Recursive residuals and model diagnostics for normal and non-normal state space models

Model diagnostics for normal and non-normal state space models are based on recursive residuals which are defined from the one-step ahead predictive distribution. Routine calculation of these residuals is discussed in detail. Various diagnostic tools are suggested to check, for example, for wrong observation distributions and for autocorrelation. The paper also discusses such topics as model diagnostics for discrete time series and model discrimination via Bayes factors. The case studies cover environmental applications such as analysing a time series of the number of daily rainfall occurrences and a time series of daily sulfur dioxide emissions.     

Prediction of non-methane hydrocarbons in Kuwait using regression and Bayesian kriged Kalman model

This article describes the hierarchical Bayesian approach for predicting average hourly concentrations of ambient non-methane hydrocarbons (NMHC) in Kuwait where records of six monitor stations located in different sites are observed at successive time points. Our objective is to predict the concentration level of NMHC in unmonitored areas. Here an attempt is made for the prediction of unmeasured concentration of NMHC at two additional locations in Kuwait. We will implement a kriged Kalman filter (KKF) hierarchical Bayesian approach assuming a Gaussian random field, a technique that allows the pooling of data from different sites in order to predict the exposure of the NMHC in different regions of Kuwait. In order to increase the accuracy of the KKF we will use other statistical models such as imputation, regression, principal components, and time series analysis in our approach. We considered four different types of imputation techniques to address the missing data. At the primary level, the logarithmic field is modeled as a trend plus Gaussian stochastic residual model. The trend model depends on hourly meteorological predictors which are common to all sites. The residuals are then modeled using KKF, and the prediction equation is derived conditioned on adjoining hours. On this basis we developed a spatial predictive distribution for these residuals at unmonitored sites. By transforming the predicted residuals back to the original data scales, we can impute Kuwait’s hourly non-methane hydrocarbons field.     

The implications of model complexity for environmental management

The purpose of this paper is to consider the implicatons of model complexity for the quality of the information provided by models of production activities that account for the processes involved in residuals generation and treatment. Using each of the three primary technologies for iron and steel-making industry and models of varying detail for each, the paper compares the estimated levels of residuals generated and treatment costs for both atmospheric and waterborne effluents. The findings suggest that there are strategic details in model construction which have fundamental implications for the design of environmental policies. Moreover, preliminary estimates of the costs of model construction and operation suggest that policymakers may not be able to afford complexity for its own sake. Rather these costs will require the development of methods to isolate the strategic details in each technology that are potentially important to environmental policies.     

关于肥满度指数的讨论

肥满度指数,也称身体状况指数,广泛应用于各个动物类群和生态学、生理、生化、遗传学以及养殖业.至今已有多种肥满度指数提出,从计算公式结构上,肥满度指数可以划分为比值法和残差法两大类.通过对各种肥满度指数的分析,Le Cren相对状态指数Kn、log10(体重)与log10(身体大小指数)线性回归的(标准化)残差这两种肥满度指数系统误差相对较小.实际应用中最好根据所考察的问题分别计算不同年龄段、性别的个体的肥满度指数来分析肥满度指数.由于定义的模糊性及其前提假设缺乏广泛验证,因此,肥满度指数在实际应用中需要谨慎考察其前提假设是否满足.参33     

Predictability of marine nematode biodiversity

In this paper, we investigated: (1) the predictability of different aspects of biodiversity, (2) the effect of spatial autocorrelation on the predictability and (3) the environmental variables affecting the biodiversity of free-living marine nematodes on the Belgian Continental Shelf. An extensive historical database of free-living marine nematodes was employed to model different aspects of biodiversity: species richness, evenness, and taxonomic diversity. Artificial neural networks (ANNs), often considered as “black boxes”, were applied as a modeling tool. Three methods were used to reveal these “black boxes” and to identify the contributions of each environmental variable to the diversity indices. Since spatial autocorrelation is known to introduce bias in spatial analyses, Moran's I was used to test the spatial dependency of the diversity indices and the residuals of the model. The best predictions were made for evenness. Although species richness was quite accurately predicted as well, the residuals indicated a lack of performance of the model. Pure taxonomic diversity shows high spatial variability and is difficult to model. The biodiversity indices show a strong spatial dependency, opposed to the residuals of the models, indicating that the environmental variables explain the spatial variability of the diversity indices adequately. The most important environmental variables structuring evenness are clay and sand fraction, and the minimum annual total suspended matter. Species richness is also affected by the intensity of sand extraction and the amount of gravel of the sea bed.     

Spatial residual analysis of six modeling techniques

In recent years alternative modeling techniques have been used to account for spatial autocorrelations among data observations. They include linear mixed model (LMM), generalized additive model (GAM), multi-layer perceptron (MLP) neural network, radial basis function (RBF) neural network, and geographically weighted regression (GWR). Previous studies show these models are robust to the violation of model assumptions and flexible to nonlinear relationships among variables. However, many of them are non-spatial in nature. In this study, we utilize a local spatial analysis method (i.e., local Moran coefficient) to investigate spatial distribution and heterogeneity in model residuals from those modeling techniques with ordinary least-squares (OLS) as the benchmark. The regression model used in this study has tree crown area as the response variable, and tree diameter and the coordinates of tree locations as the predictor variables. The results indicate that LMM, GAM, MLP and RBF may improve model fitting to the data and provide better predictions for the response variable, but they generate spatial patterns for model residuals similar to OLS. The OLS, LMM, GAM, MLP and RBF models yield more residual clusters of similar values, indicating that trees in some sub-areas are either all underestimated or all overestimated for the response variable. In contrast, GWR estimates model coefficients at each location in the study area, and produces more accurate predictions for the response variable. Furthermore, the residuals of the GWR model have more desirable spatial distributions than the ones derived from the OLS, LMM, GAM, MLP and RBF models.     

Optimal environmental policy for waste disposal and recycling when firms are not compliant

We investigate a model that considers disposal and recycling activities after the consumption of products. In the field, the deposit–refund (D–R) policy has been considered as an ideal policy for internalizing disposal costs, which can result in the realization of the first-best policy. However, the possibility of firms' illegal disposal has been neglected. We introduce a monitoring cost to prevent firms from disposing of collected residuals illegally and induce the second-best D–R policy. We find that the relation between the monitoring problem for firms and the price of the recycling market brings about a variation in the optimal level of the refunds (which is typically smaller than the first-best level). Further, we investigate an alternative policy that requires producers to take-back residuals and show how this policy works equivalently to the second-best D–R policy by applying the theory of the tradable rights market.     

Genetic influence on caste in the ant Camponotus consobrinus

Genetic influences on polyethism within social insect colonies are well known, suggesting that the determination of caste (soldiers and minor workers) may also be genetically mediated. The Australian sugar ant Camponotus consobrinus is suitable for such a study, having soldiers and minor workers that follow a complex allometry. Further, although most C. consobrinus colonies are monogynous, 13 of 42 surveyed using microsatellites were found to be polygynous. Thus, although a minority of colonies were polygynous, the great majority of queens live in polygynous colonies. From the 29 monogynous colonies studied, we inferred that the queens are monandrous. Ants from four polygynous colonies were assigned to families on the basis of microsatellite genotypes, after measurements had been taken of head width and scape length. These measurements reflect a complex allometry interpretable as soldier and minor worker growth curves with a large changeover zone. Genetic influence on caste determination was examined by testing for differences between families within colonies in the distribution of scape lengths, residuals from the overall colony allometric curve, and proportions of soldiers and minor workers (as determined by head width falling above or below the inflection point of the overall colony allometric curve). Families in all four colonies differed significantly in caste proportions and in head-width distributions, and three of the four colonies showed significant differences between families in residuals from the overall colony growth curve. Nested ANOVAs using head widths and scape-length residuals showed that when the effect of family is removed, intercolony differences in allometry are negligible. This evidence indicates genetic rather than environmental causes for the observed differences between families. We speculate that this variation may reflect some selective advantage to within-colony heterogeneity between families or that selective differences are few between a wide array of family growth patterns. Received: 16 June 1999 / Received after revision: 13 September 1999 / Accepted: 25 September 1999     

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.     

5种典型滨海养殖水体中多种类抗生素的残留特性

水产集约化养殖的迅速发展带来的抗生素环境问题已经受到各国学者的关注,尤其是环境残留抗生素对微生物耐药性的诱导和抗生素在食物中的残留,直接影响水生生态系统健康以及人类健康。应用固相萃取-高压液相色谱-串联质谱方法（SPE-LC-MS/MS）研究不同生物养殖水体（鱼塘、螃蟹池、蛏池、虾池、鸭池）中残留抗生素类型和质量浓度。结果表明,基于LC-MS/MS分析的固相萃取方法对滨海养殖水体中5类14种抗生素残留的检测具有较高的萃取效率,并且检测方法回收率在63%~124%之间;在典型滨海养殖区不同养殖水体中检出了3类7种抗生素（含磺胺类增效剂甲氧苄氨嘧啶）残留,最高质量浓度分别为诺氟沙星（3.54 ng.L-1,虾池）、氧氟沙星（14.8 ng.L-1,蛏池）、磺胺嘧啶（5.36 ng.L-1,鸭池）、磺胺二甲嘧啶（7.35 ng.L-1,虾池）、磺胺甲噁唑（18.5 ng.L-1,虾池）、氟甲砜霉素（5.00 ng.L-1,虾池）和甲氧苄氨嘧啶（40.2 ng.L-1,鸭池）,均低于已有的报道质量浓度水平。养殖水体中残留抗生素种类和质量浓度与养殖生物类型有关,螃蟹养殖水体抗生素残留种类（4种）最少,鱼和鸭养殖水体抗生素残留检出达6种,而检出的抗生素最高残留质量浓度主要来自于虾养殖水体。     

Rarity in Neotropical Forest Mammals Revisited

The identification of rare species is an important goal in conservation biology. Recent attempts to classify rare species have emphasized dichotomies in such characteristics as local population density, area of distribution, and degree of ecological specialization. In particular, Arita et al. (1990) dichotomized 100 Neotropical forest mammals according to local population density and area of distribution. Among these species of mammals, mean body mass was significantly associated with local population density and area of distribution. We argue that the effects of body mass should be removed before species are classified with respect to rarity. We re-evaluated the data on Neotropical mammal species, using regression analyses to remove the effects of body mass on population density and area of distribution, followed by analysis of residuals. This new method resulted in substantial changes in the dichotomous classification of rare species. We combined the analysis of regression residuals with a ranking procedure that assumed that local population density and area of distribution were equally important in their effects on rarity. The new ranking technique produced another different classification of the rarity of the Neotropical forest mammal species. A graphical analysis showed that ranked species differed substantially in their degree of rarity, and in the importance of local population density, area of distribution, or both, to their degree of rarity. The ranking method allows the species of greatest concern to be singled out, it can be modified to include additional variables such as niche breadth, and it should be helpful for making conservation decisions.     

Incorporating spatial autocorrelation into cellular automata model: An application to the dynamics of Chinese tamarisk (Tamarix chinensis Lour.)

Spatial autocorrelation (SAC) is frequently encountered in most spatial data in ecology. Cellular automata (CA) models have been widely used to simulate complex spatial phenomena. However, little has been done to examine the impact of incorporating SAC into CA models. Using image-derived maps of Chinese tamarisk (Tamarix chinensis Lour.), CA models based on ordinary logistic regression (OLCA model) and autologistic regression (ALCA model) were developed to simulate landscape dynamics of T. chinensis. In this study, significant positive SAC was detected in residuals of ordinary logistic models, whereas non-significant SAC was found in autologistic models. All autologistic models obtained lower Akaike's information criterion corrected for small sample size (AICc) values than the best ordinary logistic models. Although the performance of ALCA models only satisfied the minimum requirement, ALCA models showed considerable improvement upon OLCA models. Our results suggested that the incorporation of the autocovariate term not only accounted for SAC in model residuals but also provided more accurate estimates of regression coefficients. The study also found that the neglect of SAC might affect the statistical inference on underlying mechanisms driving landscape changes and obtain false ecological conclusions and management recommendations. The ALCA model is statistically sound when coping with spatially structured data, and the adoption of the ALCA model in future landscape transition simulations may provide more precise probability maps on landscape transition, better model performance and more reasonable mechanisms that are responsible for landscape changes.     

Ammonia and phosphorus removal from agricultural runoff using cash crop waste-derived biochars

• Orange tree residuals biochar had a better ability to adsorb ammonia. • Modified tea tree residuals biochar had a stronger ability to remove phosphorus. • Partially-modified biochar could remove ammonia and phosphorus at the same time. • The real runoff experiment showed an ammonia nitrogen removal rate of about 80%. • The removal rate of total phosphorus in real runoff experiment was about 95%. Adsorption of biochars (BC) produced from cash crop residuals is an economical and practical technology for removing nutrients from agricultural runoff. In this study, BC made of orange tree trunks and tea tree twigs from the Laoguanhe Basin were produced and modified by aluminum chloride (Al-modified) and ferric sulfate solutions (Fe-modified) under various pyrolysis temperatures (200°C–600°C) and residence times (2–5 h). All produced and modified BC were further analyzed for their abilities to adsorb ammonia and phosphorus with initial concentrations of 10–40 mg/L and 4–12 mg/L, respectively. Fe-modified Tea Tree BC 2h/400°C showed the highest phosphorus adsorption capacity of 0.56 mg/g. Al-modified Orange Tree BC 3h/500°C showed the best performance for ammonia removal with an adsorption capacity of 1.72 mg/g. FTIR characterization showed that P = O bonds were formed after the adsorption of phosphorus by modified BC, N-H bonds were formed after ammonia adsorption. XPS analysis revealed that the key process of ammonia adsorption was the ion exchange between K⁺ and NH₄⁺. Phosphorus adsorption was related to oxidation and interaction between PO₄^3– and Fe³⁺. According to XRD results, ammonia was found in the form of potassium amide, while phosphorus was found in the form of iron hydrogen phosphates. The sorption isotherms showed that the Freundlich equation fits better for phosphorus adsorption, while the Langmuir equation fits better for ammonia adsorption. The simulated runoff infiltration experiment showed that 97.3% of ammonia was removed by Al-modified Orange tree BC 3h/500°C, and 92.9% of phosphorus was removed by Fe-modified Tea tree BC 2h/400°C.     

Egg production in the arrow squid Nototodarus gouldi (Cephalopoda: Ommastrephidae), fast and furious or slow and steady?

The process of reproductive maturation and egg release was examined in the temperate shelf squid Nototodarus gouldi. The energy allocation between somatic and reproductive growth from juvenile to mature adult was investigated throughout the life span to determine the underlying energetic strategy adopted by individuals. The relative weight of the mantle, fin and digestive gland remained unchanged during ovarian development, with no significant correlations found between the mantle length (ML)-gonad residuals and the ML-mantle (r=0.01, P>0.05), ML-fin (r=0.07, P>0.05) and ML-digestive gland (r=0.07, P>0.05) residuals. This suggested that energy was not being diverted away from somatic growth during sexual development, and consequently neither muscle nor digestive gland was being utilised as an energy store. Since squid in all maturity stages contained some food in their stomachs (e.g. 66.7% of mature animals), it is likely that the cost of maturation in this species is largely being met by food intake. The energy investment in reproductive tissues was relatively low (mean gonado-somatic index for mature individuals was 9.29% - 0.40%), indicating that only small amounts of energy were being allocated to reproduction at anyone point in time, which is characteristic of a multiple-spawning strategy. Furthermore, oviduct weight was not correlated with body size (r=0.256, P>0.05), suggesting that eggs are not stored for a single release. In all except one individual, ovary weight was consistently heavier than oviduct weight, suggesting that the ovary is not being depleted of oocytes as mature ova move into the oviducts. Additionally, the ovaries of mature females contained a range of oocyte sizes with discrete peaks, indicating a continued production and development of oocyte cohorts. The presence of some individuals with stretched empty oviducts is further evidence that the reproductive strategy of N. gouldi is slow and steady, with eggs possibly being released in discrete batches over a period of time.     

Mapping water chemical variables with spatially correlated errors

One of the most important considerations in many environmental studies is need to allow for correlations among the variables. Monitoring and analyzing relationships between chemical environmental parameters using spatial correlation based regression modelling is the main motivation of this applied study. For this purpose, some noticeable environmental parameters of data sets obtained from two lakes have been considered and the concentrations of chemical variables such as cadmium and nitrate have been appraised by a regression-based geostatistical methodology. The modelling procedure consists of two stages. In the first stage, spatial variables are analyzed via multi-linear regression and some relationships are provided. Next, by using the spatial auto-correlations of the residuals, a type of regression-based kriging procedure is applied. The capacity of the model for appraising the water chemical variables is also tested and performance comparisons with ordinary kriging are conducted. Finally, the applications showed that analyzing water chemical variables with spatially correlated errors is a convenient and applicable approach for assessing the environmental systems.     

A linear programming model of residuals management for integrated iron and steel production

This paper briefly describes a linear programming model designed to allow the exploration of questions surrounding the management of the environmental impacts of integrated iron and steel facilities. In particular, the model can show how plant discharges will change in the absence of specific legal restrictions or effluent charges, with such variables as product mix, steel-furnace type, casting technology, and the scrap-ore price ratio. In addition, the costs implied by placing restrictions on discharges of specific residuals (e.g., BOD, oil, suspended solids, particulates) may be estimated, or response to proposed effluent charges may be predicted.     

Trajectory of a jet in crossflow in a channel bend

Mixing in rivers is an important issue with many applications in water quality and water resource management. Mixing of effluents with ambient river water is especially important, particularly in river bends, where secondary circulation complicates the mixing process. By comparing measured trajectories from dye tests to velocimetry data measured with an acoustic Doppler velocimeter, this paper models the trajectory of a jet in an open channel bend using a modified formula for a jet trajectory in a straight crossflow. The original formula is shown to be insufficient for modeling the trajectory in the bend. Modifications are proposed using the position of the centre of the main secondary circulation cell to account for the bend effects. In the absence of secondary circulation, the modified formula reduces to the original formula. Once the secondary circulation has developed, the proposed formula is shown to have better residuals, lower root mean squared error, and higher \(R^2\) than the original formula.     

Evaluation of discrete host–parasitoid models for diamondback moth and Diadegma semiclausum field time population density series

The performance of discrete mathematical models to describe the population dynamics of diamondback moth (DBM) (Plutella xylostella L.) and its parasitoid Diadegma semiclausum was investigated. The parameter values for several well-known models (Nicholson–Bailey, Hassell and Varley, Beddington, Free and Lawton, May, Holling type 2, 3 and Getz and Mills functional responses) were estimated. The models were tested on 20 consecutive sets of time series data collected at 14 days interval for pest and parasitoid populations obtained from a highland cabbage growing area in eastern Kenya. Model parameters were estimated from minimized squared difference between the numerical solution of the model equations and the empirical data using Powell's method. Maximum calculated DBM growth rates varied between 0.02 and 0.07. The carrying capacity determined at 16.5 DBM/plant by the Beddington et al. model was within the range of field data. However, all the estimated parameter values relating to the parasitoid, including the instantaneous searching rate (0.07–0.28), per capita searching efficiency (0.20–0.27), search time (5.20–5.33), handling time (0.77–0.90), and parasitism aggregation index (0.33), were well outside the range encountered empirically. All models evaluated for DBM under Durbin–Watson criteria, except the May model, were not autocorrelated with respect to residuals. In contrast, the criteria applied to the parasitoid residuals showed strong autocorrelations. Thus, these models failed to estimate parasitoid dynamics. We conclude that the interactions of the DBM with its parasitoid cannot be explained by any of the models tested. Two factors may be associated with this failure. First, the parasitoid in this integrated biological control system may not be playing a major role in regulating DBM population. Second, and perhaps more likely, poor correlations reflect gross inadequacies in the theoretical assumptions that underlie the existing models.     

Field-scale roles of density, temperature, nitrogen, and predation on aphid population dynamics

Robust analyses of noisy, stage-structured, irregularly spaced, field-scale data incorporating multiple sources of variability and nonlinear dynamics remain very limited, hindering understanding of how small-scale studies relate to large-scale population dynamics. We used a novel, complementary Bayesian and frequentist state-space model analysis to ask how density, temperature, plant nitrogen, and predators affect cotton aphid (Aphis gossypii) population dynamics in weekly data from 18 field-years and whether estimated effects are consistent with small-scale studies. We found clear roles of density and temperature but not of plant nitrogen or predators, for which Bayesian and frequentist evidence differed. However, overall predictability of field-scale dynamics remained low. This study demonstrates stage-structured state-space model analysis incorporating bottom-up, top-down, and density-dependent effects for within-season (nearly continuous time), nonlinear population dynamics. The analysis combines Bayesian posterior evidence with maximum-likelihood estimation and frequentist hypothesis testing using average one-step-ahead residuals.     

松花江水中酚类化合物生物降解性的测定及QSBR研究

以松花江水中细菌为接种源,用碘量法分别测定了１８种酚类化合物的ＢＯＤ５值采用ＱＳＡＲ程序软件计算得分子量ＭＷ、分子体积ＭＶ、疏水性参数ｌｇＰ及电离常数ｐＫａ．用ＭＭＰ软件计算了四种分子连接性指数(２ｘ,４Ｘ,２ｘＶ及４ｘＶ)．对１８种及训练组中的１４种酚类化合物ＢＯＤＴ值分别与其结构参数进行了回归分析,得到如下最佳回归方程:应用所得ＱＳＢＲ模型,拟合了１８种化合物的ＢＯＤ５值,计算了残差,预测了实验组中４个化合物的ＢＯＤＴ值,并初步探讨了生物降解机理．