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This paper evaluates the future impact of soil degradation on national food security and land occupation in Ethiopia. It applies a spatial optimization model that maximizes national agricultural revenues under alternative scenarios of soil conservation, land accessibility and technology. The constraints in the model determine whether people remain on their original site, migrate within their ethnically defined areas or are allowed a transregional migration. Key to this model is the combination of a water erosion model with a spatial yield function that gives an estimate of the agricultural yield in its geographical dependence of natural resources and population distribution. A comparison of simulated land productivity values with historical patterns shows that results are interpretable and yield more accurate outcomes than postulating straightforward reductions in yield or land area for each geographic entity. The results of the optimization model show that in absence of soil erosion control, the future agricultural production stagnates and results in distressing food shortages, while rural incomes drop dramatically below the poverty line. Soil conservation and migration support a slow growth, but do not suffice to meet the expected food demand. In a transregional migration scenario, the highly degraded areas are exchanged for less affected sites, whereas cultivation on already substantially degraded soils largely continues when resettlement is confined to the original ethnic-administrative entity. A shift to modern technology offers better prospects and moderates the migration, but soil conservation remains indispensable, especially in the long term. Finally, an accelerated growth of non-agricultural sectors further alleviates poverty in the countryside, contributing to higher income levels of the total population and, simultaneously, relieving the pressure on the land through rural-urban migration. Copyright # 2002 John Wiley & Sons, Ltd.key words: soil degradation; soil productivity; water erosion; spatial optimization; Ethiopia; migration; economics; yield function IDENTIFYING PRIORITIES FOR SOIL CONSERVATION IN ETHIOPIAThe natural conditions on the Ethiopian Highlands generally offer a favourable environment for human settlement. The positive factors are mainly attributable to the physiographic abruptness that influences the prevailing winds and results in substantially higher rainfall than in the adjacent arid lowlands in the east, while the moderate temperature prevents the occurrence of tropical diseases that prevail in the low-lying humid pockets in the west. Moreover, the volcanic parent material supplies a rich diversity of nutrients that makes soils more suitable for agriculture than in most other parts of Africa (Voortman et al., 2000). Land under PressureHowever, the blessing gradually turned into a curse as population densities and herd sizes kept on augmenting to become the highest in Africa. At present, the Highlands carry 88 per cent out of a total population of 64 million people and 86 ...

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The paper studies stochastic optimization problems in Reproducing Kernel Hilbert Spaces (RKHS). The objective function of such problems is a mathematical expectation functional depending on decision rules (or strategies), i.e. on functions of observed random parameters. Feasible rules are restricted to belong to a RKHS. This kind of problems arises in on-line decision making and in statistical learning theory. We solve the problem by sample average approximation combined with Tihonov's regularization and establish sufficient conditions for uniform convergence of approximate solutions with probability one, jointly with a rule for downward adjustment of the regularization factor with increasing sample size.