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Item Indigenous strategies and empirical models for adaptability of the maize-bean intercropping system to climate change(UZ Foundatoin, 2016-12) Mapanda, S.; Chitja, J. M.; Duffy, Kevin JanThis review article discusses on different ways of indigenous strategies and empirical models as an adaptation to climate change by smallholder farmers in Africa. Indigenous adaptation strategies are methods that enable individuals or communities to adjust to the impacts of climate change in local areas. Some of the strategies practiced are: zero tillage, mulching, soil management techniques, organic agriculture and fallow system of cultiva-tion, intercropping with legumes, early planting and use of tolerant varieties to drought, water conservation and crop diversification. Scientists developed many empirical models that are used to project the impact of climate change to agriculture. Some of the empirical models include: CERES-Maize Crop Model, Global Circulation Models (GCM) and histori-cal data records. There is also use of empirical evidence such as indigenous land unit framework, indigenous early warning systems, use of rainmakers, movement of birds, ants and crying of dogs by the indigenous smallholder farmers in Africa. Intercropping system is the best practice used as a strategy to climate change adaptability, and one of the most suitable intercropping systems is that of maize and bean. However, the current research findings revealed that there is a lack of consideration of indigenous knowledge that could enhance livelihoods that depend on natural resources directly affected by climate change.Item Understanding multiple species ecosystem dynamics using a consumer resource model(Wiley, 2016) Collins, Obiora Cornelius; Duffy, Kevin JanMost ecological systems comprise multiple species coex-isting and the dynamics of these multiple species can be important for understanding, management, and conservation. One method to study such ecological system dynamics is the use of heterogeneous models. Here we for-mulate and analyze a multiple species (n patches or groups) consumer re-source model. Initial insights are gained by analyzing the special cases n =1 and n = 2. A threshold consumption number C0 is used to investigate system stability and hence the long-term dynamics of the system. It is shown how this threshold consumption number can measure the effects and extent of multiple species coexistence in the system.Item Consumption threshold used to investigate stability and ecological dominance in consumer-resource dynamics(Elsevier, 2015) Collins, Obiora Cornelius; Duffy, Kevin JanUnderstanding 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.Item Optimal control of maize foliar diseases using the plants population dynamics(Taylor and Fancis, 2015-09-28) Collins, Obiora Cornelius; Duffy, Kevin JanPathogens 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.Item Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold(Elsevier, 2016) Duffy, Kevin Jan; Collins, Obiora CorneliusThe 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.Item 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.Item 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, DarylMany 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.Item Heavy impact on seedlings by the impala suggests a central role in woodland dynamics(Cambridge University Press, 2012-04-12) O'Kane, Christopher A. J.; Duffy, Kevin Jan; Page, Bruce R.; Macdonald, David W.Research has increasingly established that mesoherbivores influence the regeneration of woody plants. However the relationship between mesoherbivore density and degree of impact, and the spatial component of this impact, has not been well established. Using a novel sampling design, we assessed in iMfolozi Park, South Africa, the impact of impala (Aepyceros melampus) across the full complement of woody species within the home range, evaluating its spatial component and relationship to impala density. We used four GPS collars, in separate breeding herds, and a GIS to detect zones of different density of impala in the landscape, thus defining a fine-grain browsing gradient. We assessed impact on woody recruits (≤ 0.5 m height) across this gradient by means of 1600 random 1 × 1-m quadrats. Densities of woody seedlings, and mean percentage of remaining canopy, were significantly less in areas of high impala density versus low-density areas. There was a significant correlation between increasing impala density and decreasing density of favoured woody recruits. We propose a hypothesis of impala-induced patch dynamics. It seems likely that the ubiquitous impala may create and sustain a shifting mosaic of patches, and thus function as a key determinant of landscape heterogeneity.Item Using Maximum Entropy modeling to predict the potential distributions of large trees for conservation planning(Ecological Society of America, 2012-06) Smith, Alain; Page, Bruce R.; Duffy, Kevin Jan; Slotow, RobLarge trees, as keystone structures, are functionally important in savanna ecosystems, and low recruitment and slow growth makes their conservation important. Understanding factors influencing their distribution is essential for mitigation of excessive mortality, for example from management fires or large herbivores. We recorded the locations of large trees in Hluhluwe-Imfolozi Park (HiP) using GPS to record trees along 43 km of 10 m-wide transects. Maximum entropy modeling (MaxEnt) uses niche modeling to predict the distribution of a species from the probability of finding it within raster squares, based on environmental variables and recorded locations. MaxEnt is typically applied at a regional spatial scale, and here we assessed its usefulness when predicting the distribution of species at a small (local) scale. HiP has variable topography, heterogeneous soils, and a strong rainfall gradient, resulting in a wide variety of habitat types. We used locations of 179 Acacia nigrescens and 106 Sclerocarya birrea (large trees ≥ 5m), and raster environmental layers for: aspect, elevation, geology, annual rainfall, slope, soil and vegetation. A. nigrescens was largely restricted to the Imfolozi section, while S. birrea had a wider distribution across the reserve. Understanding the interaction of environmental variables dictating tree distribution may facilitate habitat restoration, and will assist planning decisions for persistence of large trees within reserves, including options to reduce fire frequency or herbivore impacts. Though the AUC (Area Under the Curve) values used to test model predictions were high for both species, the ground truthing test data showed that distribution for A. nigrescens was more accurate than that for S. birrea, highlighting the need for independent test data to assess model accuracy. We emphasize that MaxEnt can be used at finer spatial scales than those typically used for species occurrence, but models must be tested using spatially independent test data.