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.

Long-term recovery patterns of arctic tundra after winter seismic exploration

In response to the increasing global demand for energy, oil exploration and development are expanding into frontier areas of the Arctic, where slow-growing tundra vegetation and the underlying permafrost soils are very sensitive to disturbance. The creation of vehicle trails on the tundra from seismic exploration for oil has accelerated in the past decade, and the cumulative impact represents a geographic footprint that covers a greater extent of Alaska’s North Slope tundra than all other direct human impacts combined. Seismic exploration for oil and gas was conducted on the coastal plain of the Arctic National Wildlife Refuge, Alaska, USA, in the winters of 1984 and 1985. This study documents recovery of vegetation and permafrost soils over a two-decade period after vehicle traffic on snow-covered tundra. Paired permanent vegetation plots (disturbed vs. reference) were monitored six times from 1984 to 2002. Data were collected on percent vegetative cover by plant species and on soil and ground ice characteristics. We developed Bayesian hierarchical models, with temporally and spatially autocorrelated errors, to analyze the effects of vegetation type and initial disturbance levels on recovery patterns of the different plant growth forms as well as soil thaw depth. Plant community composition was altered on the trails by species-specific responses to initial disturbance and subsequent changes in substrate. Long-term changes included increased cover of graminoids and decreased cover of evergreen shrubs and mosses. Trails with low levels of initial disturbance usually improved well over time, whereas those with medium to high levels of initial disturbance recovered slowly. Trails on ice-poor, gravel substrates of riparian areas recovered better than those on ice-rich loamy soils of the uplands, even after severe initial damage. Recovery to pre-disturbance communities was not possible where trail subsidence occurred due to thawing of ground ice. Previous studies of disturbance from winter seismic vehicles in the Arctic predicted short-term and mostly aesthetic impacts, but we found that severe impacts to tundra vegetation persisted for two decades after disturbance under some conditions. We recommend management approaches that should be used to prevent persistent tundra damage.

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.

Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

A General Framework for the Analysis of Animal Resource Selection from Telemetry Data

We propose a general framework for the analysis of animal telemetry data through the use of weighted distributions. It is shown that several interpretations of resource selection functions arise when constructed from the ratio of a use and availability distribution. Through the proposed general framework, several popular resource selection models are shown to be special cases of the general model by making assumptions about animal movement and behavior. The weighted distribution framework is shown to be easily extended to readily account for telemetry data that are highly auto-correlated; as is typical with use of new technology such as global positioning systems animal relocations. An analysis of simulated data using several models constructed within the proposed framework is also presented to illustrate the possible gains from the flexible modeling framework. The proposed model is applied to a brown bear data set from southeast Alaska.

Results from the April 2009 Gulf of Alaska Line Transect Survey (GOALS) in the Navy Training Exercise Area

Little is known about the present-day occurrence of cetaceans found in offshore waters in the Gulf of Alaska; however, whaling records and a few recent surveys have shown this area to be important habitat. The U.S. Navy maintains a maritime training area in the central Gulf of Alaska, east of Kodiak Island, and has requested additional information on marine mammal presence and use of this area. To describe the occurrence and distribution of marine mammals in and around the U.S. Navy training area, a line transect visual and acoustic survey was conducted 10-20 April 2009 from the NOAA ship Oscar Dyson. The primary survey area encompassed nearshore and offshore pelagic waters of the central Gulf of Alaska. Survey lines were designed to provide equal coverage of the nearshore and offshore habitat.

Implantation of Subcutaneous Radio Transmitters in the Harbor Seal (Phoca vitulina)

Radio telemetry has become a standard tool for studying the behavior, physiology, life history traits, and population dynamics of marine mammals. Radio transmitters typically are attached to the hind flippers of pinnipeds or glued to the fur using marine epoxy or other cyanocrylare adhesives (Fedak et al. 1983, Bengtson 1993, Jeffries et al. 1993). Longterm data acquisition is difficult, however, because radio-flipper transmitters commonly tear from the webbing of the flipper and instruments that are glued to the fur are shed during the seasonal molt.

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.

Distance software: design and analysis of distance sampling surveys for estimating population size

1. Distance sampling is a widely used technique for estimating the size or density of biological populations. Many distance sampling designs and most analyses use the software Distance. 2. We briefly review distance sampling and its assumptions, outline the history, structure and capabilities of Distance, and provide hints on its use. 3. Good survey design is a crucial prerequisite for obtaining reliable results. Distance has a survey design engine, with a built-in geographic information system, that allows properties of different proposed designs to be examined via simulation, and survey plans to be generated. 4. A first step in analysis of distance sampling data is modeling the probability of detection. Distance contains three increasingly sophisticated analysis engines for this: conventional distance sampling, which models detection probability as a function of distance from the transect and assumes all objects at zero distance are detected; multiple-covariate distance sampling, which allows covariates in addition to distance; and mark–recapture distance sampling, which relaxes the assumption of certain detection at zero distance. 5. All three engines allow estimation of density or abundance, stratified if required, with associated measures of precision calculated either analytically or via the bootstrap. 6. Advanced analysis topics covered include the use of multipliers to allow analysis of indirect surveys (such as dung or nest surveys), the density surface modeling analysis engine for spatial and habitat-modeling, and information about accessing the analysis engines directly from other software. 7. Synthesis and applications. Distance sampling is a key method for producing abundance and density estimates in challenging field conditions. The theory underlying the methods continues to expand to cope with realistic estimation situations. In step with theoretical developments, state-of- the-art software that implements these methods is described that makes the methods accessible to practicing ecologists.

Demography and population viability of polar bears in the Gulf of Boothia, Nunavut

We estimated demographic parameters and harvest risks for polar bears (Ursus maritimus) inhabiting the Gulf of Boothia, Nunavut, from 1976 to 2000. We computed survival and abundance from capture–recapture and recovery data (630 marks) using a Burnham joint live–dead model implemented in program MARK. Annual mean total survival (including harvest) was 0.889 ± 0.179 ( x ± 1 SE) for cubs, 0.883 ± 0.087 for subadults (ages 1–4), 0.919 ± 0.044 for adult females, and 0.917 ± 0.041 for adult males. Abundance in the last 3 yr of study was 1,592 ± 361 bears. Mean size of newborn litters was 1.648 ± 0.098 cubs. By age 7, 0.97 ± 0.30 of available females were producing litters. Harvest averaged 38.4 ± 4.2 bears/year in the last 5 yr of study; however, the 2002–2007 kill averaged 56.4 bears/yr. We used a harvested Population Viability Analysis (PVA) to examine impacts of increasing rates of harvest. We estimated the current population growth rate, λH, to be 1.025 ± 0.032. Although this suggests the population is growing, progressive environmental changes may require more frequent population inventory studies to maintain the same levels of harvest risk.

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.

Double-Observer Line Transect Methods: Levels of Independence

Double-observer line transect methods are becoming increasingly widespread, especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain. The resulting data supplement conventional distance sampling data with two-sample mark–recapture data. Like conventional mark–recapture data, these have inherent problems for estimating abundance in the presence of heterogeneity. Unlike conventional mark–recapture methods, line transect methods use knowledge of the distribution of a covariate, which affects detection probability (namely, distance from the transect line) in inference. This knowledge can be used to diagnose unmodeled heterogeneity in the mark–recapture component of the data. By modeling the covariance in detection probabilities with distance, we show how the estimation problem can be formulated in terms of different levels of independence. At one extreme, full independence is assumed, as in the Petersen estimator (which does not use distance data); at the other extreme, independence only occurs in the limit as detection probability tends to one. Between the two extremes, there is a range of models, including those currently in common use, which have intermediate levels of independence. We show how this framework can be used to provide more reliable analysis of double-observer line transect data. We test the methods by simulation, and by analysis of a dataset for which true abundance is known. We illustrate the approach through analysis of minke whale sightings data from the North Sea and adjacent waters.

Contrasting patterns of genetic diversity at three different genetic markers in a marine mammal metapopulation

Many studies use genetic markers to explore population structure and variability within species. However, only a minority use more than one type of marker and, despite increasing evidence of a link between heterozygosity and individual fitness, few ask whether diversity correlates with population trajectory. To address these issues, we analyzed data from the Steller’s sea lion, Eumetiopias jubatus, where three stocks are distributed over a vast geographical range and where both genetic samples and detailed demographic data have been collected from many diverse breeding colonies. To previously published mitochondrial DNA(mtDNA) and microsatellite data sets,we have added new data for amplified fragment length polymorphism (AFLP) markers, comprising 238 loci scored in 285 sea lions sampled from 23 natal rookeries. Genotypic diversity was low relative to most vertebrates, with only 37 loci (15.5%) being polymorphic. Moreover, contrasting geographical patterns of genetic diversity were found at the three markers, with Nei’s gene diversity tending to be higher for AFLPs and microsatellites in rookeries of the western and Asian stocks, while the highest mtDNA values were found in the eastern stock. Overall, and despite strongly contrasting demographic histories, after applying phylogenetic correction we found little correlation between genetic diversity and either colony size or demography. In contrast, we were able to show a highly significant positive relationship between AFLP diversity and current population size across a range of pinniped species, even though equivalent analyses did not reveal significant trends for either microsatellites or mtDNA.

Health Assessment of Weddell Seals, Leptonychotes weddellii, in McMurdo Sound, Antarctica

The demography of Weddell seals in eastern McMurdo Sound, Antarctica, has been well studied during the past three decades (e.g. Stirling 1971; Siniff et al. 1977; Testa and Siniff 1987; Hastings and Testa 1998; Gelatt et al. 2001). Detailed life-history data are available on thousands of seals tagged as pups in McMurdo Sound, making this population a rich resource for wildlife health studies because health parameters can be evaluated in the light of reproductive histories and genetic relationships of several generations of tagged seals. Recently, evidence of exposure to diseases generally associated with domestic animals and feral wildlife has been detected in Antarctic wildlife (Austin and Webster 1993; Olsen et al. 1996; Gardner et al. 1997; Retamal et al. 2000; Foster et al. 2002) and this has generated concern and debate regarding the risks of disease introduction to Antarctic wildlife. Antibodies to viruses that have caused large die-offs in phocids in other areas of the world have been detected in Weddell seals (Bengtson et al. 1991), and there is a historical report of a mass die-off of crabeater seals that may have had a viral etiology (Laws and Taylor 1957).

Differential Expression of Immune Response Genes in Steller Sea Lions (Eumetopias jubatus): An Indicator of Ecosystem Health?

Characterization of the polygenic and polymorphic features of the Steller sea lion major histocompatibility complex (MHC) provides an ideal window for evaluating immunologic vigor of the population and identifying emergence of new genotypes that reflect ecosystem pressures. MHC genotyping can be used to measure the potential immunologic vigor of a population. However, since ecosystem-induced changes to MHC genotype can be slow to emerge, measurement of differential expression of these genes can potentially provide real-time evidence of immunologic perturbations. MHC DRB genes were cloned and sequenced using peripheral blood mononuclear leukocytes derived from 10 Steller sea lions from Southeast Alaska, Prince William Sound, and the Aleutian Islands. Nine unique DRB gene sequences were represented in each of 10 animals. MHC DRB gene expression was measured in a subset of six sea lions. Although DRB in genomic DNA was identical in all individuals, relative levels of expressed DRB mRNA was highly variable. Selective suppression of MHC DRB genes could be indicative of geographically disparate environmental pressures, thereby serving as an immediate and sensitive indicator of population and ecosystem health.