The floodlight problem

Given three angles summing to 2, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specied angles not exceeding can be placed at n xed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2. We give O(n log n) algorithms for both these problems

Testing for Network and Spatial Autocorrelation

Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in continuous variables. In this paper we propose two contributions to the literature on tests for autocorrelation. First, we propose a new test for autocorrelation in categorical variables. While some methods currently exist for assessing spatial autocorrelation in categorical variables, the most popular method is unwieldy, somewhat ad hoc, and fails to provide grounds for a single omnibus test. Second, we discuss the importance of testing for autocorrelation in data sampled from the nodes of a network, motivated by social network applications. We demonstrate that our proposed statistic for categorical variables can both be used in the spatial and network setting

Biophysical suitability, economic pressure and land-cover change: a global probabilistic approach and insights for REDD+

There has been a concerted effort by the international scientific community to understand the multiple causes and patterns of land-cover change to support sustainable land management. Here, we examined biophysical suitability, and a novel integrated index of “Economic Pressure on Land” (EPL) to explain land cover in the year 2000, and estimated the likelihood of future land-cover change through 2050, including protected area effectiveness. Biophysical suitability and EPL explained almost half of the global pattern of land cover (R 2 = 0.45), increasing to almost two-thirds in areas where a long-term equilibrium is likely to have been reached (e.g. R 2 = 0.64 in Europe). We identify a high likelihood of future land-cover change in vast areas with relatively lower current and past deforestation (e.g. the Congo Basin). Further, we simulated emissions arising from a “business as usual” and two reducing emissions from deforestation and forest degradation (REDD) scenarios by incorporating data on biomass carbon. As our model incorporates all biome types, it highlights a crucial aspect of the ongoing REDD + debate: if restricted to forests, “cross-biome leakage” would severely reduce REDD + effectiveness for climate change mitigation. If forests were protected from deforestation yet without measures to tackle the drivers of land-cover change, REDD + would only reduce 30 % of total emissions from land-cover change. Fifty-five percent of emissions reductions from forests would be compensated by increased emissions in other biomes. These results suggest that, although REDD + remains a very promising mitigation tool, implementation of complementary measures to reduce land demand is necessary to prevent this leakage

Exploring subtle land use and land cover changes: a framework for future landscape studies

UMR AMAP, équipe 3International audienceLand cover and land use changes can have a wide variety of ecological effects, including significant impacts on soils and water quality. In rural areas, even subtle changes in farming practices can affect landscape features and functions, and consequently the environment. Fine-scale analyses have to be performed to better understand the land cover change processes. At the same time, models of land cover change have to be developed in order to anticipate where changes are more likely to occur next. Such predictive information is essential to propose and implement sustainable and efficient environmental policies. Future landscape studies can provide a framework to forecast how land use and land cover changes is likely to react differently to subtle changes. This paper proposes a four step framework to forecast landscape futures at fine scales by coupling scenarios and landscape modelling approaches. This methodology has been tested on two contrasting agricultural landscapes located in the United States and France, to identify possible landscape changes based on forecasting and backcasting agriculture intensification scenarios. Both examples demonstrate that relatively subtle land cover and land use changes can have a large impact on future landscapes. Results highlight how such subtle changes have to be considered in term of quantity, location, and frequency of land use and land cover to appropriately assess environmental impacts on water pollution (France) and soil erosion (US). The results highlight opportunities for improvements in landscape modelling

Evaluating the spatial uncertainty of future land abandonment in a mountain valley (Vicdessos, Pyrenees-France) : insights form model parameterization and experiments

International audienceEuropean mountains are particularly sensitive to climatic disruptions and land use changes. The latter leads to high rates of natural reforestation over the last 50 years. Faced with the challenge of predicting possible impacts on ecosystem services, LUCC models offer new opportunities for land managers to adapt or mitigate their strategies. Assessing the spatial uncertainty of future LUCC is crucial for the defintion of sustainable land use strategies. However, the sources of uncertainty may differ, including the input parameters, the model itself, and the wide range of possible futures. The aim of this paper is to propose a method to assess the probability of occurrence of future LUCC that combines the inherent uncertainty of model parameterization and the ensemble uncertainty of the future based scenarios. For this purpose, we used the Land Change Modeler tool to simulate future LUCC on a study site located in the Pyrenees Mountains (France) and 2 scenarios illustratins 2 land use strategies. The model was parameterized with the same driving factors used for its calibration. The defintion of static vs. dynamic and quantitative vs. qualitative (discretized) driving factors, and their combination resulted in 4 parameterizations. The combination of model outcomes produced maps of spatial uncertainty of future LUCC. This work involves literature to future-based LUCC studies. It goes beyond the uncertainty of simulation models by integrating the unceertainty of the future to provide maps to help decision makers and land managers