Review of Applied Spatial Data Analysis with R by R. S. Bivand, E. J. Pebesma, and V. Gomez-Rubio

Most authors struggle to pick a title that adequately conveys all of the material covered in a book. When I first saw Applied Spatial Data Analysis with R, I expected a review of spatial statistical models and their applications in packages (libraries) from the CRAN site of R. The authors’ title is not misleading, but I was very pleasantly surprised by how deep the word “applied” is here. The first half of the book essentially covers how R handles spatial data. To some statisticians this may be boring. Do you want, or need, to know the difference between S3 and S4 classes, how spatial objects in R are organized, and how various methods work on the spatial objects? A few years ago I would have said “no,” especially to the “want” part. Just let me slap my EXCEL spreadsheet into R and run some spatial functions on it. Unfortunately, the world is not so simple, and ultimately we want to minimize effort to get all of our spatial analyses accomplished. The first half of this book certainly convinced me that some extra effort in organizing my data into certain spatial class structures makes the analysis easier and less subject to mistakes. I also admit that I found it very interesting and I learned a lot.

Estimating the extent of spatial association of Mycobacterium bovis infection in badgers in Ireland

Mycobacterium bovis infects the wildlife species badgers Meles meles who are linked with the spread of the associated disease tuberculosis (TB) in cattle. Control of livestock infections depends in part on the spatial and social structure of the wildlife host. Here we describe spatial association of M. bovis infection in a badger population using data from the first year of the Four Area Project in Ireland. Using second-order intensity functions, we show there is strong evidence of clustering of TB cases in each the four areas, i.e. a global tendency for infected cases to occur near other infected cases. Using estimated intensity functions, we identify locations where particular strains of TB cluster. Generalized linear geostatistical models are used to assess the practical range at which spatial correlation occurs and is found to exceed 6 in all areas. The study is of relevance concerning the scale of localized badger culling in the control of the disease in cattle.

Spatial modelling and prediction on river networks: up model, down model or hybrid?

Preservation of rivers and water resources is crucial in most environmental policies and many efforts are made to assess water quality. Environmental monitoring of large river networks are based on measurement stations. Compared to the total length of river networks, their number is often limited and there is a need to extend environmental variables that are measured locally to the whole river network. The objective of this paper is to propose several relevant geostatistical models for river modeling. These models use river distance and are based on two contrasting assumptions about dependency along a river network. Inference using maximum likelihood, model selection criterion and prediction by kriging are then developed. We illustrate our approach on two variables that differ by their distributional and spatial characteristics: summer water temperature and nitrate concentration. The data come from 141 to 187 monitoring stations in a network on a large river located in the Northeast of France that is more than 5000 km long and includes Meuse and Moselle basins. We first evaluated different spatial models and then gave prediction maps and error variance maps for the whole stream network.

Spatial methods for plot-based sampling of wildlife populations

Classical sampling methods can be used to estimate the mean of a finite or infinite population. Block kriging also estimates the mean, but of an infinite population in a continuous spatial domain. In this paper, I consider a finite population version of block kriging (FPBK) for plot-based sampling. The data are assumed to come from a spatial stochastic process. Minimizing mean-squared-prediction errors yields best linear unbiased predictions that are a finite population version of block kriging. FPBK has versions comparable to simple random sampling and stratified sampling, and includes the general linear model. This method has been tested for several years for moose surveys in Alaska, and an example is given where results are compared to stratified random sampling. In general, assuming a spatial model gives three main advantages over classical sampling: (1) FPBK is usually more precise than simple or stratified random sampling, (2) FPBK allows small area estimation, and (3) FPBK allows nonrandom sampling designs.

Spatial statistical models that use flow and stream distance

We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions.

Regional differences in the spatial and temporal heterogeneity of oceanographic habitat used by Steller sea lions

Over the past three decades, the decline and altered spatial distribution of the western stock of Steller sea lions (Eumetopias jubatus) in Alaska have been attributed to changes in the distribution or abundance of their prey due to the cumulative effects of fisheries and environmental perturbations. During this period, dietary prey occurrence and diet diversity were related to population decline within metapopulation regions of the western stock of Steller sea lions, suggesting that environmental conditions may be variable among regions. The objective of this study, therefore, was to examine regional differences in the spatial and temporal heterogeneity of oceanographic habitat used by Steller sea lions within the context of recent measures of diet diversity and population trajectories. Habitat use was assessed by deploying satellite-depth recorders and satellite relay data loggers on juvenile Steller sea lions (n = 45) over a five-year period (2000–2004) within four regions of the western stock, including the western, central, and eastern Aleutian Islands, and central Gulf of Alaska. Areas used by sea lions during summer months (June, July, and August) were demarcated using satellite telemetry data and characterized by environmental variables (sea surface temperature [SST] and chlorophyll a [chl a]), which possibly serve as proxies for environmental processes or prey. Spatial patterns of SST diversity and Steller sea lion population trends among regions were fairly consistent with trends reported for diet studies, possibly indicating a link between environmental diversity, prey diversity, and distribution or abundance of Steller sea lions. Overall, maximum spatial heterogeneity coupled with minimal temporal variability of SST appeared to be beneficial for Steller sea lions. In contrast, these patterns were not consistent for chl a, and there appeared to be an ecological threshold. Understanding how Steller sea lions respond to measures of environmental heterogeneity will ultimately be useful for implementing ecosystem management approaches and developing additional conservation strategies.

A Model-Based Approach for Making Ecological Inference from Distance Sampling Data

We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaike’s information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function.

Temporal and Spatial Variations of Ions, Isotopes and Agricultural Contaminants in Surface Waters and Groundwater of Nebraska's Rainwater Basin Wetland Region

The wetlands of south-central Nebraska’s Rainwater Basin region are considered of international importance as a habitat for millions of migratory birds, but are being endangered by agricultural practices. The Rainwater Basin extends across 17 counties and covers 4,000 square miles. The purpose of this study was to assemble baseline chemical data for several representative wetlands across the Rainwater Basin region, and determine the use of these chemical data for investigating groundwater recharge. Eight representative wetlands were chosen across the Rainwater Basin to monitor surface and groundwater chemistry. At each site, a shallow well and deep well were installed and sampled once in the summer of 2009 and again in the spring of 2010. Wetland surface water was sampled monthly from April, 2009 to May, 2010. Waters were analyzed for major ions, nutrients, pesticides and oxygen-18 and deuterium isotopes at the University of Nebraska Water Sciences Laboratory. Geochemical analysis of surface waters presents a range of temporal and spatial variations. Wetlands had variable water volumes, isotopic compositions, ion chemistries and agricultural contaminant levels throughout the year and, except for a few trends, theses variations cannot be predicted with certainty year-to-year or wetland-to-wetland. Isotopic compositions showed evaporation was a contributor to water loss, and thus, did impact water chemistry. Surface water nitrate concentrations ranged from <0.10 to 4.04 mg/L. The nitrate levels are much higher in the groundwater, ranging from <0.10 to 18.4 mg/L, and are of concern because they are found above the maximum contaminant level (MCL) of 10 mg/L. Atrazine concentrations in surface waters ranged from <0.05 to 10.3 ppb. Groundwater atrazine concentrations ranged from <0.05 to 0.28 ppb. The high atrazine concentrations in surface waters are of concern as they are above the MCL of 3 ppb, and the highest levels occur during the spring bird migration. Most sampled groundwaters had detectable tritium indicating a mix of modern (<5 to 10 years old) and submodern (older than 1950s) recharge. The groundwater also had differences in chemical and isotope composition, and in some cases, increased nitrate concentrations, between the two sampling periods. Modern groundwater tritium ages and changes in groundwater chemical and isotopic compositions may indicate connections with surface waters in the Rainwater Basin.

Contributions of demography and dispersal parameters to the spatial spread of a stage-structured insect invasion

Stage-structured models that integrate demography and dispersal can be used to identify points in the life cycle with large effects on rates of population spatial spread, information that is vital in the development of containment strategies for invasive species. Current challenges in the application of these tools include: (1) accounting for large uncertainty in model parameters, which may violate assumptions of ‘‘local’’ perturbation metrics such as sensitivities and elasticities, and (2) forecasting not only asymptotic rates of spatial spread, as is usually done, but also transient spatial dynamics in the early stages of invasion. We developed an invasion model for the Diaprepes root weevil (DRW; Diaprepes abbreviatus [Coleoptera: Curculionidae]), a generalist herbivore that has invaded citrus-growing regions of the United States. We synthesized data on DRW demography and dispersal and generated predictions for asymptotic and transient peak invasion speeds, accounting for parameter uncertainty. We quantified the contributions of each parameter toward invasion speed using a ‘‘global’’ perturbation analysis, and we contrasted parameter contributions during the transient and asymptotic phases. We found that the asymptotic invasion speed was 0.02–0.028 km/week, although the transient peak invasion speed (0.03– 0.045 km/week) was significantly greater. Both asymptotic and transient invasions speeds were most responsive to weevil dispersal distances. However, demographic parameters that had large effects on asymptotic speed (e.g., survival of early-instar larvae) had little effect on transient speed. Comparison of the global analysis with lower-level elasticities indicated that local perturbation analysis would have generated unreliable predictions for the responsiveness of invasion speed to underlying parameters. Observed range expansion in southern Florida (1992–2006) was significantly lower than the invasion speed predicted by the model. Possible causes of this mismatch include overestimation of dispersal distances, demographic rates, and spatiotemporal variation in parameter values. This study demonstrates that, when parameter uncertainty is large, as is often the case, global perturbation analyses are needed to identify which points in the life cycle should be targets of management. Our results also suggest that effective strategies for reducing spread during the asymptotic phase may have little effect during the transient phase. Includes Appendix.