Use of Monte Carlo analysis to characterize nitrogen fluxes in agroecosystems

Intensive agricultural systems are largely responsible for the increase in global reactive nitrogen compounds, which are associated with significant environmental impacts. The nitrogen cycle in agricultural systems is complex and highly variable, which complicates characterization in environmental assessments. Appropriately representing nitrogen inputs into an ecosystem is essential to better understand and predict environmental impacts, such as the extent of seasonally occurring hypoxic zones. Many impacts associated with reactive nitrogen are directly related to annual nitrogen loads, and are not adequately represented by average values that de-emphasize extreme years. To capture the inherent variability in agricultural systems, this paper employs Monte Carlo analysis (MCA) to model major nitrogen exports during crop production, focusing on corn-soybean rotations within the U.S. Corn Belt. This approach yields distributions of possible emission values and is the first step in incorporating variable nutrient fluxes into life cycle assessments (LCA) and environmental impact assessments. Monte Carlo simulations generate distributions of nitrate emissions showing that 80% of values range between 15 and 90 kg NO39-) N/ha (mean 38.5 kg NO3(-) N/ha; median 35.7 kg NO3(-) N/ha) for corn fields and 5-60 kg NO3(-) N/ha (mean 20.8 kg NO3(-) N/ha; median 16.4 kg NO3(-) N/ha) for soybean fields. Data were also generated for grain and residue nitrogen, N2O, NO(x), and NH3. Results indicate model distributions are in agreement with available measured emissions.     

Monte Carlo analysis of uncertainty attached to microbial pollutant degradation rates

Prediction of bioremediation performance relies on models of microbial activity that are typically fitted to few data, which can lead to large errors in parameter estimates and uncertain prediction of reaction rates and degradation times. This paper presents a Monte Carlo approach to propagate the uncertainty about model parameters and error component through the Michaelis-Menten equation, yielding a probability distribution for both pollutant degradation rate and time for cleanup to some prescribed level. The procedure is illustrated using data related to the degradation kinetics of halogenated hydrocarbons by Methylomicrobium album BG8. It is shown that the assumption of homoscedasticity of the error variance in the Michaelis-Menten model is usually inappropriate, and analytical expressions are derived to account for the dependence of the error variance on the concentration of substrate. Depending on the substrate, the addition of formate might have a significant impact on the expected degradation rates and times, and the proposed approach allows one to test statistically such an impact for various substrate concentrations.     

Estimating the probability of recontamination via the air using Monte Carlo simulations

Recontamination of food products can cause foodborne illnesses or spoilage of foods. It is therefore useful to quantify this recontamination so that it can be incorporated in microbiological risk assessments (MRA). This paper describes a first attempt to quantify one of the recontamination routes: via the air. Data on the number of airborne microorganisms were collected from literature and industries. The settling velocities of different microorganisms were calculated for different products by combining the data on aerial concentrations with sedimentation counts assuming that settling is under the influence of gravity only. Air movement is not explicitly considered in this study. Statistical analyses were performed to clarify the effect of different products and seasons on the number of airborne microorganisms and the settling velocity. For both bacteria and moulds, three significantly different product categories with regard to the level of airborne organisms were identified. The statistical distribution in these categories was described by a lognormal distribution. The settling velocity did not depend on the product, the season of sampling or the type of microorganism, and had a geometrical mean value of 2.7 mm/s. The statistical distribution of the settling velocity was described by a lognormal distribution as well. The probability of recontamination via the air was estimated by the product of the number of bacteria in the air, the settling velocity, and the exposed area and time of the product. For three example products, the contamination level as a result of airborne recontamination was estimated using Monte Carlo simulations. What-if scenarios were used to exemplify determination of design criteria to control a specified contamination level.     

Comparison of Monte Carlo and fuzzy math simulation methods for quantitative microbial risk assessment

The objective of food safety risk assessment is to quantify levels of risk for consumers as well as to design improved processing, distribution, and preparation systems that reduce exposure to acceptable limits. Monte Carlo simulation tools have been used to deal with the inherent variability in food systems, but these tools require substantial data for estimates of probability distributions. The objective of this study was to evaluate the use of fuzzy values to represent uncertainty. Fuzzy mathematics and Monte Carlo simulations were compared to analyze the propagation of uncertainty through a number of sequential calculations in two different applications: estimation of biological impacts and economic cost in a general framework and survival of Campylobacter jejuni in a sequence of five poultry processing operations. Estimates of the proportion of a population requiring hospitalization were comparable, but using fuzzy values and interval arithmetic resulted in more conservative estimates of mortality and cost, in terms of the intervals of possible values and mean values, compared to Monte Carlo calculations. In the second application, the two approaches predicted the same reduction in mean concentration (-4 log CFU/ ml of rinse), but the limits of the final concentration distribution were wider for the fuzzy estimate (-3.3 to 5.6 log CFU/ml of rinse) compared to the probability estimate (-2.2 to 4.3 log CFU/ml of rinse). Interval arithmetic with fuzzy values considered all possible combinations in calculations and maximum membership grade for each possible result. Consequently, fuzzy results fully included distributions estimated by Monte Carlo simulations but extended to broader limits. When limited data defines probability distributions for all inputs, fuzzy mathematics is a more conservative approach for risk assessment than Monte Carlo simulations.     

Investing in a robotic milking system: a Monte Carlo simulation analysis

This paper uses Monte Carlo simulation methods to estimate the breakeven value for a robotic milking system (RMS) on a dairy farm in the United States. The breakeven value indicates the maximum amount that could be paid for the robots given the costs of alternative milking equipment and other important factors (e.g., milk yields, prices, length of useful life of technologies). The analysis simulates several scenarios under three herd sizes, 60, 120, and 180 cows. The base-case results indicate that the mean breakeven values are $192,056, $374,538, and $553,671 for each of the three progressively larger herd sizes. These must be compared to the per-unit RMS cost (about $125,000 to $150,000) and the cost of any construction or installation of other equipment that accompanies the RMS. Sensitivity analysis shows that each additional dollar spent on milking labor in the parlor increases the breakeven value by $4.10 to $4.30. Each dollar increase in parlor costs increases the breakeven value by $0.45 to $0.56. Also, each additional kilogram of initial milk production (under a 2x system in the parlor) decreases the breakeven by $9.91 to $10.64. Finally, each additional year of useful life for the RMS increases the per-unit breakeven by about $16,000 while increasing the life of the parlor by 1 yr decreases the breakeven value by between $5,000 and $6,000.     

Simulation of deoxynivalenol intake from wheat consumption in Japan using the Monte Carlo method

The aim of this study was to evaluate the current advisory level in Japan for deoxynivalenol (DON) in foods. To this end, we estimated the intake of DON based on its presence in wheat using a probabilistic computer simulation method. Values for the concentration of DON in wheat were based on those reported in surveys of 638 wheat samples conducted from 2002 to 2004. Data regarding consumption of 108 wheat-based products according to age group were obtained from the 2002 Japan national survey on food consumption. Two data sets on the consumption of wheat-based products and contamination of DON in wheat were analysed using three DON regulatory scenarios: no regulation, 1100 μg kg(-1) and 2000 μg kg(-1). Because consumption distributions contained two peaks for each age category, it was assumed that two log-normal distributions for each age category were needed to achieve a better fit to the distribution models. The results of simulated DON intake using the Monte Carlo method showed that children aged 1-6 years have the highest DON intake. However, the 95th percentile of simulated intake of DON in each age group was below the provisional maximum tolerable daily intake (TDI) of 1 μg kg(-1) body weight using any regulation scenario. The 99th percentile of simulated DON intake in the 1-6-year-old group was greater than TDI at approximately 2 μg kg(-1) body weight. These results suggest that the current dietary intake of DON from wheat consumption does not exert a significant health effect, but we may need to reconsider the current regulation value for the 1-6-year-old age group. In addition, we may need a better method to fit the distribution to the log-normal distribution better.     

A comparison of imputation techniques for internal preference mapping, using Monte Carlo simulation

The usual algorithm for internal preference mapping requires a complete set of observations, meaning the technique cannot be used to analyse trials based on incomplete block designs.

A simulation study was carried out to compare techniques for imputing missing values under various conditions. Sets of simulated preference data with different characteristics were constructed. Monte Carlo simulation was used to create missing observations in these sets; the imputation techniques were applied to the data; and the results of preference mapping based on the imputed data compared to those from the complete data set.

Convergence problems were found with two techniques. Analysis of variance revealed that effects on performance were dominated by the proportion of data missing, the level of noise in the data, and the size of the data set. Differences in performance among the three convergent imputation techniques were small; mean substitution is recommended, as it performed as well as more complex iterative techniques.

The results were broadly confirmed by a similar study on a genuine set of preference data.     

Spatial and angular distribution of light incident on coatings using Mie-scattering Monte Carlo simulations

Eight liquid emollients (mineral oil, sunflower oil, squalane, decyl-oleate, isopropyl-myristate, octyldodecanol, dimethicone, and cyclomethicone) were characterized by instrumental and sensory methods and evaluated to determine the relationship between sensory and instrumental measures. Sensory analysis was carried out by a panel of 14 assessors, who evaluated the following attributes: difficulty of spreading, gloss, residue, stickiness, slipperiness, softness, and oiliness. The physicochemical properties measured were spreadability (at 1½ and 1 min), viscosity, and superficial tension. Data collected were statistically analysed by analysis of variance (ANOVA), principal component analysis (PCA), and linear partial least squares regression analysis (PLS). In consideration of their physicochemical characteristics, the studied emollients were sorted into three groups, in which the silicones distinctly separate from the rest. Sensory characteristics enabled the discrimination of four groups of emollients where, besides the two silicones, isopropyl myristate was also differentiated. PLS revealed that emollient sensory attributes could be well predicted by instrumental measurements.     

Simulation of deoxynivalenol intake from wheat consumption in Japan using the Monte Carlo method

The aim of this study was to evaluate the current advisory level in Japan for deoxynivalenol (DON) in foods. To this end, we estimated the intake of DON based on its presence in wheat using a probabilistic computer simulation method. Values for the concentration of DON in wheat were based on those reported in surveys of 638 wheat samples conducted from 2002 to 2004. Data regarding consumption of 108 wheat-based products according to age group were obtained from the 2002 Japan national survey on food consumption. Two data sets on the consumption of wheat-based products and contamination of DON in wheat were analysed using three DON regulatory scenarios: no regulation, 1100 µg?kg^?1 and 2000?µg?kg^?1. Because consumption distributions contained two peaks for each age category, it was assumed that two log-normal distributions for each age category were needed to achieve a better fit to the distribution models. The results of simulated DON intake using the Monte Carlo method showed that children aged 1–6 years have the highest DON intake. However, the 95th percentile of simulated intake of DON in each age group was below the provisional maximum tolerable daily intake (TDI) of 1?µg?kg^?1 body weight using any regulation scenario. The 99th percentile of simulated DON intake in the 1–6-year-old group was greater than TDI at approximately 2?µg?kg^?1 body weight. These results suggest that the current dietary intake of DON from wheat consumption does not exert a significant health effect, but we may need to reconsider the current regulation value for the 1–6-year-old age group. In addition, we may need a better method to fit the distribution to the log-normal distribution better.     

Lead concentration in meat from lead-killed moose and predicted human exposure using Monte Carlo simulation

Lead-based hunting ammunitions are still common in most countries. On impact such ammunition releases fragments which are widely distributed within the carcass. In Norway, wild game is an important meat source for segments of the population and 95% of hunters use lead-based bullets. In this paper, we have investigated the lead content of ground meat from moose (Alces alces) intended for human consumption in Norway, and have predicted human exposure through this source. Fifty-two samples from different batches of ground meat from moose killed with lead-based bullets were randomly collected. The lead content was measured by atomic absorption spectroscopy. The lead intake from exposure to moose meat over time, depending on the frequency of intake and portion size, was predicted using Monte Carlo simulation. In 81% of the batches, lead levels were above the limit of quantification of 0.03 mg kg(-1), ranging up to 110 mg kg(-1). The mean lead concentration was 5.6 mg kg(-1), i.e. 56 times the European Commission limit for lead in meat. For consumers eating a moderate meat serving (2 g kg(-1) bw), a single serving would give a lead intake of 11 μg kg(-1) bw on average, with maximum of 220 μg kg(-1) bw. Using Monte Carlo simulation, the median (and 97.5th percentile) predicted weekly intake of lead from moose meat was 12 μg kg(-1) bw (27 μg kg(-1) bw) for one serving per week and 25 μg kg(-1) bw (45 μg kg(-1) bw) for two servings per week. The results indicate that the intake of meat from big game shot with lead-based bullets imposes a significant contribution to the total human lead exposure. The provisional tolerable weekly intake set by the World Health Organization (WHO) of 25 μg kg(-1) bw is likely to be exceeded in people eating moose meat on a regular basis. The European Food Safety Authority (EFSA) has recently concluded that adverse effects may be present at even lower exposure doses. Hence, even occasional consumption of big game meat with lead levels as those found in the present study may imply an increased risk for adverse health effects. Children and women of child-bearing age are of special concern due to the neurodevelopmental effects of lead.     

Lead concentration in meat from lead-killed moose and predicted human exposure using Monte Carlo simulation

Lead-based hunting ammunitions are still common in most countries. On impact such ammunition releases fragments which are widely distributed within the carcass. In Norway, wild game is an important meat source for segments of the population and 95% of hunters use lead-based bullets. In this paper, we have investigated the lead content of ground meat from moose (Alces alces) intended for human consumption in Norway, and have predicted human exposure through this source. Fifty-two samples from different batches of ground meat from moose killed with lead-based bullets were randomly collected. The lead content was measured by atomic absorption spectroscopy. The lead intake from exposure to moose meat over time, depending on the frequency of intake and portion size, was predicted using Monte Carlo simulation. In 81% of the batches, lead levels were above the limit of quantification of 0.03?mg?kg^?1, ranging up to 110?mg?kg^?1. The mean lead concentration was 5.6?mg?kg^?1, i.e. 56 times the European Commission limit for lead in meat. For consumers eating a moderate meat serving (2?g?kg^?1 bw), a single serving would give a lead intake of 11?µg?kg^?1 bw on average, with maximum of 220?µg?kg^?1 bw. Using Monte Carlo simulation, the median (and 97.5th percentile) predicted weekly intake of lead from moose meat was 12?µg?kg^?1 bw (27?µg?kg^?1 bw) for one serving per week and 25?µg?kg^?1 bw (45?µg?kg^?1 bw) for two servings per week. The results indicate that the intake of meat from big game shot with lead-based bullets imposes a significant contribution to the total human lead exposure. The provisional tolerable weekly intake set by the World Health Organization (WHO) of 25?µg?kg^?1 bw is likely to be exceeded in people eating moose meat on a regular basis. The European Food Safety Authority (EFSA) has recently concluded that adverse effects may be present at even lower exposure doses. Hence, even occasional consumption of big game meat with lead levels as those found in the present study may imply an increased risk for adverse health effects. Children and women of child-bearing age are of special concern due to the neurodevelopmental effects of lead.     

Including spatial variability in Monte Carlo simulations of pesticide leaching

A methodology is developed to quantify the uncertainty in a pesticide leaching assessment arising from the spatial variability of non-georeferenced parameters. A Monte Carlo analysis of atrazine leaching is performed in the Dyle river catchment (Belgium) with pesticide half-life (DT50) and topsoil organic matter (OM) content as uncertain input parameters. Atrazine DT50 is taken as a non-georeferenced parameter, so that DT50 values sampled from the input distribution are randomly allocated in the study area for every simulation. Organic matter content is a georeferenced parameter, so that a fixed uncertainty distribution is given at each location. Spatially variable DT50 values are found to have a significant influence on the amount of simulated leaching. In the stochastic simulation, concentrations exist above the regulatory level of 0.1 microg L(-1), but virtually no leaching occurs in the deterministic simulation. It is axiomatic that substance parameters (DT50, sorption coefficient, etc.) are spatially variable, but pesticide registration procedures currently ignore this fact. Including this spatial variability in future registration policies would have significant consequences on the amount and pattern of leaching simulated, especially if risk assessments are implemented in a spatially distributed way.     

Prediction of time to growth of Listeria monocytogenes using Monte Carlo simulation or regression analysis,influenced by sublethal heat and recovery conditions

Stochastic models, including the variability in extent and probability of microbial growth, are useful for estimating the risk of foodborne illness (i.e. Nauta, 2000). Risk assessment typically has to embrace all sources of variability. In this paper, a stochastic approach to evaluate growth of heat damaged Listeria monocytogenes cells influenced by different stresses (pH and presence of eugenol) was performed, using an individual-based approach of growth through OD measurements. Both the lag phase duration and the “work to be done” (h₀ parameter) were derived from the growth curves obtained. From results obtained histograms of the lag phase were generated and distributions were fitted. Histograms showed a shift to longer lag phases and an increase in variability with high stress levels. Using the distributions fitted, predictions of time to unacceptable growth (10² cfu/g) of L. monocytogenes were established by Monte Carlo simulation and they were compared with results from statistical methods. It was evidenced that both methods (Monte Carlo and regression analysis) gave a good indication of the probability of a certain level of growth other than the average. Tornado plots were obtained to establish a sensitivity analysis of the influence of the conditions tested (heat, pH, eugenol) applied to the microorganism and their combinations.     

手性含氮饱和杂环醇的化学法与生物酶法合成

手性含氮饱和杂环醇是一类重要的有机化合物,是许多合成药物和天然活性物质的结构组成单元。综述了哌啶醇、奎宁醇及吡咯烷醇等手性醇的化学及生物酶法合成进展,重点介绍了生物酶法在制备手性哌啶醇、奎宁醇及吡咯烷醇中的应用。     

Monte Carlo simulations assessing the risk of salmonellosis from consumption of almonds

Recent outbreaks of salmonellosis associated with raw almonds have raised awareness of this food as a vector for foodborne illness. We performed a quantitative assessment of the risk of contracting salmonellosis from consumption of raw almonds, accounting for factors that become important after almonds reach the processor. We estimated the risk associated with the consumption of raw almonds and the risk reduction associated with almonds treated with a theoretical 5-log reduction process or treated with propylene oxide using a standard commercial process. Probability distributions were chosen to describe the chance of almond contamination and the effects of storage time, storage temperature, and processing from currently available data. A beta-Poisson model for the dose-response relationship for Salmonella was obtained from published literature. The simulation estimated a 78% chance of one or more cases of salmonellosis per year from consumption of raw almonds. The application of a commercial propylene oxide treatment reduced this risk to 0.01%. Hypothetical 5-log reduction treatments with different standard deviations (+/-1, +/-0.5, +/-0.1, and +/-0) reduced the predicted yearly risk of salmonellosis to 0.69, 0.35, 0.30, and 0.21%, respectively. These results suggest that the risk of one or more U.S. cases of salmonellosis per year from consumption of raw almonds can be reduced from 78% to less than 1% by using a process achieving a 5-log reduction in Salmonella with a process standard deviation as large as 1 log unit or by using a commercial propylene oxide treatment.     

A Monte Carlo analysis on the impact of climate change on future crop choice and water use in Uzbekistan

Central Asia is considered a hot spot for severe water stress. According to the Intergovernmental Panel on Climate Change (IPCC), over the next century this region is expected to see a rise in temperatures and experience lower amounts of rainfall, creating a more arid climate. Regional agricultural policies have dominated water resource use. The impact of climate change coupled with market distorting economic policies, inefficient irrigation systems, and lack of water rights, could lead to social instability in the region. This analysis employs two downscaled climate projections and two Relative Concentration Pathway (RCP) scenarios (4.5 and 8.5) to simulate the impact of climate change on crop production, water use, and future crop allocations in the Khorezm region of Uzbekistan. Drought scenarios show drastic changes in crop productivity and producer profitability. If production quotas are removed, this region has the ability to become self-sufficient in wheat production, increasing its capacity to achieve food security.     

Comparison of Multitrait and Single-Trait Multiple Parity Evaluations by Monte Carlo Simulation

Three methods of analysis: 1) multiparity analysis with the first three parities analyzed as correlated traits, 2) multiparity analysis with all lactations analyzed as a single trait, and 3) first parity only analysis were compared on simulated data. A selection index was used to compute multiparity evaluations from the separate parity evaluations of the multitrait analyses. Twenty simulated populations, each of 8,500 cows, were generated by an algorithm that approximated the multitrait model. Populations were simulated with both random and yield-based culling of cows after first and second parity. Populations simulated with yield-based culling were analyzed both with the first parity records of all cows included and with an arbitrary one-third of first parity records deleted. First parity records of all cows were included in the analyses of the randomly culled populations. Accuracy of evaluation, estimated by correlations between true effects and evaluations and prediction error variances, was highest by the multitrait analysis and lowest by the first parity only analysis. Evaluations obtained by the two multilactation methods were nearly identical with random culling. Regression of effect on evaluation was close to unity for the multitrait evaluation; was only .94 and .90 for the all lactation single trait evaluation with random and yield culling, respectively; and was .80 for the index of sire effects on the first parity only analysis. Single-trait multilactation method may be preferred, as it is nearly as accurate as the multitrait method and easier computationally.     

Analysis of nanoparticle agglomeration in aqueous suspensions via constant-number Monte Carlo simulation

A constant-number direct simulation Monte Carlo (DSMC) model was developed for the analysis of nanoparticle (NP) agglomeration in aqueous suspensions. The modeling approach, based on the "particles in a box" simulation method, considered both particle agglomeration and gravitational settling. Particle-particle agglomeration probability was determined based on the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and considerations of the collision frequency as impacted by Brownian motion. Model predictions were in reasonable agreement with respect to the particle size distribution and average agglomerate size when compared with dynamic light scattering (DLS) measurements for aqueous TiO(2), CeO(2), and C(60) nanoparticle suspensions over a wide range of pH (3-10) and ionic strength (0.01-156 mM). Simulations also demonstrated, in quantitative agreement with DLS measurements, that nanoparticle agglomerate size increased both with ionic strength and as the solution pH approached the isoelectric point (IEP). The present work suggests that the DSMC modeling approach, along with future use of an extended DLVO theory, has the potential for becoming a practical environmental analysis tool for predicting the agglomeration behavior of aqueous nanoparticle suspensions.     

蒙特卡洛方法及在二维随机游动问题中的应用初探

概述蒙特卡洛方法的产生与发展,并结合射击问题的求解阐述了蒙特卡洛方法的基本特点,最后就蒙特卡洛方法在二维随机游动问题中的应用进行讨论,指出可将此用在油墨印刷牢度的评价上。