Small Area Estimation of Proportions with Constraint for National Resources Inventory Survey

Motivated by the need to produce small area estimates for the National Resources Inventory survey, we develop a spatial hierarchical model based on the generalized Dirichlet distribution to construct small area estimators of compositional proportions in several mutually exclusive and exhaustive landcover categories. At the observation level, the standard design-based estimators of the proportions are assumed to follow the generalized Dirichlet distribution. After proper transformation of the design-based estimators, beta regression is applicable. We consider a logit mixed model for the expectation of the beta distribution, which incorporates covariates through fixed effects and spatial effect through a conditionally autoregressive process. In a design-based evaluation study, the proposed model-based estimators are shown to have smaller root-mean-square error and relative root-mean-square error than design-based estimators and multinomial model-based estimators. Supplementary materials accompanying this paper appear online.     

Two robust estimators of the cross‐variogram for multivariate geostatistical analysis of soil properties

If we wish to describe the coregionalization of two or more soil properties for estimation by cokriging then we must estimate and model their auto‐ and cross‐variogram(s). The conventional estimates of these variograms, obtained by the method‐of‐moments, are unduly affected by outlying data which inflate the variograms and so also the estimates of the error variance of cokriging predictions. Robust estimators are less affected. Robust estimators of the auto‐variogram and the pseudo cross‐variogram have previously been proposed and used successfully, but the multivariate problem of estimating the cross‐variogram robustly has not yet been tackled. Two robust estimators of the cross‐variogram are proposed. These use covariance estimators with good robustness properties. The robust estimators of the cross‐variogram proved more resistant to outliers than did the method‐of‐moments estimator when applied to simulated fields which were then contaminated. Organic carbon and water content of the soil was measured at 256 sites on a transect and the method‐of‐moments estimator, and the two robust estimators, were used to estimate the auto‐variograms and cross‐variogram from a prediction subset of 156 sites. The data on organic carbon included a few outliers. The method‐of‐moments estimator returned larger values of the auto‐ and cross‐variograms than did either robust estimator. The organic carbon content at the 100 validation sites on the transect was estimated by cokriging from the prediction data plus a set of variograms fitted to the method‐of‐moments estimates and two sets of variograms fitted to the robust estimates. The ratio of the actual squared prediction error to the cokriging estimate of the error variance was computed at each validation site. These results showed that cokriging using variograms obtained by the method‐of‐moments estimator overestimated the error variance of the predictions. By contrast, cokriging with the robustly estimated variograms gave reliable estimates of the error variance of the predictions.     

Estimation of Linear Models of Coregionalization by Residual Maximum Likelihood

Observations of ancillary soil properties spatially correlated to a soil property of interest may be used to increase the precision and reduce the sampling costs of a geostatistical survey. The relationship between such coregionalized properties must be expressed as a linear model of coregionalization but the conventional estimator of the linear model of coregionalization is biased unless the mean value of each property is constant across the study region. However, the mean value of a soil property may vary according to a spatial trend or a deterministic relationship with other factors which vary within the study region. We therefore propose that a linear mixed model should be fitted to coregionalized soil properties by residual maximum likelihood. This approach simultaneously fits spatial trends or deterministic relationships and random effects to the observations with minimum bias. We implement a residual maximum likelihood estimator for coregionalized properties and suggest a criterion to decide what order of spatial trend and which deterministic relationships should be included in the model. The effectiveness of the estimator is proved upon simulated data and upon observations of zinc and cadmium concentrations from the Swiss Jura.     

A Model-Based Approach to Designing a Fishery-Independent Survey

This paper uses Generalized Additive Models to evaluate model-based designs for wildlife abundance surveys where substantial pre-existing data are available. This is often the case in fisheries with historical catch and effort data. Compared to conventional stratified design or design-based designs, our model-based designs can be both efficient and flexible, for example in allowing uneven sampling due to survey logistics, and providing a general framework to answer specific design questions. As an example, we describe the design and preliminary implementation of a trawl survey for eleven fish species along the continental slope off South-East Australia.     

The Use of Calibration Weighting for Variance Estimation Under Systematic Sampling: Applications to Forest Cover Assessment

The purpose of this note is to propose a variance estimator under non-measurable designs that exploits the existence of an auxiliary variable well correlated with the survey variable of interest. Under non-measurable designs, the Sen–Yates–Grundy variance estimator generates a downward bias that can be reduced using a calibration weighting based on the auxiliary variable. Conditions of approximate unbiasedness for the resulting calibration estimator are given. The application to systematic sampling is considered. The proposal proves to be effective for estimating the variance of the forest cover estimator in remote sensing-based surveys, owing to the strong correlation between the reference data, available from a systematic sample, and the satellite map data, available for the whole population and hence exploited as an auxiliary variable. Supplementary materials accompanying this paper appear online.     

Model‐based analysis using REML for inference from systematically sampled data on soil

The general linear model encompasses statistical methods such as regression and analysis of variance (anova ) which are commonly used by soil scientists. The standard ordinary least squares (OLS) method for estimating the parameters of the general linear model is a design‐based method that requires that the data have been collected according to an appropriate randomized sample design. Soil data are often obtained by systematic sampling on transects or grids, so OLS methods are not appropriate. Parameters of the general linear model can be estimated from systematically sampled data by model‐based methods. Parameters of a model of the covariance structure of the error are estimated, then used to estimate the remaining parameters of the model with known variance. Residual maximum likelihood (REML) is the best way to estimate the variance parameters since it is unbiased. We present the REML solution to this problem. We then demonstrate how REML can be used to estimate parameters for regression and anova ‐type models using data from two systematic surveys of soil. We compare an efficient, gradient‐based implementation of REML (ASReml) with an implementation that uses simulated annealing. In general the results were very similar; where they differed the error covariance model had a spherical variogram function which can have local optima in its likelihood function. The simulated annealing results were better than the gradient method in this case because simulated annealing is good at escaping local optima.     

Models for Jointly Estimating Abundances of Two Unmarked Site-Associated Species Subject to Imperfect Detection

In ecological field surveys, it is often of interest to estimate the abundance of species. It is frequently the case that unmarked animals are counted on different sites over several time occasions. A natural starting point to model these data, while accounting for imperfect detection, is by using Royle’s N-mixture model (Biometrics 60:108–115, 2004). Subsequently, many multivariate extensions have been proposed to model communities as a whole. However, these approaches are used to study species richness and other community-level variables and do not focus on the relationship between two site-associated species. Here, we extend the N-mixture modelling framework to model two site-associated species abundances jointly and propose to measure the influence of one species’ abundance on the populations of the other and study how this changes over time and space. By including a new parameter in the abundance distribution of one of the species, linking it to abundance of the other, our proposed model treats extra variability as an effect induced by an associated species’ abundance and allows one to study how environmental covariates may affect this. Using results from simulation studies, we show that the model is able to recover true parameter estimates. We illustrate our approach using data from bald eagles and mallards obtained in the 2015 survey of the North American Breeding Bird Survey. By using the joint model, we were able to separate overdispersion from mallard-induced variability and hence what would be accounted for with a dispersion parameter in the univariate framework for the eagles was explained by covariates related to mallard abundance in the joint model. Our approach represents an attractive, yet simple, way of modelling site-associated species populations jointly. Conservation ecologists can use the approach to devise management strategies based on the strength of association between species, which may be due to direct interactions and/or environmental effects affecting both species’ populations. Also, mathematical ecologists can use this framework to develop tools for studying population dynamics under different scenarios. Supplementary materials accompanying this paper appear on-line.     

A design-based approach to the estimation of plant density using point-to-plant sampling

A relationship between plant density and the probability density function of the squared point-to-plant distance is found when a design-based approach is considered. The estimation of the probability density function (and consequently of plant density) is performed using a boundary kernel estimator. Accordingly, by means of a simulation study, the performance of the proposed estimator is evaluated with respect to some existing density estimators assuming some patterns of plant populations. Finally, an example from field data is considered.     

不同模型在渔业CPUE标准化中的比较分析

为了提高渔业数据单位捕捞努力量渔获量（catch per unite of effort,CPUE）标准化数据的质量和模型连续稳定预测能力,该文采用人工神经网络（artificial neural network,ANN）、回归树（regression trees,RT）、随机森林（random forest,RF）和支持向量机（support vector machine,SVM）等机器学习方法和传统的广义线性模型（generalized linear model,GLM）等方法,对2000－2013年大西洋大眼金枪鱼（Thunnus obesus）延绳钓CPUE数据进行标准化。采用平均绝对误差、平均均方误差、3种相关系数（Pearson's,Kendall's和Spearman's）和标准化均方误差等评价指标对不同模型标准化结果进行对比,寻找较优的标准化方法。研究结果表明,在验证数据集SVM方法得到的3种相关系数（0.596,0473和0.632）和RF（0.623,0.456,0.621）相似,高于RT(0.516,0.432和0.586)、ANN(0.428,0.249和0.365)和GLM(0.199,0.106和0.159)。SVM预测的均方误差（11.25）、平均绝对误差（2.107）和标准化均方误差（0.652）略低于RF（11.655,2.377和0.661）,明显低于RT（14.999,2.434和0.801）、ANN(16.692,2.883和0.823)和GLM（16.517,2.777和0.993）。各项指标揭示SVM方法要优于其他4种方法,RF次之,GLM计算结果在所有方法中最差,不适合渔业数据CPUE标准化。SVM和RF方法应该被优先考虑用于渔业数据CPUE标准化。研究结果为渔业资源管理和保护提供更好的支持。     

Model-Based Distance Sampling

Conventional distance sampling adopts a mixed approach, using model-based methods for the detection process, and design-based methods to estimate animal abundance in the study region, given estimated probabilities of detection. In recent years, there has been increasing interest in fully model-based methods. Model-based methods are less robust for estimating animal abundance than conventional methods, but offer several advantages: they allow the analyst to explore how animal density varies by habitat or topography; abundance can be estimated for any sub-region of interest; they provide tools for analysing data from designed distance sampling experiments, to assess treatment effects. We develop a common framework for model-based distance sampling, and show how the various model-based methods that have been proposed fit within this framework.     

Soil carbon content and relative abundance of high affinity H2-oxidizing bacteria predict atmospheric H2 soil uptake activity better than soil microbial community composition

Soil–atmosphere exchange of H₂ is controlled by gas diffusion and the microbial production and oxidation activities in soil. Among these parameters, the H₂ oxidation activity catalyzed by soil microorganisms harboring high affinity hydrogenase is the most difficult variable to parameterize because it is influenced by many unknown edaphic factors that shape microbial community structure and function. Here we seek to formulate a model combining microbiological and physicochemical variables to predict the H₂ oxidation rate (u) in soil. Soil sample replicates collected from a grassland and three forests exhibited different H₂ oxidation potentials. We examined the microbial community structure based on ribotyping analysis, the relative abundance of high affinity H₂-oxidizing bacteria (HOB) estimated by qPCR and soil physicochemical characteristics as predictors for u. A single linear regression parameterized by total carbon content and a multiple linear regression using total carbon content and HOB relative abundance in soil explained 66 and 92% of the variance in u, respectively. Microbial community composition based on 16S rRNA gene pyrosequencing profiles was not a reliable predictor for u. Indeed, we found that HOB are members of the rare biosphere, comprising less than 1% of total bacteria as estimated by qPCR. We confirmed this relationship of u with total carbon content and HOB by an independent soil survey of 14 samples collected from maize monocultures, grasslands, deciduous forests and larch plantations. Observations made from both soil surveys thus were combined to build a predictive model for u parameterized with total carbon content and HOB relative abundance. Our results show that molecular biogeochemistry is a potential approach to improve performance of classical H₂ surface flux models which estimate u empirically without considering variation in HOB distribution and activity in soil.     

Brown hyaenas on roads: Estimating carnivore occupancy and abundance using spatially auto-correlated sign survey replicates

Carnivore survey protocols that properly address spatial sampling and detectability issues are seldom feasible at a landscape-scale. This limits knowledge of large-scale patterns in distribution, abundance and their underlying determinants, hindering conservation of globally threatened carnivore populations. Occupancy analysis of data from logistically efficient sign surveys along consecutive road segments (spatially auto-correlated replicates) offers a potential solution. We adapted and applied this newly-developed method over 62,979 km² of human-modified land in South Africa. Our aims were to (1) generate unbiased estimates of brown hyaena occupancy and abundance (2) investigate two suspected determinants of occupancy using a combination of biological and socio-economic sampling techniques, and (3) use simulations to evaluate the effort required for abundance and occupancy estimates with acceptable bias, precision and power. Brown hyaena occupancy was estimated at 0.748 (±SE 0.1), and estimated overall density in agricultural land (0.15/100 km², ±SE 0.08) was an order of magnitude lower than in protected areas. Positive attitudes to carnivores and presence of wildlife farms exerted strong positive effects on occupancy, so changes in these factors may well exert monotonic impacts on local metapopulation status. Producing reliable occupancy and abundance estimates would require ?6 replicates and ?12 replicates per site respectively. Detecting 50% and 30% declines in brown hyaena occupancy with adequate power would require five annual surveys at ?65 sites and ?125 sites respectively. Our results suggest that protocols based on spatially auto-correlated sign survey replicates could be used to monitor carnivore populations at large, and possibly even country-wide spatial scales.     

Cost-effective abundance estimation of rare animals: Testing performance of small-boat surveys for killer whales in British Columbia

Top predators are often rare, subject to anthropogenic mortality, and possess life-history traits that make them inherently vulnerable to extinction. IUCN criteria recognise populations as Critically Endangered when abundance is <250 mature individuals, but estimating abundance of rare species can be more challenging than for common ones. Cost-effective methods are needed to provide robust abundance estimates. In marine environments, small boats are more widely accessible than large ships for researchers conducting sightings surveys with limited funds, but studies are needed into efficacy of small-boat surveys. This study compares line transect and mark-recapture estimates from small-boat surveys in summer 2004 and 2005 for ‘northern resident’ killer whales in British Columbia to true population size, known from censuses conducted by Fisheries and Oceans Canada. The line transect estimate of 195 animals (95% CI 27-559) used model averaging to incorporate uncertainty in the detection function, while the mark-recapture estimate of 239 animals (CI 154-370) used a simple two-sample Chapman estimator. Both methods produced estimates close to the true population size, which numbered 219 animals in 2004 and 235 in 2006, but both suffered from the small sample sizes and violations of some model assumptions that will vex most pilot studies of rare species. Initial abundance estimates from relatively low-cost surveys can be thought of as hypotheses to be tested as new data are collected. For species of conservation concern, any cost-effective attempt to estimate absolute abundance will assist status assessments, as long as estimates are presented with appropriate caveats.     

Hierarchical models of animal abundance and occurrence

Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.     

Comparison of survey estimates of the finite population variance

The Environmental Monitoring and Assessment Program (EMAP) of the U.S. Environmental Protection Agency has conducted several probability surveys of aquatic resources. Such surveys usually have unequal probability of including population elements in the sample. The Northeast lakes survey, which motivated this study of variance estimation, was such a survey. We examine ten estimators for the finite population variance using a Monte Carlo factorial experiment that considers three population characteristics. The results show that the correlation between the inclusion probabilities and the response is the most important factor that differentiates the estimators. Under conditions of low correlation (approximately <0.4), a common feature in environmental surveys, the sample variance is best, elsewhere, two ratio estimators, one based on consistency and the Horvitz-Thompson Theorem (HT) and the other based on the Yates-Grundy form, behave similarly and best.     

A Bayesian Approach to Estimating Agricultural Yield Based on Multiple Repeated Surveys

Forecasting the end-of-year crop yield is critical for agricultural decision-making and inherently difficult. Historically, a panel of commodity specialists known as the Agricultural Statistics Board convene regularly to set estimates based on expert review of a combination of survey data and administrative/auxiliary information. To make this process less subjective and more repeatable, we develop a Bayesian hierarchical model that produces superior yield forecasts/estimates, while quantifying different sources of uncertainty. The proposed hierarchical model naturally combines information from multiple monthly surveys measured on different temporal supports, including a field measurement survey and two farmer interview surveys. The dependence between the monthly updated surveys and the serial dependence of the annual yield are incorporated at different levels of the hierarchy. The effectiveness of our approach is demonstrated through an application from the US Department of Agriculture. Empirical results indicate that the hierarchical model produces superior forecasts to both the panel of experts and the composite estimator developed by Keller and Olkin (Technical Report, National Agricultural Statistics Service, 2002), while providing an accurate measure of uncertainty.     

Assessing the Impacts of Time-to-Detection Distribution Assumptions on Detection Probability Estimation

Abundance estimates from animal point-count surveys require accurate estimates of detection probabilities. The standard model for estimating detection from removal-sampled point-count surveys assumes that organisms at a survey site are detected at a constant rate; however, this assumption can often lead to biased estimates. We consider a class of N-mixture models that allows for detection heterogeneity over time through a flexibly defined time-to-detection distribution (TTDD) and allows for fixed and random effects for both abundance and detection. Our model is thus a combination of survival time-to-event analysis with unknown-N, unknown-p abundance estimation. We specifically explore two-parameter families of TTDDs, e.g., gamma, that can additionally include a mixture component to model increased probability of detection in the initial observation period. Based on simulation analyses, we find that modeling a TTDD by using a two-parameter family is necessary when data have a chance of arising from a distribution of this nature. In addition, models with a mixture component can outperform non-mixture models even when the truth is non-mixture. Finally, we analyze an Ovenbird data set from the Chippewa National Forest using mixed effect models for both abundance and detection. We demonstrate that the effects of explanatory variables on abundance and detection are consistent across mixture TTDDs but that flexible TTDDs result in lower estimated probabilities of detection and therefore higher estimates of abundance.Supplementary materials accompanying this paper appear on-line.     

Bayesian Spatial Point Process Modeling of Line Transect Data

This paper develops a Bayesian approach for spatial inference on animal density from line transect survey data. We model the spatial distribution of animals within a geographical area of interest by an inhomogeneous Poisson process whose intensity function incorporates both covariate effects and spatial smoothing of residual variation. Independently thinning the animal locations according to their estimated detection probabilities results into another spatial Poisson process for the sightings (the observations). Prior distributions are elicited for all unknown model parameters. Due to the sparsity of data in the application we consider, eliciting sensible prior distributions is important in order to get meaningful estimation results. A reversible jump Markov Chain Monte Carlo (MCMC) algorithm for simulation of the posterior distribution is developed. We present results for simulated data and a real data set of minke whale pods from Antarctic waters. The main advantages of our method compared to design-based analyses are that it can use data arising from sources other than specifically designed surveys and its ability to link covariate effects to variation of animal density. The Bayesian paradigm provides a coherent framework for quantifying uncertainty in estimation results.     

Small scale digital soil mapping in Southeastern Kenya

Digital soil mapping techniques appear to be an interesting alternative for traditional soil survey techniques. However, most applications deal with (semi-)detailed soil surveys where soil variability is determined by a limited number of soil forming factors. The question that remains is whether digital soil mapping techniques are equally suitable for exploratory or reconnaissance soil surveys in more extensive areas with limited data availability. We applied digital soil mapping in a 13,500 km² study area in Kenya with the main aim to create a reconnaissance soil map to assess clay and soil organic carbon contents in terraced maize fields. Soil spatial variability prediction was based on environmental correlation using the concepts of the soil forming factors equation. During field work, 95 composite soil samples were collected. Auxiliary spatially exhaustive data provided insight on the spatial variation of climate, land cover, topography and parent material. The final digital soil maps were elaborated using regression kriging. The variance explained by the regression kriging models was estimated as 13% and 37% for soil organic carbon and clay respectively. These results were confirmed by cross-validation and provide a significant improvement compared to the existing soil survey.     

A practical two‐step approach for mixed model‐based kriging,with an application to the prediction of soil organic carbon concentration

Soil scientists often use prediction models to obtain values at unsampled locations. The spatial variation in the soil is best captured by using the empirical best linear unbiased predictor (EBLUP) based on a restricted maximum likelihood (REML) approach that efficiently exploits available data on both mean trends and correlation structures. We proposed a practical two‐step implementation of the REML approach for model‐based kriging, exemplified by predicting soil organic carbon (SOC) concentrations in mineral soils in Estonia from the large‐scale digital soil map information and a previously established prediction model. The prediction model was a linear mixed model with soil type, physical clay content (particle size < 0.01 mm) and A‐horizon thickness as fixed effects and site, transect, plot, year, year‐transect random intercepts and site‐specific random slopes for clay content. We used only the site‐specific intercept EBLUPs for estimating spatial correlation parameters as they described most of the variation in the random effects (86.8%). Fitting an exponential correlation model to these EBLUPs resulted in an estimated range of 10.5 km and the estimated proportion of the variance from the nugget effect was 0.23. The results of a simulation study showed a downwards bias that decreased with sample size. The results were validated through an external dataset, resulting in root mean square errors (RMSE) of 1.06 and 1.07% for the two‐step approach for kriging and the model with only fixed effects (no kriging), respectively. These results indicate that using the two‐step approach for kriging may improve prediction.