Compositional diversity of rehabilitated tropical lands supports multiple ecosystem services and buffers uncertainties

High landscape diversity is assumed to increase the number and level of ecosystem services. However, the interactions between ecosystem service provision, disturbance and landscape composition are poorly understood. Here we present a novel approach to include uncertainty in the optimization of land allocation for improving the provision of multiple ecosystem services. We refer to the rehabilitation of abandoned agricultural lands in Ecuador including two types of both afforestation and pasture rehabilitation, together with a succession option. Our results show that high compositional landscape diversity supports multiple ecosystem services (multifunction effect). This implicitly provides a buffer against uncertainty. Our work shows that active integration of uncertainty is only important when optimizing single or highly correlated ecosystem services and that the multifunction effect on landscape diversity is stronger than the uncertainty effect. This is an important insight to support a land-use planning based on ecosystem services.

standard error of the estimate for a land-cover option, l. The maximum distance to the 100% achievement level was minimized for 32 uncertainty scenarios considered at each uncertainty level 0.00 x SEMl, 0.25 x SEMl, …, 2.75 x SEMl, 3.00 x SEMl, with SEMl being the standard error of the estimate for a land-cover option, l. When only one colour appears (A, B), the uncertainty considered was too small to suggest diversification. used for single objective optimization. The maximum distance to the 100% achievement level was minimized for 32 uncertainty scenarios considered at each uncertainty level 0.00 x SEMl, 0.25 x SEMl, …, 2.75 x SEMl, 3.00 x SEMl, with SEMl being the standard error of the estimate for a land-cover option, l. When only one colour appears (A, B), the uncertainty considered was too small to suggest diversification.

Supplementary Methods
Indicators. We adopted the following description from Knoke et al. 1  Because natural forest ecosystems usually show high exchange intensity, we consider a higher exchange intensity to be better than a lower intensity. Hydrological regulation of the various land-cover types are crucial elements in assessing their potential for mitigating adverse effects of water (such as erosion), but also in controlling the quantitative supply of water. To quantify these effects we use the indicators "overland flow" and "area-specific discharge". Soil quality is essential to maintain the long-term productivity, and thus the sustainability, of the provisioning services of our land-cover types. The chosen indicators are "pH value," "soil organic carbon in percent," "base saturation," and "carbon in microbial biomass," "carbon mineralization," "nitrogen mineralization" and "PO4-Phosphor". These indicators vary in response to different land-cover types; they support plant productivity and contribute to soil biodiversity. Economic indicators of the rehabilitation options are imperative for analysing the likelihood that farmers will actually implement them. Thus, we use the simulated market value to quantify benefits from timber or food production. We use the "net present value" (NPV) and the "payback periods," using two levels of discount rates (5%, and 8%) for each to quantify the economic benefits of each rehabilitation option.
NPV is the sum of all appropriately discounted net revenues over a period of 20 years.
Payback periods report the time necessary to recover the initial investment. Social preference serves as an indicator of the cultural benefit, for example the compatibility with traditional livelihoods, as well as their contribution to landscape aesthetics or preserving cultural heritage. Although people often consider both provisioning and regulating functions when expressing their preferences, they also tend to include intangible values of land use, which are largely determined by tradition, experience and personal preference. Because intangible cultural values are impossible to measure in ecological units, we use social acceptance as a meaningful proxy for cultural ecosystem benefits, benefits which existing approaches to assessing ecosystem services often ignore. We use the "preference" of the land-cover types, with and without subsidies, from an evaluation expressed by indigenous Saraguro and Mestizo farmers.

Optimization.
Here we document an alternative approach to multiple objective optimization (Supplementary equation (1)). The alternative formulation minimizes the largest distance between the maximum and the achieved level of ecosystem indicators directly through an appropriate objective function. However, this objective function is not smooth and, thus, we cannot solve it exactly 3 Fig. 17). After preselecting areas <1 ha (which were then allocated to remaining as abandoned land; 11.9% of total area), we further subdivided the remaining areas (>1 ha) into five slope classes (0-12%, 13-25%, 26-40%, 41-70% and >70%) using the ASTER digital elevation model. The prioritization was then refined accounting for the elevation (five equal classes within the complete range; the lower the better), the distance to roads (the smaller the better) and the area size (the larger the better) with descending priority. Subsequently we assigned the land-cover types (starting with the best sites for: intense pasture, low-input pasture, Alnus, Pinus and abandoned) until the allocated area proportions have been completed for each option. To make the implementation of the plan more feasible we revised the size of each resulting sub-polygon and allocated the areas < 1ha to a neighbouring rehabilitation option (same order as indicated above) within the same abandoned area, until a minimum size of 1 ha was achieved.   Table 3) is around one third lower than the amount expected from the common deforestation-based land use. However, with intense pasture being an important component of rehabilitation of abandoned lands, the food production in the restored landscapes is still quite high. The productivity or the landscape portfolios reported in this study can thus be achieved with agricultural shares of only 19 to 32% of the total rehabilitated land. However, it must be kept in mind that about 1.33 hectares of rehabilitated land would be needed to replace 1 hectare of deforestation based pastures to achieve the same level of food production.
If rehabilitation is to mitigate the pressure on the existing natural forests, the financial perspective of the farmers must also be considered. This requires calculating the opportunity costs of farmers who restore their abandoned lands instead of clearing natural forest for new pastures. Opportunity costs can be obtained by computing the annualized net present value of all future net revenues (annual return) for the various rehabilitation scenarios and by comparing this indicator with that of deforestation based land use (Supplementary Table 4).
The mean differences in annual return between the BAU land use and the single rehabilitation options ranges from US$ 25 to 168 ha -1 yr -1 . For a landscape portfolio to be rehabilitated according to the multiple-objective approach, average opportunity costs between ~US$ 70 and ~110 ha -1 yr -1 can be expected. The upper limits are two times the SEM of the differences. However, on a landscape level the diversified rehabilitation shows a much lower SEM compared with the BAU scenario, which should be considered as an advantage by risk-averse farmers. Considering the average opportunity costs instead of the upper possible limits therefore appears to be appropriate.