Spatial variogram estimation from temporally aggregated seabird count data

Seabird abundance is an important indicator for assessing impact of human activities on the marine environment. However, data collection at sea is time consuming and surveys are carried out over several consecutive days for efficiency reasons. This study investigates the validity of aggregating those data over time to estimate a spatial variogram that is representative for spatial correlation in species abundance. For this purpose we simulate four-day surveys of seabird count data that contain spatial and temporal correlation arising from temporal changes in the spatial pattern of environmental conditions. Estimates of the aggregated spatial variogram are compared to a variogram that would arise when data were collected over a single day. The study reveals that, under changing environmental conditions over surveys days, aggregating data over a four-day survey increases both the non-spatial variation in the data and the scale of spatial correlation in seabird data. Next, the effect of using an aggregated variogram on the statistical power to test the significance of an impact is investigated. The impact concerns a case of establishing an offshore wind farm resulting in seabird displacement. The study shows that both overestimation and underestimation of statistical power occurs, with power estimates differing up to a factor of two. We conclude that the spatial variation in seabird abundance can be misrepresented by using temporally aggregated data. In impact studies, such misrepresentation can lead to erroneous assessments of the ability to detect impact.     

A diagnostic test for autocorrelation in increment-averaged data with application to soil sampling

Motivated by the problem of detecting spatial autocorrelation in increment- averaged data from soil core samples, we use the Cholesky decomposition of the inverse of an autocovariance matrix to derive a parametric linear regression model for autocovariances. In the absence of autocorrelation, the off-diagonal terms in the lower triangular matrix from the Cholesky decomposition should be identically zero, and so the regression coefficients should be identically zero. The standard F-test of this hypothesis and two bootstrapped versions of the test are evaluated as autocorrelation diagnostics via simulation. Size is assessed for a variety of heteroskedastic null hypotheses. Power is evaluated against autocorrelated alternatives, including increment-averaged Ornstein-Uhlenbeck and Matérn processes. The bootstrapped tests maintain approximately the correct size and have good power against moderately autocorrelated alternatives. The methods are applied to data from a study of carbon sequestration in agricultural soils.     

Measurement error causes scale-dependent threshold erosion of biological signals in animal movement data.

Recent advances in telemetry technology have created a wealth of tracking data available for many animal species moving over spatial scales from tens of meters to tens of thousands of kilometers. Increasingly, such data sets are being used for quantitative movement analyses aimed at extracting fundamental biological signals such as optimal searching behavior and scale-dependent foraging decisions. We show here that the location error inherent in various tracking technologies reduces the ability to detect patterns of behavior within movements. Our analyses endeavored to set out a series of initial ground rules for ecologists to help ensure that sampling noise is not misinterpreted as a real biological signal. We simulated animal movement tracks using specialized random walks known as Lévy flights at three spatial scales of investigation: 100-km, 10-km, and 1-km maximum daily step lengths. The locations generated in the simulations were then blurred using known error distributions associated with commonly applied tracking methods: the Global Positioning System (GPS), Argos polar-orbiting satellites, and light-level geolocation. Deviations from the idealized Lévy flight pattern were assessed for each track after incrementing levels of location error were applied at each spatial scale, with additional assessments of the effect of error on scale-dependent movement patterns measured using fractal mean dimension and first-passage time (FPT) analyses. The accuracy of parameter estimation (Lévy mu, fractal mean D, and variance in FPT) declined precipitously at threshold errors relative to each spatial scale. At 100-km maximum daily step lengths, error standard deviations of > or = 10 km seriously eroded the biological patterns evident in the simulated tracks, with analogous thresholds at the 10-km and 1-km scales (error SD > or = 1.3 km and 0.07 km, respectively). Temporal subsampling of the simulated tracks maintained some elements of the biological signals depending on error level and spatial scale. Failure to account for large errors relative to the scale of movement can produce substantial biases in the interpretation of movement patterns. This study provides researchers with a framework for understanding the limitations of their data and identifies how temporal subsampling can help to reduce the influence of spatial error on their conclusions.     

Modeling species-habitat relationships with spatially autocorrelated observation data.

Spatial autocorrelation in wildlife observation data arises when extrinsic environmental processes and patterns that influence the spatial distribution of wildlife are themselves spatially structured, or when species are subject to intrinsic population processes, causing contagion or dispersion effects. Territoriality, Allee effects, dispersal limitations, and social clustering are examples of intrinsic processes. Both forms of autocorrelation can violate the assumptions of generalized linear regression models, resulting in biased estimation of model coefficients and diminished predictive performance. Such consequences may be avoided for extrinsic autocorrelation when autocorrelated environmental variables are available for use as model covariates, whereas intrinsic spatial autocorrelation requires an alternative modeling approach. The autologistic model provides an approach suited to the binary observations often obtained in wildlife surveys, but its performance has not been tested across widely varying sampling intensities or strengths of intrinsic spatial structure. Here we use simulated data to test the autologistic model under a range of sampling conditions. The autologistic model obtains better fits and substantially better predictive performance than the standard logistic regression model over the full range of sampling designs and intensities tested. We provide a simple Bayesian implementation of the autologistic model, which until now has not been achieved with standard statistical software alone. A step-by-step procedure is given for characterizing and modeling spatial autocorrelation in binary observation data, along with computer code for fitting autologistic models in WinBUGS, a freeware Bayesian analysis package. This approach avoids normal approximations to the pseudo-likelihood, in contrast to previous Bayesian applications of the autologistic model. We provide a sample application of the autologistic model, fitted to survey data for a gliding marsupial in southeastern Australia.     

Geographic patterns of non-carpeted floor dust loading in Syracuse, New York (USA) homes

Residential floor dust loading was measured on the smooth floor surface of 488 houses in Syracuse, New York, during the summers of 2003 and 2004. Using U.S. Environmental Protection Agency (EPA) wipe methods, pre-weighed Ghost Wipes, Lead Wipes, or Whatman Filters were employed to collect duplicate samples from (predominantly) kitchens. The collection efficiency of the various media was determined from multiple wipe tests and side-by-side comparisons. The results were normalized and aggregated at the census tract level to determine whether spatial patterns of dust loading could be observed. Loading was found to be log-normally distributed, with a geometric mean value of 0.311 g m⁻² (29 mg of dust per square foot of floor); 95% of the observations fell in the range of 0.042–2.330 g m⁻² (4–216 mg foot⁻²). The sampling for floor dust loading shows some bias for day of the week in which visits to the residential properties were made. After a first-order correction for this effect, results were aggregated by census tract and mapped in a geographic information system (GIS); strong spatial patterns can be identified in an inverse distance weighted mapping. The geographic patterns exhibit a strong correlation with socio-economic/demographic covariates extracted from the 2000 census summaries. Dust mass on the floors is positively correlated with renter-occupied properties and family size; it is negatively correlated with measures of household income.     

On spline-based approaches to spatial linear regression for geostatistical data

For spatial linear regression, the traditional approach to capture spatial dependence is to use a parametric linear mixed-effects model. Spline surfaces can be used as an alternative to capture spatial variability, giving rise to a semiparametric method that does not require the specification of a parametric covariance structure. The spline component in such a semiparametric method, however, impacts the estimation of the regression coefficients. In this paper, we investigate such an impact in spatial linear regression with spline-based spatial effects. Statistical properties of the regression coefficient estimators are established under the model assumptions of the traditional spatial linear regression. Further, we examine the empirical properties of the regression coefficient estimators under spatial confounding via a simulation study. A data example in precision agriculture research regarding soybean yield in relation to field conditions is presented for illustration.     

Modeling resource selection using polytomous logistic regression and kernel density estimates

Wildlife resource selection studies typically compare used to available resources; selection or avoidance occurs when use is disproportionately greater or less than availability. Comparing used to available resources is problematic because results are often greatly influenced by what is considered available to the animal. Moreover, placing relocation points within resource units is often difficult due to radiotelemetry and mapping errors. Given these problems, we suggest that an animal’s resource use be summarized at the scale of the home range (i.e., the spatial distribution of all point locations of an animal) rather than by individual points that are considered used or available. To account for differences in use-intensity throughout an animal’s home range, we model resource selection using kernel density estimates and polytomous logistic regression. We present a case study of elk (Cervus elaphus) resource selection in South Dakota to illustrate the procedure. There are several advantages of our proposed approach. First, resource availability goes undefined by the investigator, which is a difficult and often arbitrary decision. Instead, the technique compares the intensity of animal use throughout the home range. This technique also avoids problems with classifying locations rigidly as used or unused. Second, location coordinates do not need to be placed within mapped resource units, which is problematic given mapping and telemetry error. Finally, resource use is considered at an appropriate scale for management because most wildlife resource decisions are made at the level of the patch. Despite the advantages of this use-intensity procedure, future research should address spatial autocorrelation and develop spatial models for ordered categorical variables.     

Composite likelihood approach to the regression analysis of spatial multivariate ordinal data and spatial compositional data with exact zero values

In many environmental and ecological studies, it is of interest to model compositional data. One approach is to consider positive random vectors that are subject to a unit-sum constraint. In landscape ecological studies, it is common that compositional data are also sampled in space with some elements of the composition absent at certain sampling sites. In this paper, we first propose a practical spatial multivariate ordered probit model for multivariate ordinal data, where the response variables can be viewed as the discretized non-negative compositions without the unit-sum constraint. We then propose a novel two-stage spatial mixture Dirichlet regression model. The first stage models the spatial dependence and the presence of exact zero values, and the second stage models all the non-zero compositional data. A maximum composite likelihood approach is developed for parameter estimation and inference in both the spatial multivariate ordered probit model and the two-stage spatial mixture Dirichlet regression model. The standard errors of the parameter estimates are computed by an estimate of the Godambe information matrix. A simulation study is conducted to evaluate the performance of the proposed models and methods. A land cover data example in landscape ecology further illustrates that accounting for spatial dependence can improve the accuracy in the prediction of presence/absence of different land covers as well as the magnitude of land cover compositions.     

Design-based estimation in environmental surveys with positional errors

The recent increased availability of information about the micro-geographic positions of population units in environmental surveys has led to important developments in spatial sampling methodologies and, as a result, has improved the estimation accuracy. In real data, however, information about the location of units is often affected by inaccuracy about their exact spatial positions, and these non-sampling errors can affect the estimation procedure. This paper aims to investigate the effects of positional errors on total estimation through a Monte-Carlo simulation study based on real populations of trees. Starting from perfect positioning, we examine two typical types of coarsening that frequently impact two different species of trees. The simulation results show that the exploitation of spatial information to estimate population totals continues to be relevant in the context of environmental surveys, even in the presence of inaccuracies.     

Effects of spatial autocorrelation and sampling design on estimates of protected area effectiveness

Estimating the effectiveness of protected areas (PAs) in reducing deforestation is useful to support decisions on whether to invest in better management of areas already protected or to create new ones. Statistical matching is commonly used to assess this effectiveness, but spatial autocorrelation and regional differences in protection effectiveness are frequently overlooked. Using Colombia as a case study, we employed statistical matching to account for confounding factors in park location and accounted for for spatial autocorrelation to determine statistical significance. We compared the performance of different matching procedures—ways of generating matching pairs at different scales—in estimating PA effectiveness. Differences in matching procedures affected covariate similarity between matched pairs (balance) and estimates of PA effectiveness in reducing deforestation. Independent matching yielded the greatest balance. On average 95% of variables in each region were balanced with independent matching, whereas 33% of variables were balanced when using the method that performed worst. The best estimates suggested that average deforestation inside protected areas in Colombia was 40% lower than in matched sites. Protection significantly reduced deforestation, but PA effectiveness differed among regions. Protected areas in Caribe were the most effective, whereas those in Orinoco and Pacific were least effective. Our results demonstrate that accounting for spatial autocorrelation and using independent matching for each subset of data is needed to infer the effectiveness of protection in reducing deforestation. Not accounting for spatial autocorrelation can distort the assessment of protection effectiveness, increasing type I and II errors and inflating effect size. Our method allowed improved estimates of protection effectiveness across scales and under different conditions and can be applied to other regions to effectively assess PA performance.     

A regression tree-based method for integrating land-cover and land-use data collected at multiple scales

As data sets of multiple types and scales proliferate, it will be increasingly important to be able to flexibly combine them in ways that retain relevant information. A case in point is Amazonia, a large, data-poor region where most whole-basin data sets are limited to understanding land cover interpreted through a variety of remote sensing techniques and sensors. A growing body of work, however, indicates that the future state of much of Amazonia depends on the land use to which converted areas are put, but land use in the tropics is difficult to assess from remotely sensed data alone. An earlier paper developed new snapshots of agricultural land use in this region using a statistical fusion of satellite data and agricultural census data, an underutilized ancillary data source available across Amazonia. The creation of these land-use maps, which have the spatial detail of a satellite image and the attribute information of an agricultural census, required the development of a new statistical technique for merging data sets at different scales and of fundamentally different data types. Here we describe and assess this nonlinear technique, which reinterprets existing land cover classifications by determining what categories are most highly related to the polygon land-use data across the study area. Although developed for this region, the technique appears to hold broad promise for the systematic fusion of multiple data sets that are closely related but of different origins. The figures in the printed version of this article appear in black and white. Color figures are available from the author upon request.     

Predictive vegetation modeling for conservation: impact of error propagation from digital elevation data.

The effect of digital elevation model (DEM) error on environmental variables, and subsequently on predictive habitat models, has not been explored. Based on an error analysis of a DEM, multiple error realizations of the DEM were created and used to develop both direct and indirect environmental variables for input to predictive habitat models. The study explores the effects of DEM error and the resultant uncertainty of results on typical steps in the modeling procedure for prediction of vegetation species presence/absence. Results indicate that all of these steps and results, including the statistical significance of environmental variables, shapes of species response curves in generalized additive models (GAMs), stepwise model selection, coefficients and standard errors for generalized linear models (GLMs), prediction accuracy (Cohen's kappa and AUC), and spatial extent of predictions, were greatly affected by this type of error. Error in the DEM can affect the reliability of interpretations of model results and level of accuracy in predictions, as well as the spatial extent of the predictions. We suggest that the sensitivity of DEM-derived environmental variables to error in the DEM should be considered before including them in the modeling processes.     

Imputing Unmeasured Explanatory Variables in Environmental Epidemiology With Application to Health Impact Analysis of Air Pollution

This paper presents the results of a reconsideration of earlier work that finds an association between daily hospital admissions for respiratory distress and daily concentrations of sulphate (lag 1) as well as daily maximum concentrations of ozone (lags 1 and 3). These associations are found even after clustering the data by hospital of admission and accounting for the effects of temperature. We use an adaptation of their generalized estimating equation technique for clustered data, that daily data being for southern Ontario summers from 1983 to 1988. Like them, we adjust for daily maximum temperatures. However, unlike the earlier work returned to ours includes daily average humidity as a potential explanatory variable in our model. Our analysis also differs from theirs in that we cluster the data by census subdivision to reduce the risk of confounding pollutant levels with population size within regions. Moreover, we log-transform the explanatory variables and then high-pass filter the resulting data. We also deviate from the earlier analysis by taking account of measurement error incurred in using surrogate measures of the explanatory variables. To do so we use new methodology designed for our study but of potential value in other applications. That methodology requires a spatial predictive distribution for the unmeasured explanatory variables. Each day about 700 missing measurements for each of these variables can then be imputed over the geographical domain of the study. With these imputations we get a measure of imputation error through the covariance of the predictive distribution. Along with the predictive distribution we require an impact model to link-up with the predictive distribution. We describe that model and show how it uses the imputed measurements of the missing values of the explanatory variables. We also show how through that model, uncertainty about these values is reflected in our analysis and in commensurate uncertainties in the inferences made. Apart from its substantive objectives, our analysis serves to test the new methods with the earlier results serving as a foil. The reassuring qualitative agreement between our findings and the earlier results seems encouraging.     

Kernel-based home range method for data with irregular sampling intervals

Studies of habitat selection and movements often use radio-tracking data for defining animal home ranges. Home ranges (HR) can be approximated by a utilization density distribution (UD) that instead of assuming uniform use of areas within HR boundary provides a probabilistic measure of animal space use. In reality, radio-tracking data contain periods of frequent autocorrelated observations interspersed with temporally more independent observations. Using such temporally irregular data directly may result in biased UD estimates, because areas that have been sampled intensively receive too much weight. The problem of autocorrelation has been tackled by resampling data with an appropriate time interval. However, resampling may cause a large reduction in the data set size along with a loss of information. Evidently, biased UD estimates or reduction in data may prejudice the results on animal habitat selection and movement. We introduce a new method for estimating UDs with temporally irregular data. The proposed method, called the time kernel, accounts for temporal aggregation of observations and gives less weight to temporally autocorrelated observations. A further extension of the method accounts also for spatially aggregated observations with relatively low weights given to observations that are both temporally and spatially aggregated. We test the behaviour of the time kernel method and its spatiotemporal version using simulated data. In addition, the method is applied to a data set of brown bear locations.     

Functional regression on remote sensing data in oceanography

The aim of this study is to propose the use of a functional data analysis approach as an alternative to the classical statistical methods most commonly used in oceanography and water quality management. In particular we consider the prediction of total suspended solids (TSS) based on remote sensing (RS) data. For this purpose several functional linear regression models and classical non-functional regression models are applied to 10 years of RS data obtained from medium resolution imaging spectrometer sensor to predict the TSS concentration in the coastal zone of the Guadalquivir estuary. The results of functional and classical approaches are compared in terms of their mean square prediction error values and the superiority of the functional models is established. A simulation study has been designed in order to support these findings and to determine the best prediction model for the TSS parameter in more general contexts.     

Uncertainty analyses for calibrating a soil carbon balance model to agricultural field trial data in Sweden and Kenya

How do additional data of the same and/or different type contribute to reducing model parameter and predictive uncertainties? Most modeling applications of soil organic carbon (SOC) time series in agricultural field trial datasets have been conducted without accounting for model parameter uncertainty. There have been recent advances with Monte Carlo-based uncertainty analyses in the field of hydrological modeling that are applicable, relevant and potentially valuable in modeling the dynamics of SOC. Here we employed a Monte Carlo method with threshold screening known as Generalized Likelihood Uncertainty Estimation (GLUE) to calibrate the Introductory Carbon Balance Model (ICBM) to long-term field trail data from Ultuna, Sweden and Machang’a, Kenya. Calibration results are presented in terms of parameter distributions and credibility bands on time series simulations for a number of case studies. Using these methods, we demonstrate that widely uncertain model parameters, as well as strong covariance between inert pool size and rate constant parameters, exist when root mean square simulation errors were within uncertainties in input estimations and data observations. We show that even rough estimates of the inert pool (perhaps from chemical analysis) can be quite valuable to reduce uncertainties in model parameters. In fact, such estimates were more effective at reducing parameter and predictive uncertainty than an additional 16 years time series data at Ultuna. We also demonstrate an effective method to jointly, simultaneously and in principle more robustly calibrate model parameters to multiple datasets across different climatic regions within an uncertainty framework. These methods and approaches should have benefits for use with other SOC models and datasets as well.     

Null models reveal preferential sampling, spatial autocorrelation and overfitting in habitat suitability modelling

Nowadays, species are driven to extinction at a high rate. To reduce this rate it is important to delineate suitable habitats for these species in such a way that these areas can be suggested as conservation areas. The use of habitat suitability models (HSMs) can be of great importance for the delineation of such areas. In this study MaxEnt, a presence-only modelling technique, is used to develop HSMs for 223 nematode species of the Southern Bight of the North Sea. However, it is essential that these models are beyond discussion and they should be checked for potential errors. In this study we focused on two categories (1) errors which can be attributed to the database such as preferential sampling and spatial autocorrelation and (2) errors induced by the modelling technique such as overfitting, In order to quantify these adverse effects thousands of nulls models were created. The effect of preferential sampling (i.e. some areas where visited more frequenty than others) was investigated by comparing model outcomes based from null models sampling the actual sampling stations and null models sampling the entire mapping area (Raes and ter Steege, 2007). Overfitting is exposed by a fivefold cross-validation and the influence of spatial autocorrelation is assessed by separating test and training sets in space. Our results clearly show that all these effects are present: preferential sampling has a strong effect on the selection of non-random species models. Crossvalidation seems to have less influence on the model selection and spatial autocorrelation is also strongly present. It is clear from this study that predefined thresholds are not readily applicable to all datasets and additional tests are needed in model selection.     

闽北次生常绿阔叶林主要树种空间分布格局及其应用研究

应用聚集度指标、Ｉｗａｏ 方程和Ｔａｙｌｏｒ 幂法则模型等测定方法,研究了闽北次生常绿阔叶林９ 个主要树种的空间分布格局．研究结果表明,闽北次生常绿阔叶林９ 个主要树种的空间分布呈聚集分布,分布的基本成份为个体群,个体群分布聚集．根据Ｉｗａｏ 的Ｍ＊ 与ｘ 的回归方程,计算了９ 个树种在不同密度和允许误差下的理论抽样数．     

Spatial structure effects on the detection of patches boundaries using local operators

Landscapes exhibit various degrees of spatial heterogeneity according to the differential intensity and interactions among processes and disturbances that they are subjected to. The management of these spatially dynamical landscapes requires that we can accurately map them and monitor the evolution of their spatial arrangement through time. Such a mapping requires first the delineation of various spatial features present in the landscape such as patches and their boundaries. However, there are several environmental (spatial variability) as well as technical (spatial resolution) factors that impair our ability to accurately delineate patches and their boundaries as polygons. Here, we investigate how the spatial structure and spatial resolution of the data affect the accuracy of detecting patches and their boundaries over simulated landscapes and real data. Simulated landscapes consisted of two patches with parameterized spatial properties (patches’ level of spatial autocorrelation, mean value and variance) separated by a boundary of known location. Real data allowed the investigation of a more complex landscape where there is a known transition between two forest domains with unknown spatial properties. Boundary locations are defined using the lattice-wombling edge detector at various aggregation levels and the degree of patch homogeneity is determined using Getis-Ord’s G*. Results show that boundary detection using a local edge detector is greatly affected by the spatial conditions of the data, namely variance, abruptness of the spatial gradient between two patches and patches’ level of spatial autocorrelation. They also suggest that data aggregation is not a panacea for bringing out the ecological process creating the patches and that indicators derived from local measures of spatial association can be complementary tools for analysing spatial structures affecting boundary delineation.

Sensitivity analysis on the ecological bias for Seoul tuberculosis data

In ecological studies, researchers often try to convey the analysis results to individual level based on aggregate data. In order to do this correctly, the possibility of ecological bias should be studied and addressed. One of the key ideas used to address the ecological bias issue is to derive the ecological model from the individual model and to check whether the parameter of interest in the individual model is identifiable in the ecological model. However, the procedure depends on unverifiable assumptions, and we recommend checking how sensitive the results are to these unverifiable assumptions. We analyzed the tuberculosis data that was collected in Seoul in 2005 using a spatial ecological regression model for the aggregate count data with spatial correlation, and found that the deprivation index is likely to have a small positive effect on the occurrence risk of tuberculosis in individual level in Seoul. We considered this finding in various aspects by performing in depth sensitivity analyses. In particular, our findings are shown to be robust to the distribution assumptions for the individual exposure and missing binary covariate across various scenarios.