Zero-inflated models with application to spatial count data

Count data arises in many contexts. Here our concern is with spatial count data which exhibit an excessive number of zeros. Using the class of zero-inflated count models provides a flexible way to address this problem. Available covariate information suggests formulation of such modeling within a regression framework. We employ zero-inflated Poisson regression models. Spatial association is introduced through suitable random effects yielding a hierarchical model. We propose fitting this model within a Bayesian framework considering issues of posterior propriety, informative prior specification and well-behaved simulation based model fitting. Finally, we illustrate the model fitting with a data set involving counts of isopod nest burrows for 1649 pixels over a portion of the Negev desert in Israel.     

Bayesian modelling of extreme wind speed at Cape Town,South Africa

In the framework of generalized extreme value (GEV) distribution, the frequentist and Bayesian methods have been used to analyse the extremes of annual maxima wind speed recorded by automatic weather stations in Cape Town, Western Cape, South Africa. In the frequentist approach, the GEV distribution parameters were estimated using maximum likelihood, whereas in the Bayesian method the Markov Chain Monte Carlo technique with the Metropolis–Hastings algorithm was used. The results show that the GEV model with trend in the location parameter appears to be a better model for annual maxima data. The paper also discusses a method to construct informative priors empirically using historical data of the underlying process from other weather stations. The results from the Bayesian analysis show that posterior inference might be affected by the choice of priors and hence by the distance between a weather station used to formulate the priors and the point of interest.     

Tropical deforestation in Madagascar: analysis using hierarchical,spatially explicit,Bayesian regression models

Establishing cause–effect relationships for deforestation at various scales has proven difficult even when rates of deforestation appear well documented. There is a need for better explanatory models, which also provide insight into the process of deforestation. We propose a novel hierarchical modeling specification incorporating spatial association. The hierarchical aspect allows us to accommodate misalignment between the land-use (response) data layer and explanatory data layers. Spatial structure seems appropriate due to the inherently spatial nature of land use and data layers explaining land use. Typically, there will be missing values or holes in the response data. To accommodate this we propose an imputation strategy. We apply our modeling approach to develop a novel deforestation model for the eastern wet forested zone of Madagascar, a global rain forest “hot spot”. Using five data layers created for this region, we fit a suitable spatial hierarchical model. Though fitting such models is computationally much more demanding than fitting more standard models, we show that the resulting interpretation is much richer. Also, we employ a model choice criterion to argue that our fully Bayesian model performs better than simpler ones. To the best of our knowledge, this is the first work that applies hierarchical Bayesian modeling techniques to study deforestation processes. We conclude with a discussion of our findings and an indication of the broader ecological applicability of our modeling style.     

建立组织外植体的共培养模型(in vitro)用于预测内分泌干扰效应(in vivo)：以黑头软口鲦(Pimephales promelas)的下丘脑-垂体-性腺（HPG）轴内分泌干扰作用为例

内分泌干扰物 （Endocrine Disrupting Compounds, EDCs）可以通过干扰下丘脑-垂体-性腺（HPG）轴来影响生殖系统。虽然目前已有筛选内分泌干扰物的体外检测方法,但这些方法在用于体内实验时却有着不稳定的准确性。本文记录了以黑头呆鱼（Pimephales promelas）的下丘脑-垂体-性腺轴与肝（HPG-L）的共培养组织作为组织外植体来模拟体内反应的结果。我们对成年鱼的大脑（下丘脑）,垂体,性腺和肝进行了单独和共同培养的检测来确定可以在体内重复的情况与组合。只有共培养体表现出去甲雄三烯醇酮对于雌二醇,睾酮和卵黄生成素生成趋势的影响。较低的暴露剂量会抑制激素生成,而较高的暴露剂量则会促进激素生成,形成U型作用曲线。这些数据表明下丘脑-垂体-性腺-肝轴的全部组织的共同培养可以作为体内实验与体外实验的连接,从而预测在完整生物体内内分泌系统的扰乱。本实验中以组织为基础的下丘脑-垂体-性腺-肝系统作为一个灵活的体内系统的解构版本得到了更好的实验控制。通过分离、审查和重组需要的组织,我们能够检测到生物系统功能与对于内分泌干扰物反应中的微小变化。
精选自Theresa K. Johnston, Edward Perkins, Duncan C. Ferguson, Donald M. Cropek. Tissue explant co-culture model of the hypothalamic-pituitary-gonadal-liver axis of the fathead minnow (Pimephales promelas) as a predictive tool for endocrine disruption. Environmental Toxicology and Chemistry: Volume 35, Issue 10, pages 2530–2541, October 2016. DOI: 10.1002/etc.3415
详情请见http://onlinelibrary.wiley.com/doi/10.1002/etc.3415/full
     

Bayesian testing for trend in a power model for clustered binary data

Developmental toxicity studies are widely used to investigate the potential risk of environmental hazards. In dose–response experiments, subjects are randomly allocated to groups receiving various dose levels. Tests for trend are then often applied to assess possible dose effects. Recent techniques for risk assessment in this area are based on fitting dose–response models. The complexity of such studies implies a number of non-trivial challenges for model development and the construction of dose-related trend tests, including the hierarchical structure of the data, litter effects inducing extra variation, the functional form of the dose–response curve, the adverse event at dam or at fetus level, the inference paradigm, etc. The purpose of this paper is to propose a Bayesian trend test based on a non-linear power model for the dose effect and using an appropriate model for clustered binary data. Our work is motivated by the analysis of developmental toxicity studies, in which the offspring of exposed and control rodents are examined for defects. Simulations show the performance of the method over a number of samples generated under typical experimental conditions.     

Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.     

Model averaging,missing data and multiple imputation: a case study for behavioural ecology

Model averaging, specifically information theoretic approaches based on Akaike’s information criterion (IT-AIC approaches), has had a major influence on statistical practices in the field of ecology and evolution. However, a neglected issue is that in common with most other model fitting approaches, IT-AIC methods are sensitive to the presence of missing observations. The commonest way of handling missing data is the complete-case analysis (the complete deletion from the dataset of cases containing any missing values). It is well-known that this results in reduced estimation precision (or reduced statistical power), biased parameter estimates; however, the implications for model selection have not been explored. Here we employ an example from behavioural ecology to illustrate how missing data can affect the conclusions drawn from model selection or based on hypothesis testing. We show how missing observations can be recovered to give accurate estimates for IT-related indices (e.g. AIC and Akaike weight) as well as parameters (and their standard errors) by utilizing ‘multiple imputation’. We use this paper to illustrate key concepts from missing data theory and as a basis for discussing available methods for handling missing data. The example is intended to serve as a practically oriented case study for behavioural ecologists deciding on how to handle missing data in their own datasets and also as a first attempt to consider the problems of conducting model selection and averaging in the presence of missing observations.     

An isobole-based statistical model and test for synergism/antagonism in binary mixture toxicity experiments

Synergism and antagonism are often defined in relation to the model of Concentration Addition (CA). Hence, it is vital for the conclusion of mixture toxicity studies to be able to test whether an observed deviation from CA reflects a true deviation or whether it is simply due to random variation. In this paper we consider a non-linear regression model for the classical ray designs for binary mixture experiments. The model combines dose–response curves for each mixture in the experiment with an isobole model, describing possible deviations from CA. The method allows us to test whether the chosen isobole model is reasonable for the data and to test the hypothesis of CA. Furthermore, it provides us with a measure of the degree of synergism/antagonism. The method is flexible since both the dose–response relationships and the isobole model can be chosen arbitrarily. We demonstrate the use of the method on datasets where combinations of pesticides are tested on a floating plant, Lemna minor, and an algae, Pseudokirchneriella subcapitata. Furthermore, we conduct a simulation study in order to explore the power with which a specific deviation from CA can be distinguished in different test-systems.     

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.     

Use of Surrogates to Predict the Stressor Response of Imperiled Species

Abstract: Rare or narrowly distributed species may be threatened by stressors to which they have never been exposed or for which data are very limited. In such cases the species response cannot be predicted on the basis of directly measured data, but may be inferred from the response of one or more appropriate surrogate species. Here, I propose a practical way to use the stressor response of one or more surrogate species to develop a working hypothesis or model of the stressor response of the target species. The process has 4 steps: (1) identify one or more candidate surrogate species, (2) model the relationship between the stressor and the response variable of interest for the surrogate species, (3) adapt the stressor–response relationship from the surrogate species to a model for the target species, possibly using Bayesian methods, and (4) incorporate additional data as they become available and adjust the response model of the target species appropriately. I applied the approach to an endangered fish species, the amber darter (Percina antesella), which is potentially threatened by urbanization. I used a Bayesian approach to combine data from a surrogate species (the bronze darter[Percina palmaris]) with available data for the amber darter to produce a model of expected amber darter response. Although this approach requires difficult decisions on the part of the manager, especially in the selection of surrogate species, its value lies in the fact that all assumptions are clearly stated in the form of hypotheses, which may be scrutinized and tested. It therefore provides a rational basis for instituting management policy even in the face of considerable uncertainty.     

Time-varying models for extreme values

We propose a new approach for modeling extreme values that are measured in time and space. First we assume that the observations follow a Generalized Extreme Value (GEV) distribution for which the location, scale or shape parameters define the space–time structure. The temporal component is defined through a Dynamic Linear Model (DLM) or state space representation that allows to estimate the trend or seasonality of the data in time. The spatial element is imposed through the evolution matrix of the DLM where we adopt a process convolution form. We show how to produce temporal and spatial estimates of our model via customized Markov Chain Monte Carlo (MCMC) simulation. We illustrate our methodology with extreme values of ozone levels produced daily in the metropolitan area of Mexico City and with rainfall extremes measured at the Caribbean coast of Venezuela.     

Constrained additive ordination

For several decades now, ecologists have sought to determine the shape of species' response curves and how they are distributed along unknown underlying gradients, environmental latent variables, or ordination axes. Its determination has important implications for both continuum theory and community analysis because many theories and models in community ecology assume that responses are symmetric and unimodal. This article proposes a major new technique called constrained additive ordination (CAO) that solves this problem by computing the optimal gradients and flexible response curves. It allows ecologists to see the response curves as they really are, against the dominant gradients. With one gradient, CAO is a generalization of constrained quadratic ordination (CQO; formerly called canonical Gaussian ordination or CGO). It supplants symmetric bell-shaped response curves in CQO with completely flexible smooth curves. The curves are estimated using smoothers such as the smoothing spline. Loosely speaking, CAO models are generalized additive models (GAMs) fitted to a very small number of latent variables. Being data driven rather than model driven, CAO allows the data to "speak for itself" and does not make any of the assumptions made by canonical correspondence analysis. The new methodology is illustrated with a hunting spider data set and a New Zealand tree species data set.     

Nutrient criteria for lakes,ponds, and reservoirs: A Bayesian TREED model approach

We develop regional-scale eutrophication models for lakes, ponds, and reservoirs to investigate the link between nutrients and chlorophyll-a. The Bayesian TREED (BTREED) model approach allows association of multiple environmental stressors with biological responses, and quantification of uncertainty sources in the empirical water quality model. Nutrient data for lakes, ponds, and reservoirs across the United States were obtained from the Environmental Protection Agency (EPA) National Nutrient Criteria Database. The nutrient data consist of measurements for both stressor variables (such as total nitrogen and total phosphorus), and response variables (such as chlorophyll-a), used in the BTREED model. Markov chain Monte Carlo (McMC) posterior exploration guides a stochastic search through a rich suite of candidate trees toward models that better fit the data. The Bayes factor provides a goodness of fit criterion for comparison of resultant models. We randomly split the data into training and test sets; the training data were used in model estimation, and the test data were used to evaluate out-of-sample predictive performance of the model. An average relative efficiency of 1.02 between the training and test data for the four highest log-likelihood models suggests good out-of-sample predictive performance. Reduced model uncertainty relative to over-parameterized alternative models makes the BTREED models useful for nutrient criteria development, providing the link between nutrient stressors and meaningful eutrophication response.     

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.     

Information-theory approach to allometric growth of marine organisms

Allometric growth investigations are usually conducted by fitting the allometric model (L) (y, x are morphometric characters and b the allometric exponent), which is quite simple both conceptually and mathematically, and its parameters are easy to estimate by linear regression. However b is not necessarily constant and it may change either continuously or abruptly at specific breakpoints; thus, the simple L model quite often fails to describe allometric growth successfully. In the current context, a better alternative is proposed, based on Kullback–Leibler (K-L) information theory and multi-model inference (MMI). Allometric growth was investigated in eight marine species: the bivalves Pecten jacobaeus and Pinna nobilis, the squids Todarodes sagittatus and Todaropsis eblanae, the crab Pachygrapsus marmoratus (females), the ghost shrimp Pestarella tyrrhena (males), and the fishes Trachurus trachurus and Sparus aurata. In each of the eight species, a pair of body parts was measured and the allometric growth of one body part in relation to the other (reference dimension) was studied, by fitting five different candidate models including: the simple allometric model, two models assuming that b changed continuously and two other assuming that b had a breakpoint. For each species, the ‘best’ model was selected by minimizing the small-sample, bias-corrected form of the Akaike Information Criterion. To quantify the plausibility of each model, given the data and the set of five models, the ‘Akaike weight’ w _i of each model was calculated; based on w _i the average model was estimated for each case. MMI is beneficial, more robust, and may reveal more information than the classical approach. As demonstrated with the given examples, estimation of b from the linear model, when it was not supported by the data, revealed some characteristic pitfalls, such as concluding positive allometry when there is actually negative or vice versa, or reporting allometry when the data in reality support isometric growth or vice versa.     

A Poisson–Gamma model for analysis of ecological non-negative continuous data

The statistical analysis of continuous data that is non-negative is a common task in quantitative ecology. An example, and our motivation, is the weight of a given fish species in a fish trawl. The analysis task is complicated by the occurrence of exactly zero observations. It makes many statistical methods for continuous data inappropriate. In this paper we propose a model that extends a Tweedie generalised linear model. The proposed model exploits the fact that a Tweedie distribution is equivalent to the distribution obtained by summing a Poisson number of gamma random variables. In the proposed model, both the number of gamma variates, and their average size, are modelled separately. The model has a composite link and has a flexible mean-variance relationship that can vary with covariates. We illustrate the model, and compare it to other models, using data from a fish trawl survey in south-east Australia.     

The territorial flight of male houseflies (Fannia canicularis L.)

Summary The heart rate (HR) of three male and five female European blackbirds (Turdus merula) was monitored by radiotelemetry under three conditions: in a dark cage, in a lighted cage, and in an outdoor aviary. In all three, the response to recorded bird song was tested.The resting HR in the cage ranged from 4.8 to 6.3 beats per second. The HR of all the birds changed in response to playback of conspecific song as well as of the songs of other species. In 68% of trials a typical biphasic HR curve was obtained, with acceleration followed by deceleration (Fig. 2). The time from stimulus onset to the second curve inflection (t _iII) averaged 15–18 s; this was significantly longer for conspecific than for heterospecific song. The parameter t _iII was used as a basic measure of the response.The reaction of the males was longer-lasting than that of the females. The possibility that this reflects the territorial role of the songs is discussed. Response durations were longest in the dark cage, and shortest in the aviary. The reason is thought to be the gradation in total stimulus input available to the bird.The results suggest that the HR response consists of an unspecific component (acceleration) plus a component specific to bird sounds (deceleration). At this fundamental level of stimulus processing it is possible to study reactions to single strophes not only in males, as with more traditional methods, but also in females and young birds.     

Sea level extremes in the U.S.-Affiliated Pacific Islands—a coastal hazard scenario to aid in decision analyses

The objective of this study is to provide a perspective on the extremes of sea-level variability and predictability for the U.S.-Affiliated Pacific Islands (USAPI) on seasonal time-scales. Based on the Generalized Extreme Value (GEV) model, the L-moments method has been used to estimate the model parameters. The bootstrap method has been used to define the exceedance probability level of upper and lower bounds of the return periods at the 90% confidence interval. On the basis of these return calculations and expected extremes of high sea level, the seasonal maxima of sea level and the varying likelihood of extreme events have been estimated. For analyzing the predictability of the extremes of sea-level, a canonical correlation analysis (CCA) statistical model has been developed. Findings reveal that there is seasonal climatology of extreme events in the vicinity of USAPI that are variable on temporal and spatial scales. Some of the islands (Yap and Saipan) display considerably higher seasonal extremes than the others for 20 to 100 year return periods because of typhoon-related storm surges. These surges are likely to cause huge tidal large sea-level inundations and increased erosion to low-lying atolls/islands and result in considerable damage to roads, harbors, unstable sandy beaches, and other major infrastructures. Finally, the need for evaluating the extreme events and associated typhoons from a regional perspective has been stressed for coastal hazard management decision analyses in the USAPI.     

Constrained ordination analysis with flexible response functions

Canonical correspondence analysis (CCA) is perhaps the most popular multivariate technique used by environmental ecologists for constrained ordination; it is an approximation to the maximum likelihood solution of the Gaussian response model. In this article, we look at the constrained ordination problem from a slightly different point of view and argue that it is this particular point of view that CCA implicitly adopts. This gives us additional insights into the nature of CCA. We then exploit the new perspective to generalize the Gaussian response model to incorporate more flexible response functions. A real example is presented to illustrate the use of the more flexible model.     

Costs and Benefits of Trap‐Neuter‐Release and Euthanasia for Removal of Urban Cats in Oahu,Hawaii

Our goal was to determine whether it is more cost‐effective to control feral cat abundance with trap‐neuter‐release programs or trap and euthanize programs. Using STELLA 7, systems modeling software, we modeled changes over 30 years in abundance of cats in a feral colony in response to each management method and the costs and benefits associated with each method . We included costs associated with providing food, veterinary care, and microchips to the colony cats and the cost of euthanasia, wages, and trapping equipment in the model. Due to a lack of data on predation rates and disease transmission by feral cats the only benefits incorporated into the analyses were reduced predation on Wedge‐tailed Shearwaters (Puffinus pacificus). When no additional domestic cats were abandoned by owners and the trap and euthanize program removed 30,000 cats in the first year, the colony was extirpated in at least 75% of model simulations within the second year. It took 30 years for trap‐neuter‐release to extirpate the colony. When the cat population was supplemented with 10% of the initial population size per year, the colony returned to carrying capacity within 6 years and the trap and euthanize program had to be repeated, whereas trap‐neuter‐release never reduced the number of cats to near zero within the 30‐year time frame of the model. The abandonment of domestic cats reduced the cost effectiveness of both trap‐neuter‐release and trap and euthanize. Trap‐neuter‐release was approximately twice as expensive to implement as a trap and euthanize program. Results of sensitivity analyses suggested trap‐neuter‐release programs that employ volunteers are still less cost‐effective than trap and euthanize programs that employ paid professionals and that trap‐neuter‐release was only effective when the total number of colony cats in an area was below 1000. Reducing the rate of abandonment of domestic cats appears to be a more effective solution for reducing the abundance of feral cats. Costos y Beneficios de Captura‐Esterilización‐Liberación y Eutanasia para la Remoción de Gatos Urbanos en Oahu, Hawaii