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>Magister Scientiae - MSc / The sustainable use of natural resources is of utmost importance for every community. In particular, it is important for every given generation to plan in such a way that proper provision is made for future generations. The scientific understanding of resources use and appreciation for its life-supporting capacity is therefore essential. Mathematical modeling has proved useful to inform the planning and management of strategies for sustainable use of natural resources. Some specific topics in resource management has been studied intensively through many decades. In particular, mining, fisheries, forestry and water resources are among these. Instead of presenting a study of the latter topics, this dissertation presents a variety of cases of mathematical modeling in resource management. The aim is to improve the general understanding of the relevant problems. We expand on existing literature, papers of other authors, and add to such studies by focusing on specific items in the work, illuminating it with further explanations and graphs, or by modifying the models through the introduction of stochastic perturbations. In particular this dissertation makes contributions by giving more explanation, on the so-called environmental Fisher information or EFI for brevity (Section 2.4 and Chapter 6), and by introducing stochasticity into a pest control model (Chapter 4) and into a savanna vegetation model (Chapter 5). In Chapter 3 we present a model from the literature pertaining to the problem of shifting cultivation, i.e, the use of forest land when used for subsistence level agricultural purposes, until the land is so degraded that the occupants abandon it and move on to a new stand. The model used to study the shifting period is similar to the forest rotation problem. A model, already in the literature, for biological control of a pest is studied in Chapter 4. Onto the deterministic model we impose a stochastic perturii bation, so that we obtain a stochastic differential equation model. We prove stochastic stability of the disease-free state, when the basic reproduction number of the pest is below unity. We have performed simulations of solutions of the stochastic system. In Chapter 5 we review an existing ordinary differential equation model for the competition between trees and grass in savanna environment. The competition between them is for soil water, fed by annual rainfall. On the other hand, trees and grass are perturbed by fire, and some other environmental forcings such as herbivores. For this ODE model, we introduce stochastic perturbations. The stochastic perturbations are in the form of three mutually independent Brownian motions. Simulations to illustrate the effect of the stochasticity are shown. We present a three-tiered predator-prey model and consider its stability in terms of Fisher information. This appears as Chapter 6. The Fisher information is defined on the basis of the so-called sustainable measures hypotheses. The model is already in the literature and in the dissertation we present several computations to show the influence of carrying capacity of prey and of mortality rate on EFI. Another problem that we consider, in Chapter 7, is that of lake eutrophication caused by excessive phosphorus inflow. The computation illustrates the management of the runoff nutrients into or out of the lake. Necessary and the sufficient conditions for an optimal utility management are obtained using standard optimal control theory. The results of this dissertation demonstrate the modeling techniques in the sustainable use of natural resources. Sustainability is the quest for equal opportunities over all generations. The manner in which this sustainability is quantified in models is being debated and improved all the time. The discourse on sustainability is especially important in view of a growing world population, and with forcings such as climate change. The most important original contribution in this dissertation is the stochastic analysis on the pest control model and the savanna model.

In rural districts of Sub-Saharan Africa, livelihoods typically centre around peasant agriculture and herding. While historically effective, changing resource constraints associated with rapid population growth and resource degradation have put these livelihoods under strain. Dramatic shifts over recent years in agricultural policy and the prices of agricultural inputs and outputs have not helped. Together, such changes arguably amount to a set of destabilising influences and a relative paucity of advantageous opportunities. The question is whether local people successfully adapt their land-use strategies to these changing circumstances. 'Sustainable agriculture' technologies such as agroforestry practices represent an obvious means of adaptation to change in low-potential areas, which largely lack access to purchased agricultural inputs. Yet despite the promise these technologies have shown in farm trials, their adoption by farmers has generally been hesitant and limited. This has been widely interpreted as evidence that these technologies do not respond effectively to the needs of target beneficiaries. Based on a household survey from Shinyanga District, Tanzania, the study revisits the issues of adaptation to changing circumstances and technology adoption. It highlights the possibility that some households adapt to change more effectively than others, with some adopting advantageous available technologies while others do not. Its focus is on the differing knowledge and perceptions informing decisions vis-à-vis tree management, with a view to identifying distinct knowledge types within the wider body of local knowledge. The study posits then tests a theoretical model problematising local knowledge. It finds that integrating local knowledge variables into regressions of tree management practice greatly increases their explanatory power, suggesting that these variables do not simply reflect incentives, as suggested by contemporary theory. The implication is that problematic local knowledge may critically constrain rural livelihoods in areas facing unprecedented challenges and opportunities. Finally, diverse associations with observed knowledge patterns are considered, suggesting promising ways to build on this work.

That countries with high natural resource abundance should experience slower economic growth than those with low resource abundance seems contrary to what would be expected, considering the developmental head-start such resources afford. Yet Sachs and Warner (1997) found that economies with a high share of natural resource exports in national income in 1970 tended to experience slower economic growth in the two decades that followed. This finding, that natural resources are a “curse” rather than a blessing, has become generally accepted. This thesis sought to test whether the conclusion drawn from their data – that higher natural resource abundance leads to slower economic growth – is still correct. It sought to test their findings first by correcting for their use of resource intensity (natural resources share of exports) as a proxy for abundance. Using measures of resource abundance for 1995 as a proxy for abundance in previous decades, it was found that higher resource abundance was not associated with lower economic growth in the 1970s and 1980s. This finding is contrary to that of Sachs and Warner (1997, 2001). Secondly, this thesis tested whether the natural resource curse effect was still present for the period 1995–2010. This was done by observing the effect of both resource abundance and resource intensity on economic growth during 1995–2010. In both cases no resource curse effect was found, for this more recent period. The resource curse had disappeared regardless of whether one uses Sachs and Warner’s (1997, 2001) measure of resource intensity or a measure of resource abundance. Natural resources should therefore no longer be considered a “curse”. In explaining the difference for the impact of resource intensity between the 1970-90 period measured by Sachs and Warner (1997, 2001) and the more recent period 1995-2010 it was found that the Dutch Disease effect has decreased significantly since the 1970s and 1980s. This could partly explain why the resource curse has disappeared when measured in terms of resource intensity. Thus it was concluded that the natural resource curse existed in the period 1970-90 only when measured in terms of resource intensity but not when measured relative to resource abundance. The negative effects of natural resources on economic growth have disappeared in terms of both resource intensity and resource abundance in the more recent time period.

Tree management practices in the tropical dry forest region of Nicaragua were examined to determine opportunities and factors influencing tree-planting initiatives and forest recovery within the agricultural matrix. A 217.11 ha tree inventory and 44 social surveys were conducted in three rural communities. The inventory found 88 species, 66.68% were native, and 70 valued for multiple uses. Farmers’ reasons for maintaining trees varied, emphasizing live fencing, wood, and fruit. The landscape also contains a tree plantation and a riparian forest, and the origins and management of these tree cover components of the landscape are also considered. Tree planting interventions should supplement extant stakeholder motivation with technical training and basic materials only as explicitly requested by participants, rather than imposing costly or inappropriate project preferences. Initiatives should also focus on smallholders and on multi-use native species suggested by stakeholders in order to maximize the economic, social and environmental benefits provided.

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Anthropogenic stressors are increasingly changing conditions in coastal areas and impacting important habitats. But, when multiple stressors act simultaneously, their effects on ecosystems become more difficult to predict. In Chesapeake Bay, USA, predictions suggest that anthropogenic stressors from climate change, such as warming temperatures, may increase the frequency and severity of storm events, leading to increased freshwater, nutrient, and sediment inputs. Coastal development, another source of anthropogenic stressors, continues to increase with growing coastal populations, and may lead to altered sediment characteristics, habitat fragmentation, altered food webs, and loss of vegetated habitats. Community processes may interact with stressors, for example, immigration of propagules between habitat patches may alter diversity, and modify community response to stressors. Changes in biodiversity might alter ecosystem functioning and services, but diverse ecosystems may be more stable especially in the face of multiple stressors. Many habitats are vulnerable to anthropogenic stressors, including seagrass systems, which provide many valuable ecosystem services. Understanding how multiple stressors and community processes interact now is key to maintaining ecosystem services in the future. Using a model seagrass (Zostera marina) system, I tested the effects of multiple stressors and their interactions with crustacean grazer immigration and diversity on ecosystem properties in a series of fully-factorial mesocosm experiments. I found that despite grazer species having varied responses to individual stressors, grazing pressure was largely maintained in spite of multiple stressors. More diverse grazer assemblages generally stabilized epiphytic algal biomass in the face of stressors, thereby increasing the resistance stability of this important component of the fouling community. Immigration of crustacean grazers did not interact significantly with stressors, and had little effect overall except to increase grazer biomass. Stressors generally reduced primary producer biomass, although in some cases they favored epiphytic algae. Generally, I did not find interactions among stressors and grazer immigration or diversity, even though diverse grazer assemblages stabilized epiphytic algal biomass. to assess potential impacts of coastal development, I surveyed twenty seagrass beds in lower Chesapeake Bay, VA and assessed local shoreline development effects on adjacent seagrass beds. I sampled primary producers, consumers, water quality, and sediment characteristics in seagrass beds, and characterized development along the adjacent shoreline. I found that development significantly affected sediment characteristics, while epifaunal and epiphytic algal biomass was significantly higher on the Western versus the Eastern side of the bay. Grazer and predator biomass did not differ with either development or bay region. Thus, in seagrass communities, various factors appear to drive sediment and biological community properties on different spatial scales. This may be an important consideration for management, because efforts that incorporate spatial scales of ecosystem processes will likely have more impact. Overall, these results suggest that stressor impacts in seagrass ecosystems generally do not interact but are sometimes context specific, while grazer diversity may have a limited but potentially important role in buffering certain ecosystem properties again stressors. Different factors appear to influence ecosystem properties at various spatial scales, an important consideration for predicting future impacts of multiple anthropogenic stressors in submerged vegetated systems.

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Seeding deteriorated range lands efficiently and economically has become one of the most promising means of improving the agricultural economy of the western range states. By providing the most rapid means of increasing the quantity and improving the quality of forage for livestock, and aiding in the prevention of soil erosion, artificial seeding contributes directly to the stability of agriculture.

The particular purpose of this study was to determine the effects of large-scale sagebrush reseeding projects on sage grouse populations and whether such effects were partly or entirely beneficial, neutral, or detrimental to the survival of such populations. During two seasons of field work, the studies initiated on a short-time basis had the following specific objectives: To compare the utilization by sage grouse of reseeded and non-reseeded lands for the seasonal activities of mating, nesting, raising a brood, fall coveying, and wintering. To compare the utilization by sage grouse of reseeded and non-reseeded lands for daily activities of feeding, watering, resting, hiding, and roosting. To determine fall and winter movements of the grouse in relation to reseeded lands. To determine the food and cover available to grouse on randomly selected sample plots To arrive at an index to food preferences through comparison of stomach analysis and food availability studies. To determine the effect of livestock grazing of reseeded lands on sage grouse. To determine the effect of plant succession on availability of food and cover within reseeded lands.