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.     

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.     

An Inverse Gaussian distribution of tree frequencies based on tree size

Forest stand management often depends on data from a single fixed area inventory plot located at random in a forest stand. The plot provides detailed information about tree size distribution but not about per unit area tree frequency distribution unless one assumes a Poisson (POI) distribution. The POI assumption ignores any relationship between a tree's size and its demand for growing space. This study argues for the Inverse Gaussian (IG) distribution as a more realistic model. Maximum likelihood estimates of the IG parameters are obtained from a transformation of tree size data (diameter) to proxies of tree counts. Data from two stands indicated that an IG model was better at predicting the tree frequency distribution than a POI model.     

Maximum likelihood method for parameter estimation in non-linear models with below detection data

The maximum likelihood (ML) method for regression analyzes of censored data (below detection limit) for nonlinear models is presented. The proposed ML method has been translated into an equivalent least squares method (ML-LS). A two stage iterative algorithm is proposed to estimate statistical parameters from the derived least squares translation. The developed algorithm is applied to a nonlinear model for prediction of ambient air CO concentration in terms of concentrations of respirable particulate matter (RSPM) and NO₂. It has been shown that if censored data are ignored or estimated through simplifications such as (i) censored data are equal to detection limit, (ii) censored data are half of the difference between detection limit and lower limit (e.g., zero or background level) or (iii) censored data are equal to lower limit, this can cause significant bias in estimated parameters. The developed ML-LS method provided better estimates of parameters than any of the simplifications in censored data.     

Linear regression with Type I interval- and left-censored response data

Laboratory analyses in a variety of contexts may result in left- and interval-censored measurements. We develop and evaluate a maximum likelihood approach to linear regression analysis in this setting and compare this approach to commonly used simple substitution methods. We explore via simulation the impact on bias and power of censoring fraction and sample size in a range of settings. The maximum likelihood approach represents only a moderate increase in power, but we show that the bias in substitution estimates may be substantial.     

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.     

Bimodality of the combined removal and signs-of-activities estimator for sampling closed animal populations

The possibility of a bimodal log-likelihood function arises with certain data when the combined removal and signs-of-activities estimator is used. Bimodal log-likelihoods may, in turn, yield disjoint confidence intervals for certain confidence levels. The hypothesis that bimodality is caused by the violation of the equal catchability assumption of the removal model, leading to the combination of contradictory data/models in the combined estimator is set forth. Simulations exploring the effect of the violation of removal model assumptions on estimation and inference showed that the assumption of unequal capture probability influenced the frequency of bimodal likelihoods; similarly, extreme parameter values for probability of capture influenced the number of excessively large confidence intervals produced. A sex-specific combined estimator is developed as a remedial model tailored to the problem. The simulations suggest that both the signs-of-activities estimator and the sex-specific estimator perform equally well over the range of simulations presented, though the signs-of-activities estimator is easier to implement.     

Differences in distributions,assembly mechanisms,and putative interactions of AOB and NOB at a large spatial scale

● Nitrifiers in WWTP were investigated at large spatial scale. ● AOB populations varied greatly but NOB populations were similar among cities. ● Drift dominated both AOB and NOB assembling processes. ● DO did not show a significant effect on NOB. ● NOB tended to cooperate with AOB and non-nitrifying microorganisms. Ammonia-oxidizing bacteria (AOB) and nitrite-oxidizing bacteria (NOB) play crucial roles in removing nitrogen from sewage in wastewater treatment plants (WWTPs) to protect water resources. However, the differences in ecological properties and putative interactions of AOB and NOB in WWTPs at a large spatial scale remain unclear. Hence, 132 activated sludge (AS) samples collected from 11 cities across China were studied by utilizing 16S rRNA gene sequencing technology. Results indicated that Nitrosomonas and Nitrosospira accounted for similar ratios of the AOB community and might play nearly equal roles in ammonia oxidation in AS. However, Nitrospira greatly outnumbered other NOB genera, with proportions varying from 94.7% to 99.9% of the NOB community in all WWTPs. Similar compositions and, hence, a low distance–decay turnover rate of NOB (0.035) across China were observed. This scenario might have partly resulted from the high proportions of homogenizing dispersal (~13%). Additionally, drift presented dominant roles in AOB and NOB assembling mechanisms (85.2% and 81.6% for AOB and NOB, respectively). The partial Mantel test illustrated that sludge retention time and temperature were the primary environmental factors affecting AOB and NOB communities. Network results showed that NOB played a leading role in maintaining module structures and node connections in AS. Moreover, most links between NOB and other microorganisms were positive, indicating that NOB were involved in complex symbioses with bacteria in AS.     

Probability distributions and statistical inference for axial data

Observations on axes which lack information on the direction of propagation are referred to as axial data. Such data are often encountered in enviromental sciences, e.g. observations on propagations of cracks or on faults in mining walls. Even though such observations are recorded as angles, circular probability models are inappropriate for such data since the constraint that observations lie only in [0, π) needs to be enforced. Probability models for such axial data are argued here to have a general structure stemming from that of wrapping a circular distribution on a semi-circle. In particular, we consider the most popular circular model, the von Mises or circular normal distribution, and derive the corresponding axial normal distribution. Certain properties of this distribution are established. Maximum likelihood estimation of its parameters are shown to be surprisingly, in contrast to trigonometric moment estimation, numerically quite appealing. Finally we illustrate our results by several real life axial data sets. Received: September 2004/ Revised: December 2004     

长春市不同土地利用生境土壤昆虫幼虫群落组成与生态分布

对长春市郊区天然次生林、市内公园风景林、郊区防护林和农田等土地利用生境进行土壤昆虫幼虫调查,研究土地利用差异对土壤昆虫幼虫群落特征的影响。研究区共捕获土壤昆虫幼虫35科411只,其中鞘翅目幼虫14科319只,双翅目幼虫13科64只,鳞翅目幼虫8科28只。研究结果表明:不同土地利用生境土壤昆虫幼虫群落组成与生态分布存在差异,防护林和农田土壤昆虫幼虫的类群数和个体密度显著减少;除农田外,其他生境土壤昆虫幼虫群落个体密度和类群数主要集中分布在0～5cm土壤层,生境凋落物的移除对土壤昆虫幼虫群落组成影响不明显;此外,鞘翅目、双翅目和鳞翅目幼虫对土地利用和植被类型变化的响应也不同。     

2000—2010年深圳湾及其邻近海域溶解无机氮的时空分布

依据2000—2010年每月一次的调查资料,简要描述和讨论了深圳湾及邻近水域中溶解无机氮(DIN)质量浓度的时空分布,并结合现场盐度(S)、氨氮(NH3-N)、亚硝酸盐氮(NO2-N)和硝酸盐氮(NO3-N)实测数据探讨DIN的组成和来源.结果表明,深圳湾和伶仃洋东部沿岸多年平均DIN质量浓度分别为(2.445±1.841) mg·L-1和(0.517±0.366) mg·L-1.在深圳湾,DIN质量浓度的年内变化特征为丰水期较低,枯水期较高.在伶仃洋东部沿岸,DIN质量浓度的年内变化呈明显的年周期循环特征,夏季达到最高而冬季最低.11 a研究期间,伶仃洋东部沿岸DIN质量浓度略呈上升趋势;深圳湾DIN质量浓度在2000—2004年呈上升趋势,2005—2010年则呈下降趋势.各形态DIN质量分数的大小顺序从深圳湾内的NH3-N>NO3-N>NO2-N转变至湾外的 NO3-N>NH3-N>NO2-N.DIN 与 S 之间存在着显著的负相关,依二元混合质量平衡模式估算的伶仃洋东部沿岸 DIN的陆源质量分数约为77.9%,而深圳湾的都>92%.     

Co-benefits and additionality of the clean development mechanism: An empirical analysis

The Clean Development Mechanism (CDM) allows industrialized countries to comply with the Kyoto Protocol by using carbon offsets from developing countries. There are two puzzles within this carbon market: additionality (the proposed activity would not have occurred in its absence) and co-benefits (the project has other environmental benefits besides climate mitigation). This paper proposes an econometric approach to evaluate the CDM effect on sulfur dioxide emission reductions and assess its additionality indirectly. Our empirical model is applied to China's emissions at the prefecture level. We found that the CDM does not have a statistically significant effect in lowering sulfur dioxide emissions. This result casts doubt on additionality of these CDM activities, that is, they would have happened anyway.     

Comparing discriminant analysis, neural networks and logistic regression for predicting species distributions: a case study with a Himalayan river bird

We assessed the occurrence of a common river bird, the Plumbeous Redstart Rhyacornis fuliginosus, along 180 independent streams in the Indian and Nepali Himalaya. We then compared the performance of multiple discrimant analysis (MDA), logistic regression (LR) and artificial neural networks (ANN) in predicting this species’ presence or absence from 32 variables describing stream altitude, slope, habitat structure, chemistry and invertebrate abundance. Using the entire data (=training set) and a threshold for accepting presence in ANN and LR set to P≥0.5, ANN correctly classified marginally more cases (88%) than either LR (83%) or MDA (84%). Model performance was assessed from two methods of data partitioning. In a ‘leave-one-out’ approach, LR correctly predicted more cases (82%) than MDA (73%) or ANN (69%). However, in a holdout procedure, all the methods performed similarly (73–75%). All methods predicted true absence (i.e. specificity in holdout: 81–85%) better than true presence (i.e. sensitivity: 57–60%). These effects reflect species’ prevalence (=frequency of occurrence), but are seldom considered in distribution modelling. Despite occurring at only 36% of the sites, Plumbeous Redstarts are one of the most common Himalayan river birds, and problems will be greater with less common species. Both LR and ANN require an arbitrary threshold probability (often P=0.5) at which to accept species presence from model prediction. Simulations involving varied prevalence revealed that LR was particularly sensitive to threshold effects. ROC plots (received operating characteristic) were therefore used to compare model performance on test data at a range of thresholds; LR always outperformed ANN. This case study supports the need to test species’ distribution models with independent data, and to use a range of criteria in assessing model performance. ANN do not yet have major advantages over conventional multivariate methods for assessing bird distributions. LR and MDA were both more efficient in the use of computer time than ANN, and also more straightforward in providing testable hypotheses about environmental effects on occurrence. However, LR was apparently subject to chance significant effects from explanatory variables, emphasising the well-known risks of models based purely on correlative data.     

Modelling Ecological Presence–absence Data along an Environmental Gradient: Threshold Levels of the Environment

A methodology for estimating environmental thresholds of binary presence–absence data is presented where the level of the threshold is parameterised. Presence–absence data is fitted to three complementary different models: an independent null-model, a monotonically increasing or decreasing model, and an optimum model. The range of the three models is strictly between zero and one and the models are therefore well suited for modelling presence probabilities. The results of the three models may be combined by using Bayesian model selection methodologies. The proposed methodology is exemplified on observed binary presence–absence data of Bauera rubioides along an elevation gradient. Received: May 2005 / Revised: July 2005 An erratum to this article is available at.     

Modelling the forest carbon budget of a Mediterranean region through the integration of ground and satellite data

This paper introduces an innovative modelling strategy aimed at simulating the main terms of net forest carbon budget (net primary production, NPP and net ecosystem exchange, NEE) in Tuscany (Central Italy). The strategy is based on the preliminary calibration and application of parametric and bio-geochemical models (C-Fix and BIOME-BGC, respectively), which simulate the behaviour of forest ecosystems close to equilibrium condition (climax). Next, the ratio of actual over-potential tree volume is computed as an indicator of ecosystem distance from climax and is combined with the model outputs to estimate the NPP and NEE of real forests. The per-pixel application of the new modelling strategy was made possible by the collection of several data layers (maps of forest type and volume, daily meteorological data and monthly normalized difference vegetation index (NDVI) images for the years 1999–2003) which served to characterize the eco-climatic and forest features of the region. The obtained estimates of forest NPP and NEE were evaluated against ground measurements of accumulated woody biomass and net carbon exchange. The results of these experiments testify the good potential of the proposed strategy and indicate some problem areas which should be the subject of future research.     

Modelling the impact of defoliation and leaf damage on forest plantation function and production

After presenting a short review of process-based model requirements to capture the plant dynamic response to defoliation, this paper describes the development and testing of a model of crown damage and defoliation for Eucalyptus. A model that calculates light interception and photosynthetic production for canopies that vary spatially and temporally in leaf area and photosynthetic properties is linked to the forest growth model CABALA. The process of photosynthetic up-regulation following defoliation is modelled with a simple conditional switch that triggers up-regulation when foliar damage or removal causes the ratio of functional leaf area to living tissue in the tree to change.We show that the model predicts satisfactorily when validated with trees of Eucalyptus nitens and Eucalyptus globulus from a range of sites of different ages, subject to different types of stress and different types of defoliation events (R² = 0.96 across a range of sites). However, the complexity of particular situations can cause the model to fail (e.g. very heavy defoliation events where branch death occurs).It is concluded that while the model will not cope with all situations, an appropriate level of generality has been captured to represent many of the physiological processes and feedbacks that occur following defoliation or leaf damage. This makes the model useful for guiding management interventions following pest attack and allows the development of scenarios including climate change impact analyses and decision-making on the merits of post-defoliation fertilisation to expedite recovery.     

Modelling the effect of in-stream and overland dispersal on gene flow in river networks

Modelling gene flow across natural landscapes is a current challenge of population genetics. Models are essential to make clear predictions about conditions that cause genetic differentiation or maintain connectivity between populations. River networks are a special case of landscape matrix. They represent stretches of habitat connected according to a branching pattern where dispersal is usually limited to upstream or downstream movements. Because of their peculiar topology, and the increasing concern about conservation issues in hydrosystems, there has been a recent revival of interest in modelling dispersal in river networks. Network complexity has been shown to influence global population differentiation. However, geometric characteristics are likely to interact with the way individuals move across space. Studies have focused on in-stream movements. None of the work published so far took into consideration the ability of many species to disperse overland between branches of the same network though. We predicted that the relative contribution of these two dispersal modalities (in-stream and overland) would affect the overall genetic structure. We simulated dispersal in synthetic river networks using an individual-based model. We tested the effect of dispersal modalities, i.e. the ratio of overland/in-stream dispersal, and two geometric parameters, bifurcation angle between branches and network complexity. Data revealed that if geometrical parameters affected population differentiation, dispersal parameters had the strongest effect. Interestingly, we observed a quadratic relationship between p the proportion of overland dispersers and population differentiation. We interpret this U-shape pattern as a balance between isolation by distance caused by in-stream movements at low values of p and intense migrant exchanges within the same branching unit at high values of p. Our study is the first attempt to model out-of-network movements. It clearly shows that both geometric and dispersal parameters interact. Both should be taken into consideration in order to refine predictions about dispersal and gene flow in river network.