Bayes methods for combining disease and exposure data in assessing environmental justice

Environmental justice reflects the equitable distribution of the burden of environmental hazards across various sociodemographic groups. The issue is important in environmental regulation, siting of hazardous waste repositories and prioritizing remediation of existing sources of exposure. We propose a statistical framework for assessing environmental justice. The framework includes a quantitative assessment of environmental equity based on the cumulative distribution of exposure within population subgroups linked to disease incidence through a dose-response function. This approach avoids arbitrary binary classifications of individuals solely as 'exposed' or 'unexposed'. We present a Bayesian inferential approach, implemented using Markov chain Monte Carlo methods, that accounts for uncertainty in both exposure and response. We illustrate our method using data on leukaemia deaths and exposure to toxic chemical releases in Allegheny County, Pennsylvania.     

部分除草剂与重金属混合物对发光菌的毒性

以5种不同类型除草剂和4种重金属为混合物组分,探索混合物毒性变化规律.应用微板毒性分析方法,测定了百草敌、磺草灵、西草净、除草定、环嗪酮、CdCl2·2.5H2O、Ni(NO3)2·6H2O、CoSO4·7H2O和ZnSO4·7H2O对淡水发光菌—青海弧菌Q67(Vibrio qinghaiensis sp.—Q67)的发光抑制毒性.应用非线性最小二乘拟合技术模拟实验剂量-效应数据.结果表明,5种除草剂与4种重金属化合物的剂量-效应曲线(DRC)均可用Weibull函数有效表征.为了全面考察各种不同浓度组成的混合物对Q67的毒性,设计了9个组分同时存在的3个等效应浓度比(EECR)混合物和10个均匀设计浓度比(UDCR)混合物.同样应用微板毒性分析方法测定了各个混合物对Q67的抑制毒性,并应用非线性最小二乘拟合技术模拟了其剂量-效应曲线.通过剂量加和(DA)与独立作用(IA)模型综合分析了各个混合物对发光菌的毒性变化规律.结果表明,不同类型除草剂与多种重金属的各种浓度组合的混合物毒性均可用DA模型进行预测和评估.     

Using the negative binomial distribution to model overdispersion in ecological count data

A Poisson process is a commonly used starting point for modeling stochastic variation of ecological count data around a theoretical expectation. However, data typically show more variation than implied by the Poisson distribution. Such overdispersion is often accounted for by using models with different assumptions about how the variance changes with the expectation. The choice of these assumptions can naturally have apparent consequences for statistical inference. We propose a parameterization of the negative binomial distribution, where two overdispersion parameters are introduced to allow for various quadratic mean-variance relationships, including the ones assumed in the most commonly used approaches. Using bird migration as an example, we present hypothetical scenarios on how overdispersion can arise due to sampling, flocking behavior or aggregation, environmental variability, or combinations of these factors. For all considered scenarios, mean-variance relationships can be appropriately described by the negative binomial distribution with two overdispersion parameters. To illustrate, we apply the model to empirical migration data with a high level of overdispersion, gaining clearly different model fits with different assumptions about mean-variance relationships. The proposed framework can be a useful approximation for modeling marginal distributions of independent count data in likelihood-based analyses.     

环境内分泌干扰物低剂量-效应研究进展

环境内分泌干扰物(EDCs)的低剂量-效应已成为生态毒理学界的研究热点.环境内分泌干扰物在接近或低于无可见不良效应浓度水平(NOAEL)时仍可诱发生物效应并存在非单调剂量-效应关系,这对现行的动物繁殖和发育毒理学检测规程以及环境内分泌干扰物风险评价的理论和方法提出了挑战.此外,由于环境中内分泌干扰物呈低剂量长期暴露的特征,研究低剂量-效应对正确进行生态风险评价具有重大的科学意义.在总结国内外相关研究的基础上,对当前环境内分泌干扰物低剂量-效应的研究进展进行了综述.     

Continuous dose-response modeling and risk analysis with the gamma and reciprocal gamma distributions

Kodell and West (1993) describe two methods for calculating pointwise upper confidence limits on the risk function with normally distributed responses and using a certain definition of adverse quantitative effect. But Banga et al. (2000) have shown that these normal theory methods break down when applied to skew data. We accordingly develop a risk analysis model and associated likelihood-based methodology when the response follows either a gamma or reciprocal gamma distribution. The model supposes that the shape (index) parameter k of the response distribution is held fixed while the logarithm of the scale parameter is a linear model in terms of the dose level. Existence and uniqueness of the maximum likelihood estimates is established. Asymptotic likelihood-based upper and lower confidence limits on the risk are solutions of the Lagrange equations associated with a constrained optimization problem. Starting values for an iterative solution are obtained by replacing the Lagrange equations by the lowest order terms in their asymptotic expansions. Three methods are then compared for calculating confidence limits on the risk: (i) the aforementioned starting values (LRAL method), (ii) full iterative solution of the Lagrange equations (LREL method), and (iii) bounds obtained using approximate normality of the maximum likelihood estimates with standard errors derived from the information matrix (MLE method). Simulation is used to assess coverage probabilities for the resulting upper confidence limits when the log of the scale parameter is quadratic in the dose level. Results indicate that coverage for the MLE method can be off by as much as 15% points and converges very slowly to nominal coverage levels as the sample size increases. Coverage for the LRAL and LREL methods, on the other hand, is close to nominal levels unless (a) the sample size is small, say N < 25, (b) the index parameter is small, say k 1, and (c) the direction of adversity is to the left for the gamma distribution or to the right for the reciprocal gamma distribution.     

Using the functional response of a consumer to predict biotic resistance to invasive prey

Predators sometimes provide biotic resistance against invasions by nonnative prey. Understanding and predicting the strength of biotic resistance remains a key challenge in invasion biology. A predator's functional response to nonnative prey may predict whether a predator can provide biotic resistance against nonnative prey at different prey densities. Surprisingly, functional responses have not been used to make quantitative predictions about biotic resistance. We parameterized the functional response of signal crayfish (Pacifastacus leniusculus) to invasive New Zealand mud snails (Potamopyrgus antipodarum; NZMS) and used this functional response and a simple model of NZMS population growth to predict the probability of biotic resistance at different predator and prey densities. Signal crayfish were effective predators of NZMS, consuming more than 900 NZMS per predator in a 12-h period, and Bayesian model fitting indicated their consumption rate followed a type 3 functional response to NZMS density. Based on this functional response and associated parameter uncertainty, we predict that NZMS will be able to invade new systems at low crayfish densities (< 0.2 crayfish/m2) regardless of NZMS density. At intermediate to high crayfish densities (> 0.2 crayfish/m2), we predict that low densities of NZMS will be able to establish in new communities; however, once NZMS reach a threshold density of -2000 NZMS/m2, predation by crayfish will drive negative NZMS population growth. Further, at very high densities, NZMS overwhelm predation by crayfish and invade. Thus, interacting thresholds of propagule pressure and predator densities define the probability of biotic resistance. Quantifying the shape and uncertainty of predator functional responses to nonnative prey may help predict the outcomes of invasions.     

多组分苯胺类混合物对发光菌的抑制毒性

以淡水发光菌——青海弧菌(Q67)为指示生物,96微孔板为实验反应载体,微板光度计为发光强度测试设备,测定了苯胺、邻甲基苯胺、对甲基苯胺、邻硝基苯胺、对硝基苯胺及其混合物对发光菌的发光抑制毒性,应用非线性最小二乘拟合技术与剂量加和(DA)及独立作用(IA)原理研究了混合物的毒性规律.1)分别测定每种化合物的剂量-效应数据并进行非线性拟合.结果表明,5种苯胺类化合物的剂量-效应曲线(DRC)均可用Logit与Weibull函数有效表征,从这些模型估算的半数效应浓度负对数值(-logEC50)分别为2.11、2.35、2.49、3.60和3.88(EC50单位:mol·L-1),可知其对发光菌的毒性大小顺序为:苯胺<邻甲基苯胺<对甲基苯胺<邻硝基苯胺<对硝基苯胺.2)根据组分EC50、EC10和EC1设计3个等效应浓度比混合物进行混合物毒性实验,并对混合物剂量-效应数据进行非线性拟合得到混合物DRC.结果表明,混合物DRC可用Box-Cox-Logit与Box-Cox-Weibull函数有效表征.3)根据单一化合物DRC模型,分别应用剂量加和(DA)与独立作用(IA)模型对混合物DRC进行预测.结果表明,无论考察混合浓度比例还是效应水平,剂量加和模型都能准确预测苯胺类混合物的毒性,而独立作用模型倾向于高估混合物毒性.     

Reassessment of the Cross-Florida Barge Canal: A probability approach

This reassessment of the Corps of Engineers' study of the Cross-Florida Canal demonstrates the application of the Weibull probability distribution to handle uncertainty in benefit-cost analysis and illustrates the distribution's use to incorporate environmental considerations in project analysis. With range and probability assumptions to reflect the criticisms of the Corps' study, it is shown that the Canal was a high-risk project even with the inappropriately low discount rate used. Use of the Weibull distribution is shown to be superior to the usual point estimates and range sensitivity tests in benefit-cost analysis.     

5种取代酚化合物对淡水发光菌的联合毒性

以新型淡水发光菌——青海弧菌Q67(Vibrio-qinghaiensissp.—Q67)为检验生物,以VeritasTM微孔板光度计为发光强度测试设备,分别测定了3,5-二羟基甲苯、2,3-二甲基苯酚、对氯苯酚、邻氯苯酚、2,4-二氯苯酚对淡水发光菌的发光抑制毒性及其混合物的联合毒性.结果表明,5种取代酚的剂量-效应关系都可用Weibull模型有效描述,从这些模型估算的半数效应浓度负对数值(-logEC50)分别为2.69、3.08、3.43、2.81和3.66,可知其对发光菌的毒性大小顺序为:2,4-二氯苯酚>对氯苯酚>2,3-二甲基苯酚>邻氯苯酚>3,5-二羟基甲苯.分别设计浓度等于各自之EC50和EC10的2个等效应浓度比混合物以及3个不同效应浓度比混合物进行联合毒性实验,结果发现,在所实验的浓度范围内各个混合物的剂量加和(DA)模型与独立作用(IA)模型具有相似的作用规律,其联合毒性既可用DA模型也可用IA模型进行预测.     

Morphologische Parameter als Biomarker in der Ökotoxikologie – natürliche und schadstoffinduzierte Variabilität

Background Ecotoxicology utilizes alterations of biological parameters of organisms as biomarkers of toxic exposure or effects. In environmental monitoring, biomarkers function as sensitive indicators of chemical pollution or as early warning signal of late effects Aim The pre-requisite for using a biological parameter as biomarker is the ability to unequivocally distinguish between the natural or normal and the induced or abnormal expression of the marker. This article discusses problems in discriminating between the normal and induce state, using morphological biomarkers as an example. Results and Discussion Morphological and/or anatomical parameters are intuitively considered to be rather invariable. This article shows for the example of gonad morphology of fish that this expectation is not always correct, but that morphological markers may display pronounced baseline variability. The reasons for this variability are often not understood. This is limiting the utility and interpretation of the biomarker response, in particular when organisms are not only exposed to chemical but to multiple stressors. Outlook The problem of discriminating between natural and induced variability of biomarkers is of particular relevance in low dose exposure scenarios, when stressors other than toxic chemicals may confound the toxicant-induced changes of the biomarker status. To better handle this problem and to be able to distinguish between adaptive and adverse changes, ecotoxicology has to set out for improved understanding of the phenotypic plasticity of organisms and genotypes,     

The effect of species response form on species distribution model prediction and inference

Ecological theory and current evidence support the validity of various species response curves according to a variety of environmental gradients. Various methods have been developed for building species distribution models but it is not well known how these methods perform under various assumptions about the form of the underlying species response. It is also not well known how spatial correlation in species occurrence affects model performance. These effects were investigated by applying an environmental envelope method (BIOCLIM) and three regression-based methods: logistic regression (LR), generalized additive modelling (GAM), and classification and regression tree (CART) to simulated species occurrence data. Each simulated species was constructed as a sum of responses with varying weights. Three basic species response curves were assumed: Gaussian (bell-shaped), Beta (skew) and linear. The two non-linear responses conform to standard ecological niche theory. All three responses were applied in turn to three simulated environmental variables, each with varying degrees of spatial autocorrelation. GAM produced the most consistent model performance over all forms of simulated species response. BIOCLIM and CART were inclined to underrate the performance of variables with a linear response. BIOCLIM was less sensitive to data density. LR was susceptible to model misspecification. The use of a linear function in LR underestimated the performance of variables with non-linear species response and contributed to increased spatial autocorrelation in model residuals. Omission of important environmental variables with non-linear species response also contributed to increased spatial autocorrelation in model residuals. Adding a spatial autocovariate term to the LR model (autologistic model) reduced the spatial autocorrelation and improved model performance, but did not correct the misidentification of the dominant environmental determinant. This is to be expected since the autologistic approach was designed primarily for prediction and not for inference. Given that various forms of species response to environmental determinants arise commonly in nature: (1) higher order functions should always be tested when applying LR in modelling species distribution; (2) spatial autocorrelation in species distribution model residuals can indicate that environmental determinants with non-linear response are missing from the model; and (3) deficiencies in LR model performance due to model misspecification can be addressed by adding a spatial autocovariate to the model, but care should be taken when interpreting the coefficients of the model parameters.     

Beta-normal distribution in dose–response modeling and risk assessment for quantitative responses

To establish allowable daily intakes for humans from animal bioassay experiments, benchmark doses corresponding to low levels of risk have been proposed to replace the no-observed-adverse-effect level for non-cancer endpoints. When the experimental outcomes are quantal, each animal can be classified with or without the disease. The proportion of affected animals is observed as a function of dose and calculation of the benchmark dose is relatively simple. For quantitative responses, on the other hand, one method is to convert the continuous data to quantal data and proceed with benchmark dose estimation. Another method which has found more popularity (Crump, Risk Anal 15:79–89; 1995) is to fit an appropriate dose–response model to the continuous data, and directly estimate the risk and benchmark doses. The normal distribution has often been used in the past as a dose–response model. However, for non-symmetric data, the normal distribution can lead to erroneous results. Here, we propose the use of the class of beta-normal distribution and demonstrate its application in risk assessment for quantitative responses. The most important feature of this class of distributions is its generality, encompassing a wide range of distributional shapes including the normal distribution as a special case. The properties of the model are briefly discussed and risk estimates are derived based on the asymptotic properties of the maximum likelihood estimates. An example is used for illustration.

Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling

Many of the most popular sampling schemes used in forestry are probability proportional to size methods. These methods are also referred to as size-biased because sampling is actually from a weighted form of the underlying population distribution. Length- and area-biased sampling are special cases of size-biased sampling where the probability weighting comes from a lineal or areal function of the random variable of interest, respectively. Often, interest is in estimating a parametric probability density of the data. In forestry, the Weibull function has been used extensively for such purposes. Estimating equations for method of moments and maximum likelihood for two- and three-parameter Weibull distributions are presented. Fitting is illustrated with an example from an area-biased angle-gauge sample of standing trees in a woodlot. Finally, some specific points concerning the form of the size-biased densities are reported.     

Modeling leaf dispersal in mixed hardwood forests using a ballistic approach

In mixed-species stands, modeling leaf litter dispersal is important to predict the physical and chemical characteristics of the forest floor, which plays a major role in nutrient cycling and in plant population dynamics. In this study, a spatially explicit model of leaf litterfall was developed and compared with two other models. These three models were calibrated for a mixed forest of oak and beech using litterfall data from mapped forest plots. All models assumed that an allometric equation described individual leaf litter production, but they strongly differed in the modeling of the probability density of leaf shedding with distance from source trees. Two models used a negative exponential function to account for leaf dispersal with distance, and this function was allowed to vary according to wind direction in one of them. In contrast, our approach was based on a simple ballistic equation considering release height, wind speed, wind direction, and leaf fall velocity; the distributions of wind speeds and wind directions were modeled according to a Weibull and a Von Mises distribution, respectively. Using an independent validation data set, all three models provided predictions well correlated to measurements (r > 0.83); however, the two models with a direction-dependent component were slightly more accurate. In addition, parameter estimates of the ballistic model were in close agreement with a foliar litter production equation derived from the literature for beech and with wind characteristics measured during leaf litterfall for both species. Because of its mechanistic background, such a spatially explicit model might be incorporated as a litterfall module in larger models (nutrient cycling, plant population dynamics) or used to determine the manner in which patch size in mixed-species stands influences litter mixture.     

RBCA、CLEA及CalTOX模型在苯并[a]芘污染场地健康风险评估中的应用比较

为探讨不同模型对污染场地健康风险评估结果的影响,以苯并[a]芘为例,采用RBCA、CLEA和CalTOX模型对某工业污染场地表层土壤进行健康风险评估,分析了评估结果的差异和原因,同时对模型的主要暴露参数进行了敏感性分析,并推导出基于风险概率分布的土壤修复限值。结果表明,RBCA、CLEA和CalTOX模型计算的苯并[a]芘致癌总风险分别为2.40×10-4、6.32×10-4和7.04×10-6,且经口摄入和皮肤接触2个途径对人体健康造成的危害最大。降解作用是影响CalTOX模型风险评估结果不同于RBCA和CLEA模型的重要因素,3个模型间参数取值及方法学的差异也会导致风险评估结果不同。各模型暴露参数的敏感性排序也有差异。采用基于风险概率分布的方法推导土壤修复限值,RBCA、CLEA和CalTOX模型所得结果分别为0.18、0.08、0.13(不考虑降解作用CalTOX模型)和10.74(考虑降解作用CalTOX模型)mg·kg-1,为各模型直接推导值的1.5～2.6倍。基于风险概率分布的方法可有效降低风险评估过程中参数不确定性的影响,为工业污染场地土壤修复值的制定提供参考。     

水环境中重金属铜暴露下青鳉鱼的行为响应

本研究采用生物行为传感器监测青鳉鱼重金属铜暴露下的行为数据，分析不同暴露浓度(20、10、5、1和0.1 TU)下青鳉鱼的行为响应。20、10、5、1和0.1 TU的暴露浓度下青鳉鱼对重金属污染的行为反应模式符合环境胁迫阈值模型，且不同浓度梯度重金属对青鳉鱼产生不同的行为毒性效应。通过本研究，利用重金属作用下青鳉鱼的行为变化来研究重金属环境胁迫导致的生物行为响应机制，从而得到重金属暴露下生物行为的实时变化过程和趋势，可对水环境生态系统质量进行综合评价。     

水环境中重金属铜暴露下青鳉鱼的行为响应

采用生物行为传感器监测青鳉鱼在重金属铜暴露下的行为数据,分析不同暴露浓度(20、10、5、1和0.1 TU)下青鳉鱼的行为响应。20、10、5、1和0.1 TU的暴露浓度下青鳉鱼对重金属污染的行为反应模式符合环境胁迫阈值模型,且不同浓度梯度重金属对青鳉鱼产生不同的行为毒性效应。利用重金属作用下青鳉鱼的行为变化来研究重金属环境胁迫导致的生物行为响应机制,从而得到重金属暴露下生物行为的实时变化过程和趋势,可对水环境生态系统质量进行综合评价。     

Modulation of predator-prey interactions by the Allee effect

An Allee effect arising from density-dependent mating success can have significant impacts at the ecosystem level when considered in the context of predator-prey interactions. These are captured by a mathematical model for the exchange of biomass between a structured predator population (continuous weight distribution) and a resource. Because the predator’s mating success affects the amount of resources required for the production of offsprings and their future growth into mature organisms, it influences the flux of biomass between trophic levels. Under simple assumptions, the equations can be reduced to an equivalent unstructured predator-prey model in which the Allee effect modulates the predation rate: the mating probability multiplies the rate of predator growth as well as the rate of resource depletion. Implications of the Allee effect for the bifurcation structure and equilibrium densities are examined. The model is compared to a modified version in which the Allee effect instead modulates the assimilation efficiency, hence the mating probability does not appear in the dynamical equation for the resource density. Both models exhibit qualitatively similar dynamics. However, compared to the model in which the Allee effect modulates predation, the model in which the Allee effect modulates assimilation efficiency predicts (i) unrealistically inefficient resource assimilation when predator density is low, (ii) a higher risk of catastrophic extinction resulting from a change in the parameter controlling the strength of the Allee effect, and (iii) no possibility of an increase in population size when the density dependence is enhanced.     

Total release fogger exposures reported to Texas poison centers, 2000–2009

Total release foggers or “bug bombs” are products designed to fill an area such as a home or workplace with insecticide. Because of their method of action, unintentional exposures may occur. Cases for this retrospective study were all fogger exposures reported to Texas poison centers during 2000–2009. The distribution of cases was identified for various demographic and clinical factors. There were 2855 fogger exposures. Among the patients 56.0% were females and 69.5% were 20 years or older. Considering the exposure circumstances 95.6% were unintentional and 62.2% occurred through inhalation. The management site was 75.2% on site. The medical outcomes were no effect (11.8%), minor effect (25.1%), moderate effect (7.4%), major effect (0.1%), not followed (no effects expected) (3.5%), not followed (minimal effects expected) (39.3%), not followed (potentially toxic) (4.9%), and effects probably unrelated to exposure (7.7%). The most frequently reported clinical effects were cough (25.4%), vomiting (13.3%), nausea (9.2%), dyspnea (8.7%), throat irritation (7.9%), and headache (5.6%). The public needs to be educated about the potential hazard of exposures to foggers. However, most fogger exposures reported to poison centers are not likely to be seriously toxic and can be managed at home.     

Statistical analysis of bioassays,based on hazard modelling

A stochastic model is proposed to describe time-dependent lethal effects of toxic compounds. It is based on simple mechanistic assumptions and provides a measure for the toxicity of a chemical compound, the so-called killing rate. The killing rate seems a promising alternative for the LC50. The model also provides the no-effect level and the LC50, both as a function of exposure time. The model is applied to real data and to simulated data.