Crop growth,soil water and nitrogen balance simulation on three experimental field plots using the Opus model—A case study

Over a period of 5 years, the agro-ecosystem model Opus was used to simulate soil water and nitrogen balance as well as crop growth for three experimental field plots. At these plots, different agricultural management practices were applied. The data set obtained from these plots consists of automatically recorded time series of daily volumetric soil water contents measured by TRIME-probes as well as daily pressure heads measured by tensiometer. Aboveground total biomass, yield, nitrogen-uptake by crops as well as nitrate contents in the soil were measured at 6–10 sample times per year. The objective of this study was an evaluation of the accuracy of Opus regarding the simulation of crop growth, soil water and nitrogen balance. The simulations of soil water contents and pressure heads correspond with the commonly measured trends in soil depths shallower than 60 cm. In depths deeper than 60 cm, some differences between measured and simulated soil water contents as well as pressure heads could be observed. Nitrate contents in the root zone and the aboveground total biomass were simulated satisfactorily. In contrast to that, simulated and observed yields show greater discrepancies. This indicates the need of a site specific calibration of crop growth parameters within the Opus model.     

Soil drying in a tropical forest: Three distinct environments controlled by gap size

Soil water and temperature regimes in the tropical moist forest on Barro Colorado Island, Panama, were simulated directly from meteorological data using the model SWEAT. Separate field observations from root-exclusion, litter-removal and control treatments in one small and one large forest gap were used for calibration and validation. After irrigating all treatments to field capacity, soil matric potential and temperature were measured over 17 days at four depths ≤50 mm using the filter-paper technique and bead thermistors. Understorey environments were also simulated under the same initial conditions. The results suggest that three distinct scenarios, controlled by gap size, describe how the above- and below-ground processes controlling soil drying are coupled: (1) in the large gap, root water extraction by surrounding trees is negligible so soil drying is dominated by evaporation from the soil surface. Soil temperature is dominated by direct solar heating and cooling due to evaporation. (2) In the small gap, root water extraction dominates soil drying with soil evaporation playing a minor role. Soil temperature is still dominated by direct sunlight with some cooling due to evaporation. (3) In the understorey, root water extraction dominates soil drying. Soil temperature is dominated by heat conduction from deep soil layers with some evaporation and sensible heat transfer. The contrasting soil drying regimes imposed by variation in canopy structure enhance micro-environmental heterogeneity and the scope for differential germination and seedling establishment in coexisting tropical tree species.     

基于修正遗传算法的夏玉米作物系数及蒸散发估算

农田蒸散量是作物蒸腾量和土壤蒸发量的总和,准确估算农田蒸散量对制定合理的灌溉计划至关重要,进而对农作物的增产保收具有重要的意义。研究作物系数及蒸散量估算模型已成为一个热点科学问题。淮河流域是中国主要的农业生产基地,而夏玉米是淮河流域最主要的粮食作物之一。为研究夏玉米全生育期蒸散估算模型,反映夏玉米逐日作物系数及蒸散量的变化,为当地的农业生产活动提供指导,采用五道沟水文实验站称重式蒸渗仪及气象要素实测数据,应用遗传算法,构建夏玉米全生育期单作物系数蒸散模型,得到其4个生长阶段的作物系数估算值。其中,参考作物蒸散量采用FAO PenmanMonteith公式计算;对估算误差较大的发育期,利用叶面积指数和发育期天数构建调整模型,对发育期作物系数进行数值修正,取得了较好的效果,并进一步估算蒸散量,最终得到遗传算法与多项式回归相结合的夏玉米蒸散估算模型。结果表明:全生育期内,修正后作物系数计算值与实际值的平均绝对误差为0.09,均方根误差为0.12,准确率(绝对误差<0.3)为96.2%;蒸散量计算值与实际值的平均绝对误差为0.89 mm·d^-1,均方根误差为1.28 mm·d^-1,准确率(绝对误差<4 mm·d^-1)为100%;相比FAO推荐的作物系数模型,修正遗传算法模型作物系数和蒸散量的拟合准确率均明显提高,达到精度要求,该文修正遗传算法模型可用于夏玉米的蒸散估算。     

Influence des conditions hivernales sur les productions phyto- et zooplanctoniques en Méditerranée Nord-Occidentale. II. Biomasse et production phytoplanctonique

Hydrological observations, and measurements of nutrient chemistry, plankton biomass, and production were carried out during the Médiprod I cruise of the R.V. “Jean-Charcot”. The March cruise was characterized by almost winter conditions, exhibiting strong vertical mixing of water masses in the offshore region and nutrient transport up to the photic zone. According to the working hypothesis, the strong vertically mixed area (e.g. Station 15) and the surrounding oligotrophic area are separated by an intermediate zone, where both nutrients and stability have produced phytoplankton-bloom conditions. During the April cruise, highest biomass and production rates were encountered everywhere in the offshore region, and especially in the previously mixed area of central divergence. Production was as high as 2 gC·m^-2 day^-1, and the standing crop of chlorophyll was 3 mg·m^-3; such values are rather important for the so called “poor” Mediterranean Sea. Salinity-phosphate and chlorophyll-phosphate diagrams are presented. Biomass and production rates are in agreement with the potential fertility based on the nutrient content of the waters. The disappearance of 1 μatg P·PO₄ by photosynthetic uptake corresponds to 7.7 mg chlorophyll a, which represents the autotrophic biomass remaining after grazing by the simultaneous zooplankton bloom. Biomass and production features are analyzed in regard to interaction of both nutrient availability and the stability of water masses. Stability conditions can be created either by intrusion of local mixing in a stratified oligotrophic area (“winter bloom”), or by thermal stratification of the upper layer (“spring bloom”). In the latter case, the highest biomasses are present in the zone where the nutrients were previously introduced by mixing. The oligotrophic situation remained constant during the two crunises in the surrounding coastal area, which is characterized by low-salinity water and, therefore, absence of vertical nutrient transport into the photic zone. Chlorophyll pigment concentration and photosynthetic rates in the “Cote d'Azur” region are similar to those in the “Provence” region; this situation may result more from upwelling of nutrient-rich intermediate water than from the mixing process which predominates in the latter region.     

Modeling compensated root water and nutrient uptake

Plant root water and nutrient uptake is one of the most important processes in subsurface unsaturated flow and transport modeling, as root uptake controls actual plant evapotranspiration, water recharge and nutrient leaching to the groundwater, and exerts a major influence on predictions of global climate models. In general, unsaturated models describe root uptake relatively simple. For example, root water uptake is mostly uncompensated and nutrient uptake is simulated assuming that all uptake is passive, through the water uptake pathway only. We present a new compensated root water and nutrient uptake model, implemented in HYDRUS. The so-called root adaptability factor represents a threshold value above which reduced root water or nutrient uptake in water- or nutrient-stressed parts of the root zone is fully compensated for by increased uptake in other soil regions that are less stressed. Using a critical value of the water stress index, water uptake compensation is proportional to the water stress response function. Total root nutrient uptake is determined from the total of active and passive nutrient uptake. The partitioning between passive and active uptake is controlled by the a priori defined concentration value c_max. Passive nutrient uptake is simulated by multiplying root water uptake with the dissolved nutrient concentration, for soil solution concentration values below c_max. Passive nutrient uptake is thus zero when c_max is equal to zero. As the active nutrient uptake is obtained from the difference between plant nutrient demand and passive nutrient uptake (using Michaelis–Menten kinetics), the presented model thus implies that reduced passive nutrient uptake is compensated for by active nutrient uptake. In addition, the proposed root uptake model includes compensation for active nutrient uptake, in a similar way as used for root water uptake. The proposed root water and nutrient uptake model is demonstrated by several hypothetical examples, for plants supplied by water due to capillary rise from groundwater and surface drip irrigation.     

Coupling soil water and shoot dynamics in three grass species: A spatial stochastic model on water competition in Neotropical savanna

Savannas are ecosystems known for their high environmental and economic value. They cover at least 20% of the global land surface and, in some cases, can act as a boundary between tropical rainforest and deserts. Water is an important determinant of savanna ecosystems.In this paper, we present a theoretical stochastic model of root competition for water, which couples, soil water availability, phenology, and root and shoot architecture applied to three Neotropical savanna grasses. Soil moisture was simulated using a daily balance, as proposed by Rodriguez-Iturbe et al. [Rodriguez-Iturbe, I., Porporato, A., Ridolfi, L., Isham, V., Cox, D.R., 1999. Probabilistic modelling of water balance at a point: the role of climate, soil and vegetation. Proc. R. Soc. London, Ser. A 455, 3789–3805.]. To simulate rainfall stochasticity, we used daily precipitation data from the airport weather station in the State of Barinas, Venezuela, for the period 1991–2007. Competition among neighbouring plants took into account the spatial distribution of the individuals. As a final step, the model allowed us to calculate the shoot dynamic of the species as a function of soil water availability.Using these data, we compared the behaviour of isolated plants, pairs and trios, and we found below-ground competition to be a fundamental component of global (shoot + root) competition. Finally, our model suggests various circumstances that allow poor competitor plants to coexist in competition for water with more successful competitors. Apparently, this is not only due to transpiration rates, but also to differences in shoot emergence and shoot growth.     

SPACSYS: Integration of a 3D root architecture component to carbon, nitrogen and water cycling—Model description

It is an ongoing challenge to develop and demonstrate management practices that increase the sustainability of agricultural systems. Soil carbon and nitrogen dynamics directly affect soil quality, crop productivity and environmental impacts. Root systems are central to the acquisition of water and nutrients by plants, but are also a major pathway for the inputs of carbon and nutrients to soil. The complexity of both biotic and abiotic interactions, combined with stochastic changes in root architecture, makes it difficult to understand below-ground dynamics on the basis of experimentation alone. The integration of dynamic models of above-ground growth, three-dimensional root system demography, and interactions between plants and the environment, into one single model is a major challenge because of the complexity of the systems.In order to understand the interaction between a plant and the environment, it is advantageous to develop a model framework to integrate submodels that simulate various plant and environmental components. The objective of this paper is to outline a mechanistic and process-based model, which is capable of simulating interactions among environmental conditions around plants, plant growth and development, nitrogen and carbon cycles, with a three-dimensional root system submodel as an interface.The model presented in this paper is a mixed dimensional, multi-layer, field scale, weather-driven and daily time-step dynamic simulation model. The current version includes a plant growth and development component, a nitrogen cycling component, a carbon cycling component, plus a soil water component that includes representation of water flow to field drains as well as downwards through the soil layers, together with a heat transfer component. The components themselves and linkage among components are designed using object-oriented techniques, which makes the model robust, understandable and reusable. The components are implemented in the C++ programming language, and inputs and outputs of all components are organised as a database in either Microsoft^® SQL Server 2000, Access 2000 or MySQL5.0. Root architecture is visualised by using the OpenGL graphics system. Preliminary validation with two separate experimental datasets shows that the model can reasonably simulate root systems, nitrogen cycling, water movement and plant growth.     

Remote sensing of crop production in China by production efficiency models: models comparisons,estimates and uncertainties

Regional estimates or prediction of crop production is critical for many applications such as agricultural lands management, food security warning system, food trade policy and carbon cycle research. Remote sensing offers great potential for regional production monitoring and estimates, yet uncertainties associated with are rarely addressed. Moreover, although crops are one of critical biomes in global carbon cycle research, few evidences are available on the performance of global models of terrestrial net primary productivity (NPP) in estimating regional crop NPP. In this study, we use high quality weather and crop data to calibrate model parameter, validate and compare two kinds of remote sensing based production efficiency models, i.e. the Carnegie-Ames-Stanford-Approach (CASA) and Global Production Efficiency Model Version 2.0 (GLO-PEM2), in estimating maize production across China. Results show that both models intend to underestimate maize yields, although they also overestimate maize yields much at some regions. There are no significant differences between the results from CASA and GLO-PEM2 models in terms of both estimated production and spatial pattern. CASA model simulates better in the areas with dense crop and weather data for calibration. Otherwise GLO-PEM2 model does better. Whether the water soil-moisture down-regulator is used or not should depend on the percent of irrigation lands at the regions. The improved and validated models can be used for many applications. Further improvement can be expected by increasing remote sensing image resolution and the number of surface data stations.     

Estimating travel time of recharge water through a deep vadose zone using a transfer function model

We estimate the travel time of percolating water through a deep vadose zone at the regional scale using a transfer function model and a physical based conceptual flow model (Hydrus-1D), thereby exploiting the time series of precipitation, actual evapotranspiration and groundwater piezometry and generic vadose zone data. With the transfer function model we observe a high variability of estimated travel time varying from 0.9 to 3.1 years, corresponding to estimated vertical water flux velocities varying from 6.6 to 28.0 m/year. These results were compared with the travel time estimated from the physical based conceptual model. With the flow model, estimated travel time varies between 4.7 and 15.5 years, corresponding to water flux velocities varying between 1.7 and 4.1 m/year. The estimated travel time calculated with the flow model were therefore about five times larger than those estimated with the transfer function model. This could be explained by the fact that the transfer function model considers heterogeneous recharge from the vadose zone as well as from the vicinity of the piezometer through the so called “pushing effect”. In addition, the flow model requires various hydrogeological and hydrodynamic parameters which were estimated using generic parametrisation approaches, that are largely affected by uncertainty and may not reflect the local conditions. In contrast, the transfer function model only exploits available measurable time series and has the advantage of being site-specific.     

城市生态气象监测评估初步研究与实践——以北京为例

气象条件作为影响生态系统最活跃、最直接的驱动因子,影响着生态系统的质量和人类生存的环境,关系着生态保护和建设的成果,而城市生态系统具有与其他系统不一样的气候特征,目前还未形成一套有关城市的生态气象监测评估方法。基于生态气象学理论,分别从城市气候环境、与气候相关的陆表环境、大气环境、人居环境以及城市高影响天气气候事件等5个方面选择不同的要素和指标开展了城市生态气象监测评估初步研究,并以北京为例,利用2018年国家和区域自动气象站资料、大气成分观测资料、2002—2018年MODIS卫星资料、Landsat及环境一号卫星资料,开展了2018年北京城市生态气象监测评估。监测评估显示,(1)2018年北京城市“热岛”和“干岛”气候特征明显,并在北京二环与五环之间存在一个“冂”形风速低值区。(2)2018年北京陆表生态环境、大气环境、人居环境进一步好转:其中植被覆盖度达61.6%,创2002年以来新高,气象条件贡献率达50%,生态涵养区植被生态质量处于正常偏好的面积比例达93.2%;中心城区陆表温度为2011年以来最低值;重要水源地密云水库、官厅水库水体面积均为2000年以来最大值;气溶胶光学厚度、霾日数、大气静稳指数分别较过去4年平均值下降14%、31%和8%,大气扩散条件偏好,对霾日减少贡献率达21%,外地污染传输对PM2.5贡献达到53%;城市生态冷源较2013年明显增加,城市“热岛”得到缓解。(3)历史罕见的夏季高温闷热、冬季阶段低温、极端强降水以及持续无降水等高影响天气气候事件给城市安全运行和生态环境带来不利影响。综合评估表明2018年北京气象条件总体利于陆表生态环境改善,有利的气候条件提高了生态环境的质量,但城市生态质量仍面临着极端天气气候事件、城市热岛、低风速以及外来大气污染输送等风险。     

Verhalten von PAK im system boden/Pflanze

The results of lysimeter experiments conducted since 1991 dealing with the behavior of PAH in soil/plant systems demonstrate that the PAH pollution to cultivated plants may be caused by both atmospheric deposition and by the soil-to-plant transfer observed in contaminated sites. In the latter, a “direct contamination” of plant surfaces with PAH-loaded soil particles and the subsequent PAH turnover by desorption/adsorption processes is seen to dominate—at least for the most relevant PAHs toxic to humans, benzo(a)pyrene and dibenz(a,h)anthracene. Leafy vegetables growing close to the soil surface are therefore endangered most by a PAH contamination of the soil. The soil-to-plant transfer via “direct contamination” can be reduced to a high degree by covering the contaminated soil with different mulch materials. Systematic PAH transfer via root uptake could not generally be observed. From the reported results, a trigger value in the soil of 1 mg·kg^?1 for benzo(a)pyrene is proposed to make a judgement on PAH contaminated soils with regard to the soil-to-plant transfer pathways. Soils with excessive concentrations of benzo(a)pyrene demand special attention when considering the recommendations for the growth and consumption of cultivated vegetables. The “soil”as well as the “deposition pathways” must be integrated into a complete risk assessment of locations with food plant production, especially in urban areas.     

谷子根系对群体压力胁迫的生物学响应

采用根管土柱栽培的方法,比较了在相同根管土柱体积上种植不同株数谷子时谷子根系的主要特征,如根系数量,根系入土最大深度,根系SOD、POD活性,总根长,根系MDA含量及根系总吸收面积与活性吸收面积等对群体密度变化的可塑性.结果表明,不同群体下,谷子单株根数前期差异小,中后期差异大;而单位土体中的根量前期差异大,后期差异小.群体大(密度高),谷子根量、总根长及根系总吸收面积与活性吸收面积达到高峰的时间早,但衰亡时期也早,且入土深度较浅.群体小根量高峰出现得迟但维持的时间较长,根系在土体中的延伸深度也较大,有利于后期营养的获取和产量的提高.群体在作物生长中起着量的决定作用,而个体生长发育由于群体不同而引起质的差异.在生产上要想获得理想的产量,既要有足够量的保证,又要求达到一定质的标准,以使群体与个体协调发展.表4图2参18     

Transport of the insecticides chlorpyrifos,chlorfenvinphos, carbofuran,carbosulfan, and furathiocarb from soil into the foliage of cauliflower and Brussels sprouts plants grown in the field

In several field assays made in different locations in 1988 and 1989, cauliflower and Brussels sprouts plants were treated some days after plantation by pouring onto soil around the stem of the plant one of the insecticides chlorpyrifos, chlorfenvinphos, carbofuran, carbosulfan, or furathiocarb, for protection against the root fly. During plant growth, each of the insecticides (and their soil metabolites) was transported from soil into the plant foliage, where it could give—during a certain period of time—a secondary plant protection against the foliage insects. The foliage concentrations of the non systemic chlorpyrifos and chlorfenvinphos were equal or greater than 1 mg/kg fresh weight during a period of about 44 days after soil treatment in Brussels sprouts crops, and 35 days in cauliflower crops. Comparison of 1988 and 1989 however showed that these periods of time changed according to the weather conditions, especially rainfall. These periods of time were greater when the insecticide soil concentrations were greater—and thus when the rates of insecticide soil metabolism were smaller— and when the rainfall were greater—water transporting the insecticides from soil to the foliage. Similar relationships were observed with the systemic insecticides carbofuran, carbosulfan and furathiocarb; the weights per plant of insecticide compounds transported from soil into the foliage however were greater with these systemic insecticides than they were with the non systemic chlorpyrifos and chlorfenvinphos. The extreme values observed for the periods of time of insecticide foliage concentrations equal or greater than 1 mg/kg fresh weight thus were: 1. in cauliflower crops: 21 to 36 days for chlorpyrifos, and 23 to 39 days for chlorpyrifos + oxon; 24 to 37 days for chlorfenvinphos; 20 to 48 days for carbofuran; 2. in Brussels sprouts crops: 43 to 49 days for chlorpyrifos; 47 to 53 days for chlorpyrifos + oxon; 41 to 45 days for chlorfenvinphos; between 2 to 3 months for carbofuran, carbofuran + carbosulfan, and carbofuran + furathiocarb in the fields treated respectively with either carbofuran, carbosulfan, or furathiocarb. Moreover, in the spring and summer cauliflower crops made on fields onto which continuous cauliflower crops—with their soil insecticide treatments—had been made since a greater number of years (greater soil “history”), the insecticide compounds soil and foliage concentrations generally were lower.     

种稻土壤CH4排放规律的研究

通过盆栽试验研究了水稻生长期CH4排放的规律。结果表明,CH4排放存在明显的日变化,最大值出现在下午4点左右,最小值出现在凌晨4点左右。土壤温度的变化是导致CH4排放日变化的主要因素。水稻生长期CH4排放的季节变化受前茬季节作物种植及稻草还田时间的显著影响。前茬季节种植紫云英及休闲且水稻移栽前施用稻草处理在水稻生长初期即有大量CH4排放,且在水稻生长的前期、中期和后期分别出现3个CH4排放峰;前茬季节种植小麦和休闲且在前茬季节前施用稻草处理的,直至水稻生长的中期才有少量CH4排放。烤田期间CH4的排放峰值出现在土壤呈微于松软状态时;烤田至土壤干裂时,CH4排放通量降至零。     

A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

Modelling nutrient uptake by crops implies considering and integrating the processes controlling the soil nutrient supply, the uptake by the root system and relationships between the crop growth response and the amount of nutrient absorbed. We developed a model that integrates both dynamics of maize growth and phosphorus (P) uptake. The crop part of the model was derived from Monteith's model. A complete regulation of P-uptake by the roots according to crop P-demand and soil P-supply was assumed. The soil P-supply to the roots was calculated using a diffusion equation and assuming that roots behave as zero-sinks. The actual P-uptake and crop growth were calculated at each time step by comparing phosphate and carbohydrate supply–demand ratios. Model calculations for P-uptake and crop growth were compared to field measurements on a long term P-fertilization trial. Three P-fertilization regimes (no P-fertilization, 42.8 kg P ha⁻¹ year⁻¹ and 94.3 kg P ha⁻¹ year⁻¹) have led to a range of P-supply. Our model correctly simulated both the crop development and growth for all P-treatments. P-uptake was correctly predicted for the two non-limiting P-treatments. Nevertheless, for the limiting P-treatment, P-uptake was correctly predicted during the early period of growth but it was underestimated at the last sampling date (61 day after sowing). Several arguments for under-prediction were considered. However, most of them cannot explain the observed magnitude in discrepancy. The most likely reason might be the fact that biomass allocation between shoot and root must be modelled more precisely. Despite this mismatch, the model appears to provide realistic simulations of the soil–plant dynamic of P in field conditions.     

Nachhaltigkeit in der Pflanzenproduktion

Part I gives an overview on the origin and the development of the term “sustainability” in general and for agriculture in particular. This overview shows that the term “sustainability” is used widely in discussing ecological, social and economic aspects; however, there is no generally accepted definition for this term neither for the different aspects, nor for a concept including all the discussed aspects of “sustainability”. This makes a determination and practical implementation of the term “sustainability” difficult. Therefore a definition for a sustainable crop production from the ecological point of view is elaborated based on the discussion of the development of the term and on the identification of the most important applied aspects. This definition forms the basis for a methodological approach to the practical implementation of a sustainable crop production (»part II).     

Plant Bioavailability of “natural” and “model” Humic acid‐bound [14c] Atrazine residues

The release of bound [14C] atrazine residues and their uptake by maize plants was investigated.

“Natural”; humic acids, extracted from a brown soil, and “model”; humic acids, prepared from catechol, both containing bound [14C] atrazine residues were incubated with plants in soil. After 21 days, the maize plants contained 0.7% (plants grown in soil mixed with “natural”; humic acids) to 1.7% (plants grown in soil mixed with “model”; humic acids) of the radioactivity originally introduced.

The roots contained 55 to 70% of the [14C] residues whereas the remainder was present in the shoots. A significant amount of the total [14C] residues (29 to 53%) became again bound in plant tissues, whereas the, majority of extractable [14C] residues was present in the form of conjugates.

The behaviour of “model”; humic acid‐bound residues was comparable to that of “natural”; humic acid‐bound residues or soil‐bound residues.     

三峡库区生态系统服务功能重要性评价及其空间分布研究

以长江上游重点生态脆弱区三峡库区(重庆段)为研究区,结合RS和GIS软件,选取生物多样性维护功能、水源涵养功能和水土保持功能为评价指标,采用植被净初级生产力(vegetation net primary productivity,NPP)定量指标评估法,综合分析研究区2020年生态系统服务功能的重要性程度以及空间分异特...     

Berücksichtigung von Variabilität und Unsicherheit in quantitativen Risikoabschätzungen (QRA)

Using the example of residential living on a contaminated site, a probabilistic exposure assessment is performed with variability and uncertainty being modelled separately. Probability distributions are used in the exposure model in order to characterize person-related variables (e.g. body weight) only; chemical-specific parameters are being held constant. In addition, uncertainty concerning one selected variable (soil ingestion rate) was modelled. Comparing these results to conventional “worst case” estimates, we find those estimates located in the uppermost range of the probabilistic estimates. The worst case estimates tend to be highly conservative and possibly unrealistic.     

OPEC versus the West: A robust equilibrium

Suppose that both OPEC and the West possess stocks of oil which can be extracted at constant and identical cost. Consumption takes place only in the West. Suppose, hypothetically, that the West behaves as a single agent and, more realistically, that OPEC does also. Each agent makes a strategic choice of the pattern of exploitation over time of its own reserve. The Nash equilibrium obtained is “robust” in that it is also a “Stackelberg equilibrium” in which each agent is “right for the right reason.” Further, the equilibrium obtained is equivalent to that obtained when Western oil companies constitute a competitive fringe to the OPEC monopoly.