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In this paper we use a simulation approach to explore the effect of variation in taxon parameters and landscape patterning on relevant source area of pollen. We use the Prentice-Sugita model, assume constant atmospheric conditions and basin morphology, and take a reductionist approach to explore the behaviour of pollen dispersal and deposition in a simple landscape scenario. Individual factors within the scenario (pollen fall speed, relative pollen productivity, size of basic unit in the landscape mosaic, patch size, rarity of individual taxa and overall number of taxa present in the landscape) are varied while all other parameters are kept constant. thus pennitting exploration of the role of different components of the system. These simulations suggest that, for basins of given size under fixed atmospheric conditions, the relevant source area of pollen is primarily an expression of the patterning of the different vegetation elements within the landscape. This has important implications for the interpretation of palaeoecological records and reconstruction of past environments. Reconstruction, especially quantitative reconstruction, requires some estimate of past relevant source area of pollen. If, as our results suggest, vegetation patterning is an important determinant of this, then it must also be taken into account when attempting to reconstruct past vegetation communities.

Facilities and their services can be lost due to natural disasters as well as to intentional strikes, either by terrorism or an army. An intentional strike against a system is called interdiction. The geographical distribution of facilities in a supply or service system may be particularly vulnerable to interdiction, and the resulting impacts of the loss of one or more facilities may be substantial. Critical infrastructure can be defined as those elements of infrastructure that, if lost, could pose a significant threat to needed supplies (e.g., food, energy, medicines), services (e.g., police, fire, and EMS), and communication or a significant loss of service coverage or efficiency. In this article we introduce two new spatial optimization models called the r‐interdiction median problem and the r‐interdiction covering problem. Both models identify for a given service/supply system, that set of facilities that, if lost, would affect service delivery the most, depending upon the type of service protocol. These models can then be used to identify the most critical facility assets in a service/supply system. Results of both models applied to spatial data are also presented. Several solutions derived from these two interdiction models are presented in greater detail and demonstrate the degree to which the loss of one or more facilities disrupts system efficiencies or coverage. Recommendations for further research are also made.

Terrestrial gross primary production (GPP) is the basis of food production and 24 vegetation growth globally 1 , and plays a critical role in regulating atmospheric CO2 through its 25 impact on ecosystem carbon balance. Even though higher CO2 concentrations in future decades 26 can increase GPP 2 , low soil water availability, heat stress, and disturbances associated with 27 droughts could reduce the benefits of such CO2 fertilization. Here we analyzed outputs of 13 28 Earth System Models (ESMs) to show an increasingly stronger impact on GPP by extreme 29 droughts than mild and moderate droughts over the 21 st century. Due to a dramatic increase in 30 the frequency of extreme droughts, the magnitude of globally-averaged reductions in GPP 31 associated with extreme droughts was projected to be nearly tripled by the last quarter of this 32 century (2075-2099) relative to that of the historical period (1850-1999) under both high and 33 intermediate greenhouse gas emission scenarios. In contrast, the magnitude of GPP reduction 34 associated with mild and moderate droughts was not projected to increase substantially. Our 35 analysis indicates a high risk of extreme droughts to the global carbon cycle with atmospheric 36 warming; however, this risk can be potentially mitigated by positive anomalies of GPP 37 associated with favorable environmental conditions. 38 39 3 The terrestrial biosphere absorbed ~30% of anthropogenic carbon emissions from fossil 40 fuels during 1990-2007 3 , making it a critical component of the global carbon sink that mitigates 41 fossil fuel CO2 emissions and associated climate warming. GPP is a measure of fixation of CO2 42 into an ecosystem through photosynthesis and plays a key role in the net carbon balance of the 43 terrestrial biosphere and the terrestrial CO2 absorption. However, despite our knowledge of CO2 44 fertilization effects on plant productivity 2 , the future trend of GPP under elevated CO2 levels 45 remains highly uncertain due to the impact of many factors such as nutrient limitation 4 and 46 increasing frequency and intensity of drought 5 . Drought is already the most widespread factor 47