The application of generalized linear mixed models to multi-level sampling for insect population monitoring

Iwao's quadratic regression or Taylor's Power Law (TPL) are commonly used to model the variance as a function of the mean for sample counts of insect populations which exhibit spatial aggregation. The modeled variance and distribution of the mean are typically used in pest management programs to decide if the population is above the action threshold in any management unit (MU) (e.g., orchard, forest compartment). For nested or multi-level sampling the usual two-stage modeling procedure first obtains the sample variance for each MU and sampling level using ANOVA and then fits a regression of variance on the mean for each level using either Iwao or TPL variance models. Here this approach is compared to the single-stage procedure of fitting a generalized linear mixed model (GLMM) directly to the count data with both approaches demonstrated using 2-level sampling. GLMMs and additive GLMMs (AGLMMs) with conditional Poisson variance function as well as the extension to the negative binomial are described. Generalization to more than two sampling levels is outlined. Formulae for calculating optimal relative sample sizes (ORSS) and the operating characteristic curve for the control decision are given for each model. The ORSS are independent of the mean in the case of the AGLMMs. The application described is estimation of the variance of the mean number of leaves per shoot occupied by immature stages of a defoliator of eucalypts, the Tasmanian Eucalyptus leaf beetle, based on a sample of trees within plots from each forest compartment. Historical population monitoring data were fitted using the above approaches.     

A new algorithm for estimating the parameters of the spatial generalized linear mixed models

Non-Gaussian spatial responses are usually modeled using a spatial generalized linear mixed model with location specific latent variables. The likelihood function of this model cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. So far, several numerical algorithms to solve the problem of calculating maximum likelihood estimates of this model have been presented. In this paper to estimate the parameters an approximate method is considered and a new algorithm is introduced that is much faster than existing algorithms but just as accurate. This is called the Approximate Expectation Maximization Gradient algorithm. The performance of the proposed algorithm and is illustrated with a simulation study and on a real data set.     

Hierarchical linear mixed models in multi-stage sampling soil studies

The issue of variances of different soil variables prevailing at different sampling scales is addressed. This topic is relevant for soil science, agronomy and landscape ecology. In multi-stage sampling there are randomness components in each stage of sampling which can be taken into account by introducing random effects in analysis through the use of hierarchical linear mixed models (HLMM). Due to the nested sampling scheme, there are several hierarchical sub-models. The selection of the best model can be carried out through likelihood ratio tests (LRTs) or Wald tests, which are asymptotically equivalent under standard conditions. However, when the comparison leads to a restricted hypothesis of variance components, standard conditions are not maintained, which leads to more elaborated versions of LRTs. These versions are not disseminated among environmental scientists. The present study shows the modeling of soil data from a sampling where sites, fields within sites, transects within fields, and sampling points within transects were selected in order to take samples from different vegetation types (open and shade). For soil data, several sub-models were compared using Wald tests, classic LRTs and adjusted LRTs where the distribution of the test statistic under the null hypothesis is the Chi-square mixture of Chi-square distributions. The inclusion of random effects via HLMM and suggested by the latest version of LRT allowed us to detect effects of vegetation type on soil properties that were not detected under a classical ANOVA.     

Qualitative analysis of generalized volterra models

Generalized Volterra models are analyzed qualitatively to provide some information concerning their applicability as ecological-model estimators. For the general two-population system (including prey-predator, competitive, and other cases), the stability of the equilibrium points and other properties of the phase representation are investigated. For n-population systems, stability analysis is carried out mainly by means of several Liapunov functions. The persistence (or global stability of nontrivial equilibrium) of n-population systems is investigated, leading to an interaction-exclusion principle which implies restrictions on the interaction structure of the system, especially in the case of trophic systems.     

Relative stability of ecosystem linear models

A method to test the relative stability of ecosystem linear models is developed. This method uses the eigenvalue sensitivity to parameter perturbations to compute the relative stability of the model. The procedure is applied to the analysis of two models describing the ca;cium cycle in a forested watershed ecosystem and the magnesium cycle in a tropical rain forest respectively.     

Eigengroup analyses of linear ecosystem models

Eigenvalue analysis has been widely used for characterization of model ecosystems, and utilization of the total eigensystem information has been demonstrated for ecosystem models. Solution of the unique eigenvectors, termed eigengroups, associated with specified perturbation initial conditions allows proper assignment of the ecosystem model content to each exponential decay function. Such eigengroup solutions of Monte Carlo assigned perturbations are reported here for a nine-compartment tropical moist forest phosphorus model and for a set of seven six-compartment general nutrient cycling models. Confirmed by CSMP III STIFF numerical integration, results indicate that the dynamics of these multi-compartment models, each having many internal closed cycles, are adequately described by only one or two exponential decay functions, even at massive perturbation levels. For these models, conjugate complex noncritical eigenvalues were found to be common, but the decay rates of the envelopes of oscillation are consistently so rapid that system-intrinsic oscillations are undetectable. The techniques used here are presented as efficient means of identifying the transient response space of linear ecosystem models.     

An application of Bayesian variable selection to spatial concurrent linear models

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the spatial processes, but in applications the data may display strong nonstationary patterns. In this article, we propose a Bayesian variable selection approach based on wavelet tools to address this problem. The proposed approach does not involve any stationarity assumptions on the priors, and instead we impose a mixture prior directly on each wavelet coefficient. We introduce an option to control the priors such that high resolution coefficients are more likely to be zero. Computationally efficient MCMC procedures are provided to address posterior sampling, and uncertainty in the estimation is assessed through posterior means and standard deviations. Examples based on simulated data demonstrate the estimation accuracy and advantages of the proposed method. We also illustrate the performance of the proposed method for real data obtained through remote sensing.     

Analysis of chromium and copper by cathodic stripping voltammetry with mixed ligands

Cathodic adsorptive stripping voltammetry is one of the most sensitive analytical methods for ultratrace analysis. The detection limit is usually lower than 10⁻⁹ mol/L. Most adsorptive stripping procedures have been focused on the one ligand/one analyte approach. In order to reduce analysis time and sample volume, the possibility of simultaneously determining several metals by cathodic stripping voltammetry using a mixture of ligands was explored, e.g., by Colombo and van den Berg (1997). Here, we describe a new procedure for quantifying chromium and copper using 2,2′-bipyridine and 8-hydroxyquinoline (oxine). The effect of various operational parameters such as buffer type, ligand concentration, potential and time collection were assessed and optimized. Possible interferences by trace metals and organic matter were also investigated. Applicability for fresh water is illustrated. Electronic Publication     

Evaluating predictive errors of a complex environmental model using a general linear model and least square means

A general linear model (GLM) was used to evaluate the deviation of predicted values from expected values for a complex environmental model. For this demonstration, we used the default level interface of the regional mercury cycling model (R-MCM) to simulate epilimnetic total mercury concentrations in Vermont and New Hampshire lakes based on data gathered through the EPAs Regional Environmental Monitoring and Assessment Program (REMAP). The response variable for the GLM was defined as R-MCMs predictive error: the difference between observed mercury concentrations and modeled mercury concentrations in each lake. Least square means of the response variable are used as an estimate of the magnitude and significance of bias, i.e., a statistically discernable trend in predictive errors for a given lake type, e.g., acidic, stratified, or oligotrophic. Using our approach, we determined lake types where significant over-prediction and under-prediction of epilimnetic total mercury concentration was occurring, i.e., regions in parameter space where the model demonstrated significant bias was distinguished from regions where no significant bias existed. This technique is most effective for finding regions of parameter space where bias is significant. Drawing conclusions concerning regions that show no significant bias can be misleading. The significant interaction terms in the GLM demonstrated that addressing this problem using univariate statistical techniques would lead to a loss of important information.     

Comparison between linear and non-linear forms of pseudo-first-order and pseudo-second-order adsorption kinetic models for the removal of methylene blue by activated carbon

The best-fit equations of linear and non-linear forms of the two widely used kinetic models, namely pseudo-first-order and pseudo-second-order equations, were compared in this study. The experimental kinetics of methylene blue adsorption on activated carbon was used for this research. Both the correlation coefficient (R ²) and the normalized standard deviation Δq(%) were employed as error analysis methods to determine the best-fitting equations. The results show that the non-linear forms of pseudo-first-order and pseudo-second-order models were more suitable than the linear forms for fitting the experimental data. The experimental kinetics may have been distorted by linearization of the linear kinetic equations, and thus, the non-linear forms of kinetic equations should be primarily used to obtain the adsorption parameters. In addition, the Δq(%) method for error analysis may be better to determine the best-fitting model in this case.     

Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions

Two statistical modelling techniques, generalized additive models (GAM) and multivariate adaptive regression splines (MARS), were used to analyse relationships between the distributions of 15 freshwater fish species and their environment. GAM and MARS models were fitted individually for each species, and a MARS multiresponse model was fitted in which the distributions of all species were analysed simultaneously. Model performance was evaluated using changes in deviance in the fitted models and the area under the receiver operating characteristic curve (ROC), calculated using a bootstrap assessment procedure that simulates predictive performance for independent data. Results indicate little difference between the performance of GAM and MARS models, even when MARS models included interaction terms between predictor variables. Results from MARS models are much more easily incorporated into other analyses than those from GAM models. The strong performance of a MARS multiresponse model, particularly for species of low prevalence, suggests that it may have distinct advantages for the analysis of large datasets. Its identification of a parsimonious set of environmental correlates of community composition, coupled with its ability to robustly model species distributions in relation to those variables, can be seen as converging strongly with the purposes of traditional ordination techniques.     

Analysis of brood sex ratios: implications of offspring clustering

Generalized linear models (GLMs) are increasingly used in modern statistical analyses of sex ratio variation because they are able to determine variable design effects on binary response data. However, in applying GLMs, authors frequently neglect the hierarchical structure of sex ratio data, thereby increasing the likelihood of committing 'type I' error. Here, we argue that whenever clustered (e.g., brood) sex ratios represent the desired level of statistical inference, the clustered data structure ought to be taken into account to avoid invalid conclusions. Neglecting the between-cluster variation and the finite number of clusters in determining test statistics, as implied by using likelihood ratio-based L²-statistics in conventional GLM, results in biased (usually overestimated) test statistics and pseudoreplication of the sample. Random variation in the sex ratio between clusters (broods) can often be accommodated by scaling residual binomial (error) variance for overdispersion, and using F-tests instead of L²-tests. More complex situations, however, require the use of generalized linear mixed models (GLMMs). By introducing higher-level random effects in addition to the residual error term, GLMMs allow an estimation of fixed effect and interaction parameters while accounting for random effects at different levels of the data. GLMMs are first required in sex ratio analyses whenever there are covariates at the offspring level of the data, but inferences are to be drawn at the brood level. Second, when interactions of effects at different levels of the data are to be estimated, random fluctuation of parameters can be taken into account only in GLMMs. Data structures requiring the use of GLMMs to avoid erroneous inferences are often encountered in ecological sex ratio studies.     

Analysis of competition models in periodic medium

We propose special models (the so-called D-systems) with periodic delta-functions being used as the growth velocities of the populations. This allows to build, in a practically explicit form, corresponding Poincare mapping and to reveal a series of “paradoxical” phenomena and selection criteria in the dynamics of the competitors. For the analysis of non-autonomous models, new general principle of inheritance of a series of local properties by the global Poincare shift mapping is worked up. Specifically, key heritable properties are determined for non-autonomous competition models. The selection criterion for competitive selection, based on the concept of the universal allowance constant, is derived in this work.     

Use of principal component scores in multiple linear regression models for prediction of Chlorophyll-a in reservoirs

Chlorophyll-a is a well-accepted index for phytoplankton abundance and population of primary producers in an aquatic environment. The relationships between Chlorophyll-a and 16 chemical, physical and biological water quality variables in Çamlıdere reservoir (Ankara, Turkey) were studied by using principal component scores (PCS) in multiple linear regression analysis (MLR) to predict Chlorophyll-a levels. Principal component analysis was used to simplify the complexity of relations between water quality variables. Score values obtained by PC scores were used as independent variables in the multiple linear regression models. Two approaches were used in the present statistical analysis. In the first approach, only five selected score values obtained by PC analysis were used for the prediction of Chlorophyll-a levels and predictive success (R²) of the model found as 56.3%. In the second approach, where all score values obtained from the PC analysis were used as independent variables, predictive power was turned out to be 90.8%. Both approaches could be used to predict Chlorophyll-a levels in reservoirs successfully.     

Condition-dependent sex allocation by clones of a galling aphid

Local mate competition (LMC) has been postulated to be the primary factor of female-biased sex allocation. In animals such as aphids that exhibit seasonal alternations of clonal and sexual reproduction, there is a high possibility of intra-clonal mating and LMC. This possibility is more plausible for more fecund clones, but outbreeding is predicted for less fecund clones. We hypothesize that clones that are more fecund will gain higher fitness returns by reducing investment in males because of more intense LMC among clonal males. We tested this hypothesis by elucidating the clonal sex allocation patterns of the galling aphid Kaltenbachiella japonica, in which inbreeding and LMC appear to be common. Winged mothers that emerge from a gall, belonging to the same clone, produced males and sexual females asexually on a branch, without dispersing to other trees. The heavier the gall, the more winged mothers were produced from the gall. Individual mothers produced a constant number of males and a variable number of females. The clonal sex allocation to males was 39.8?%, on average, and decreased with increasing gall weight. This result showed that clones that were more fecund exhibited more female-biased sex allocation and thus supported our hypothesis. Furthermore, our results corroborated Stubblefield and Seger’s hypothesis for sex allocation in patch structure rather than Yamaguchi’s constant male hypothesis. We conclude that K. japonica clones are able to adjust their sex allocation patterns adaptively depending on the quality of resources in the galls.     

电化学氧化处理丙烯腈废水及对可生化性的提高

以丙烯腈废水为研究对象,进行废水预处理对提高废水的可生化性和后续好氧生物处理效率的研究。实验采用电化学氧化法对难降解丙烯腈废水处理效果进行了单因子试验,分析了电压、电解时间、氯离子质量浓度对废水色度及CODcr的去除效果,以及对废水可生化性的影响。实验结果显示,电化学氧化法在电压5V,pH为3.00,反应时间6h,搅拌速率为250r·min^-1,氯离子质量浓度为5000mg·L^-1的条件下,对CODCr1156mg·L^-1,色度512倍的丙烯腈废水中CODcr去除率达到60%,色度的去除率达到90%,并使废水的可生化性明显提高。CODCr去除率和色度去除率随电解时间、电压增加而增大,电解时间达5h、电压大于5V以后使水电解副反应更容易发生,对有机物的降解速率减小,同时随电解时间延长,能耗逐渐增大,处理成本增大;氯离子质量浓度对电解效果影响较大,适量增大氯离子质量浓度,可以提高CODCr的去除率。     

Evolutionary relationships of deep-sea mussels inferred by mitochondrial DNA sequences

In order to elucidate the evolutionary process of deep-sea Bathymodiolus mussels, we investigated the phylogenetic relationships of 16 species worldwide by analyzing nucleotide sequences of the mitochondrial COI and ND4 genes. Deep-sea mussels were clustered into three groups by basal trichotomous divergence. The first was composed of four species found in Japanese waters and one species from the Gulf of Mexico, which contain methanotrophic endosymbiotic bacteria. The second included nine species distributed in the West and East Pacific, Indian, and Atlantic Oceans. Members of the second group were trichotomously divided into the Indo-West Pacific, Atlantic, and East Pacific subclusters. The Indo-West Pacific subcluster was composed of three very closely related species with mutual genetic distances at the intraspecific level (av. 0.019 in COI and 0.009 in ND4 relative to av. 0.156 in COI and 0.265 in ND4 among Bathymodiolus species other than Cluster A species), suggesting some gene flow among these species. The third consisted of two West Pacific species. Species in the second and third groups contain mainly thioautotrophic endosymbionts, including some species harboring both methanotrophs and thioautotrophs.     

基于灰色-马尔可夫藕合模型的区域建设用地需求预测

建设用地需求的中长期准确预测是当前土地资源规划和利用的重点和难点。本文将灰色和马尔可夫两种预测模型相结合,建立灰色-马尔可夫藕合模型,以广东省揭阳市为例,对1997到2010年间主要建设用地规模进行了需求预测,同时与其它几种常规的预测方法进行了比较。结果表明,人文驱动力相关预测法误差相对较大,其中国内生产总值(GDP)相关法准确度要优于人口相关法。趋势线法计算简单,预测准确度也相对较高,但只适于短期预测。灰色预测法精确度较高,计算需要模型的支持、专业性强。灰色-马尔可夫预测法由于是对灰色预测的偏离值进行了纠正,因而准确度最高。尽管该方法需要大量数据的支持,计算量大,但仍是值得推荐的高准确度的区域建设用地的专业预测方法。     

Emergy and emergy algebra explained by means of ingenuous set theory

Emergy is an important concept that has originated several effects in ecology, systems ecology and sustainability science. Its communication, however, has always presented several problems, since it does not follow the same rules of conservation as other energy-based approaches. Attempts have been made to clarify emergy by means of more formal/mathematical approaches, but the problem persists. In this paper, we have introduced a view of emergy and of its algebra based on ingenuous set theory. By means of this simple tool, emergy can be defined as the set of solar exergy that is directly and indirectly necessary to make a product. The operation that correctly sums the emergy “carried” by the inputs to a process is the union. This definition and the operation of union are able to account for all the rules of emergy algebra.     

Modelling collective foraging by means of individual behaviour rules in honey-bees

An individual-oriented model is constructed which simulates the collective foraging behaviour of a colony of honey-bees, Apis mellifera. Each bee follows the same set of behavioural rules. Each rule consists of a set of conditions followed by the behavioural act to be performed if the conditions are fulfilled. The set of conditions comprises the state of external information available to the bee (e.g. the dancing of other bees) and internal information variables (like memorised location of a food source and homing motivation). The rules are partly observational (i.e. they capture the observable regularities between the present external information and the individual bee's behaviour), and partly involve hypothesised internal-state variables (e.g. abandoning tendency and homing motivation), because no observable (physiological) aspect has as yet been detected in the bee which correlates with changes in the internal motivation. Our aim is to obtain a set of rules that is necessary and sufficient for the generation of the collective foraging behaviour observed in real bees. We simulated an experiment performed by Seeley et al. in which a colony of honey-bees chooses between two nectar sources of different profitabilities which are switched at intervals. A good fit between observed and simulated collective forager patterns was obtained when the model included rules in which the bees (1) relied on the information acquired from previous flights to a source (e.g. profitability and time of day when the source was found), (2) used positional information obtained by attending recruitment dances and (3) did not abandon a (temporarily) deteriorated source too fast or too slowly. The significance of the following issues is discussed: the role of internal and external information, source profitability, the spatial precision of the dance communication, the ability to search for a source after the source position has been transmitted, the tendency to abandon a deteriorated source, and the concepts of scout, recruit, (un)employed forager, and foraging history. Received: 26 January 1998 / Accepted after revision: 16 May 1998