsevier, 2015) Collins, Obiora Cornelius; Duffy, Kevin Jan
    Understanding consumer resource population dynamics can be important to an understanding of the overall ecology of systems. For example, the tree-grass continuum dynamics of savannas, an important ecological biome, is influenced by the population dynamics. Here we investigate herbivory driven popu-lation dynamics of a savanna using a simple model of the interactions of the dominant players, namely: trees, grasses, browsers, grazers and mixed browsers-grazers. We introduce a consumption threshold that summarises some of the parameters and this is used as a guide to understanding the dynamics. This number is used in investigating system stability and sensitivity to parameter fluctuations. It is also used to identify degrees of ecological dominance.
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    Optimal control of maize foliar diseases using the plants population dynamics
    (Taylor and Fancis, 2015-09-28) Collins, Obiora Cornelius; Duffy, Kevin Jan
    Pathogens and insects can have important negative effects on yields of crops cultivated by humans. These effects can be important for the food security or financial well-being of individuals. In particular, maize is a very important staple crop worldwide and is vulnerable to diseases. We formulate here a mathematical model to evaluate the impacts of foliar diseases on the population dynamics of maize plants. Qualitative analyses of the important mathematical features of the model are carried out. We show how this methodology can be extended to reducing the spread of foliar diseases through effective control measures with minimum costs.
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    Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold
    (Elsevier, 2016) Duffy, Kevin Jan; Collins, Obiora Cornelius
    The existence, or not, of cyclic dynamics is one of the pivotal aspects of ecological populations. This work considers a consumer resource model found in ecology that can describe both cyclic and non-cyclic dynamics depending on parameter conditions. A threshold consumption number C0 is introduced, similar to the basic reproduction in epidemiological models. It is shown that consumer survival requires C0 > 1 and that a Hopf bifurcation occurs at , where is defined here and is greater than 1. This result is discussed with an example and extensions to other more complicated models.
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    Model highlights likely long-term influences of mesobrowsers versus those of elephants on woodland dynamics
    (Wiley Online Library, 2014-06) O'Kane, Christopher A. J.; Duffy, Kevin Jan; Page, Bruce R.; Macdonald, David W.
    The potential long-term influences of mesobrowsers versus those of savannah elephants on woodland dynamics have not been explored. This may be a critical omission especially in southern African savannahs, where efforts to preserve existing woodlands are typically directed at elephant man-agement. We describe a simple browse–browser model, parameterized from an extensive review of the literature and our own data, including quantitative assessment of impala impact, from the study site, iMfolozi Park, South Africa. As there is a paucity of species-specific demographic data on savannah woody species, we modelled, in a novel approach, functional groups of plant species typical of Acacia wood-lands. Outputs suggest that over the long term (100 years), low-to-moderate densities of impala will have a similar impact on woodland structure, in terms of density of adult trees, as low-to-moderate densities of elephant. Further, the outputs highlight the apparently strong synergistic effect impala and elephant impacts combined have on woodland dynamics, suggesting that reduction or removal of either impala or elephant will radically reduce long-term destruc-tion of savannah woodlands. Recorded changes in adult tree numbers in iMfolozi broadly supported the model’s outputs.
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    Stable isotope turnover and variability in tail hairs of captive and free-ranging African elephants (Loxodonta africana) reveal dietary niche differences within populations
    (NRC Research Press, 2013) Codron, Jacqueline; Kirkman, Kevin; Duffy, Kevin Jan; Sponheimer, Matt; Lee-Thorp, Julia A.; Ganswindt, Andre; Clauss, Marcus; Codron, Daryl
    Many herbivore species expand their dietary niche breadths by switching from browse-rich diets in dry seasons to grass-rich diets in rainy seasons, in response to phenological changes in plant availability and quality. We analyzed stable isotope series along tail hairs of captive and free-ranging African elephant (Loxodonta africana (Blumenbach, 1797)) to compare patterns of seasonal dietary variability across individuals. Results from elephants translocated from the wild into captivity, where their diets are semicontrolled, revealed tail hair growth rates of 0.34 mm/day, on average, and relatively rapid isotope turnover through the transition from wild into captivity. Sampling hairs at 10 mm increments thus archives dietary chronologies at a resolution suitable for tracking diet switches at seasonal, and even subseasonal, scales. Hairs of free-ranging elephants showed extensive carbon isotopic variability within individuals, consistent with seasonal switches between C3-browsing and C4-grazing. Similarly extensive, but asynchronous, shifts in nitrogen isotope ratios were also observed, suggesting an influence of factors other than seasonality. Across individuals, switching patterns differed across habitats, and across age classes, with older, larger animals including increasing amounts of C3 browse into their diets. These results demonstrate how stable isotope approaches characterize complex patterns of resource use in wildlife populations.