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 Management of Wildlife Disease

The spread of wildlife diseases is a major threat to livestock, human health, resource-based recreation, and biodiversity conservation (Cleaveland, Laurenson, and Taylor). The development of economically sound wildlife disease-management strategies requires an understanding of the links between ecological functions (e.g., disease transmission and wildlife dispersal) and economic choices, and the associated tradeoffs. Spatial linkages are particularly relevant. Yet while ecologists have long-argued that space is important (Hudson et al.), prior economic work has largely ignored spatial issues. For instance, Horan and Wolf analyzed a case study of bovine tuberculosis (bTB) in Michigan deer, a problem where the disease appears to be confined to a single, spatially confined, wildlife population—an island. But wildlife disease matters generally are not spatially confined. Barlow, in analyzing bTB in possums in New Zealand, accounted for immigration of susceptible possums into a disease reservoir. However, he modeled immigration as fixed and unaffected by management. Bicknell, Wilen, and Howitt, also focusing on possums in New Zealand, developed a model that incorporates simple density-dependent net migration. This allowed the authors to account for endogenous immigration when deriving optimal culling strategies.

Spatial and Temporal Spread of Bovine Tuberculosis in Wild White-Tailed Deer in Michigan

In 1975, a wild white-tailed deer infected with bovine tuberculosis was shot in the northeastern Lower Peninsula, Michigan. The shooting of a second infected deer in the same area in 1994 triggered ongoing disease surveillance in the region. By 2002, bovine tuberculosis had been confirmed in 12 Michigan counties: from 449 deer; two elk; 41 non-cervid wildlife; one captive cervid facility and 28 cattle herds. We analyzed geographic spread of disease since the surveillance began and investigated factors influencing the prevalence of disease within the infected area. These analyses reveal that 78 percent of tuberculous deer came from within a 1560 km2 'core' area, within which the prevalence of apparent disease averaged 2.5 percent. Prevalence declined dramatically outside of the core and was an order of magnitude lower 30 km from its boundary. This prevalence gradient was highly significant (P<0.0001) and did not alter over the 6 year surveillance period (P= 0.98). Within the core, deer density and supplemental feeding by hunters were positively and independently correlated with tuberculosis prevalence in deer. Together, these two factors explained 55 percent of the variation in prevalence. We conclude that bovine tuberculosis was already well established in the deer population in 1994, that the infected area has not expanded significantly since that time, and that deer over-abundance and food supplementation have both contributed to ongoing transmission of disease. Managers are currently enforcing prohibitions on deer feeding in the core and are working to lower deer numbers there through increased hunting pressure.

Spatial Relationships Among Young Cercocarpus ledifolius (Curlleaf Mountain Ylahogany)

This study analyzed spatial location patterns of Cercocarpus ledifolius Nutt. (curlleaf mountain mahogany) plants, classified as current-year seedling, established seedling, juvenile, and immature individuals, at a central Nevada study site. Most current-year seedlings were located in mahogany stands in which large, mature individuals had the greatest abundance. These stands had greater litter cover and a thicker layer of litter than areas with few current- year seedlings. Most established young Cercocarpus were located in adjacent Artemisia tridentata ssp. vaseyana (mountain big sagebrush) communities, or in infrequent canopy gaps between relatively few large, mature Cercocarpus. We discuss potential roles of plant litter, root growth characteristics, nurse plants, and herbivory in the establishment and renewal of Cercocarpus communities.

Determining spatial and temporal scales for management: lessons from whaling

Selection of the appropriate management unit is critical to the conservation of animal populations. Defining such units depends upon knowledge of population structure and upon the timescale being considered. Here, we examine the trajectory of eleven subpopulations of five species of baleen whales to investigate temporal and spatial scales in management. These subpopulations were all extirpated by commercial whaling, and no recovery or repopulation has occurred since. In these cases, time elapsed since commercial extinction ranges from four decades to almost four centuries. We propose that these subpopulations did not recover either because cultural memory of the habitat has been lost, because widespread whaling among adjacent stocks eliminated these as sources for repopulation, and/or because segregation following exploitation produced the abandonment of certain areas. Spatial scales associated with the extirpated subpopulations are frequently smaller than those typically employed in management. Overall, the evidence indicates that: (1) the time frame for management should be at most decadal in scope (i.e., <100 yr) and based on both genetic and nongenetic evidence of population substructure, and (2) at least some stocks should be defined on a smaller spatial scale than they currently are.

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.

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.

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.

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.

Generalizing the dynamic field theory of spatial cognition across real and developmental time scales

Within cognitive neuroscience, computational models are designed to provide insights into the organization of behavior while adhering to neural principles. These models should provide sufficient specificity to generate novel predictions while maintaining the generality needed to capture behavior across tasks and/or time scales. This paper presents one such model, the Dynamic Field Theory (DFT) of spatial cognition, showing new simulations that provide a demonstration proof that the theory generalizes across developmental changes in performance in four tasks—the Piagetian A-not-B task, a sandbox version of the A-not-B task, a canonical spatial recall task, and a position discrimination task. Model simulations demonstrate that the DFT can accomplish both specificity—generating novel, testable predictions—and generality—spanning multiple tasks across development with a relatively simple developmental hypothesis. Critically, the DFT achieves generality across tasks and time scales with no modification to its basic structure and with a strong commitment to neural principles. The only change necessary to capture development in the model was an increase in the precision of the tuning of receptive fields as well as an increase in the precision of local excitatory interactions among neurons in the model. These small quantitative changes were sufficient to move the model through a set of quantitative and qualitative behavioral changes that span the age range from 8 months to 6 years and into adulthood. We conclude by considering how the DFT is positioned in the literature, the challenges on the horizon for our framework, and how a dynamic field approach can yield new insights into development from a computational cognitive neuroscience perspective.

Tests of the Dynamic Field Theory and the Spatial Precision Hypothesis: Capturing a Qualitative Developmental Transition in Spatial Working Memory

This study tested a dynamic field theory (DFT) of spatial working memory and an associated spatial precision hypothesis (SPH). Between 3 and 6 years of age, there is a qualitative shift in how children use reference axes to remember locations: 3-year-olds’ spatial recall responses are biased toward reference axes after short memory delays, whereas 6-year-olds’ responses are biased away from reference axes. According to the DFT and the SPH, quantitative improvements over development in the precision of excitatory and inhibitory working memory processes lead to this qualitative shift. Simulations of the DFT in Experiment 1 predict that improvements in precision should cause the spatial range of targets attracted toward a reference axis to narrow gradually over development, with repulsion emerging and gradually increasing until responses to most targets show biases away from the axis. Results from Experiment 2 with 3- to 5-year-olds support these predictions. Simulations of the DFT in Experiment 3 quantitatively fit the empirical results and offer insights into the neural processes underlying this developmental change.

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.

Temporal and Spatial Patterns of Avifauna on Wetlands in the Vicinity of Bush Field Airport, Augusta, Georgia, USA

Responding to a U.S. Federal court order to improve discharged wastewater quality, Augusta, Georgia initiated development of artificial wetlands in 1997 to treat effluents. Because of the proximity to Augusta Regional Airport at Bush Field, the U.S. Federal Aviation Administration expressed concern for potential increased hazard to aircraft posed by birds attracted to these wetlands. We commenced weekly low-level aerial surveys of habitats in the area beginning January, 1998. Over a one-year period, 49 surveys identified approximately 42,000 birds representing 52 species, including protected Wood Storks and Bald Eagles, using wetlands within 8 km of the airport. More birds were observed during the mid-winter and fall/spring migratory seasons (1,048 birds/survey; October - April) than during the breeding/post-breeding seasons (394 birds/survey; May - September). In winter, waterfowl dominated the avian assemblage (65% of all birds). During summer, wading birds were most abundant (56% of all birds). Habitat changes within the artificial wetlands produced fish kills and exposed mudflats, resulting in increased use by wading birds and shorebirds. No aquatic birds were implicated in 1998 bird strikes, and most birds involved could safely be placed within songbird categories. Airport incident reports further implicated songbirds. These findings suggested that efforts to decrease numbers of songbirds on the airport property must be included in the development of a wildlife hazard management plan. Seasonal differences in site use among species groups should also be considered in any such plan. Other wetlands within 8 km of the airport supported as many or more birds than the artificial wetlands. With proper management of the artificial wetlands, it should be possible to successfully displace waterfowl and wading birds to other wetlands further from the airport.