Jay M. Ver Hoef

A mixed-model moving-average approach to geostatistical modeling in stream networks

Spatial autocorrelation is an intrinsic characteristic in freshwater stream environments where nested watersheds and flow connectivity may produce patterns that are not captured by Euclidean distance. Yet, many common autocovariance functions used in geostatistical models are statistically invalid when Euclidean distance is replaced with hydrologic distance. We use simple worked examples to illustrate a recently developed moving-average approach used to construct two types of valid autocovariance models that are based on hydrologic distances. These models were designed to represent the spatial configuration, longitudinal connectivity, discharge, and flow direction in a stream network. They also exhibit a different covariance structure than Euclidean models and represent a true difference in the way that spatial relationships are represented. Nevertheless, the multi-scale complexities of stream environments may not be fully captured using a model based on one covariance structure. We advocate using a variance component approach, which allows a mixture of autocovariance models (Euclidean and stream models) to be incorporated into a single geostatistical model. As an example, we fit and compare mixed models, based on multiple covariance structures, for a biological indicator. The mixed model proves to be a flexible approach because many sources of information can be incorporated into a single model.

Slow climate velocities of mountain streams portend their role as refugia for cold-water biodiversity

Significance Many studies predict climate change will cause widespread extinctions of flora and fauna in mountain environments because of temperature increases, enhanced environmental variability, and invasions by nonnative species. Cold-water organisms are thought to be at particularly high risk, but most predictions are based on small datasets and imprecise surrogates for water temperature trends. Using large stream temperature and biological databases, we show that thermal habitat in mountain streams is highly resistant to temperature increases and that many populations of cold-water species exist where they are well-buffered from climate change. As a result, there is hope that many native species dependent on cold water can persist this century and mountain landscapes will play an important role in that preservation. The imminent demise of montane species is a recurrent theme in the climate change literature, particularly for aquatic species that are constrained to networks and elevational rather than latitudinal retreat as temperatures increase. Predictions of widespread species losses, however, have yet to be fulfilled despite decades of climate change, suggesting that trends are much weaker than anticipated and may be too subtle for detection given the widespread use of sparse water temperature datasets or imprecise surrogates like elevation and air temperature. Through application of large water-temperature databases evaluated for sensitivity to historical air-temperature variability and computationally interpolated to provide high-resolution thermal habitat information for a 222,000-km network, we estimate a less dire thermal plight for cold-water species within mountains of the northwestern United States. Stream warming rates and climate velocities were both relatively low for 1968–2011 (average warming rate = 0.101 °C/decade; median velocity = 1.07 km/decade) when air temperatures warmed at 0.21 °C/decade. Many cold-water vertebrate species occurred in a subset of the network characterized by low climate velocities, and three native species of conservation concern occurred in extremely cold, slow velocity environments (0.33–0.48 km/decade). Examination of aggressive warming scenarios indicated that although network climate velocities could increase, they remain low in headwaters because of strong local temperature gradients associated with topographic controls. Better information about changing hydrology and disturbance regimes is needed to complement these results, but rather than being climatic cul-de-sacs, many mountain streams appear poised to be redoubts for cold-water biodiversity this century.

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 Akaikes information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function.

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 Alaskas 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.

A comparison of the spatial linear model to Nearest Neighbor (k-NN) methods for forestry applications.

Forest surveys provide critical information for many diverse interests. Data are often collected from samples, and from these samples, maps of resources and estimates of aerial totals or averages are required. In this paper, two approaches for mapping and estimating totals; the spatial linear model (SLM) and k-NN (k-Nearest Neighbor) are compared, theoretically, through simulations, and as applied to real forestry data. While both methods have desirable properties, a review shows that the SLM has prediction optimality properties, and can be quite robust. Simulations of artificial populations and resamplings of real forestry data show that the SLM has smaller empirical root-mean-squared prediction errors (RMSPE) for a wide variety of data types, with generally less bias and better interval coverage than k-NN. These patterns held for both point predictions and for population totals or averages, with the SLM reducing RMSPE from 9% to 67% over some popular k-NN methods, with SLM also more robust to spatially imbalanced sampling. Estimating prediction standard errors remains a problem for k-NN predictors, despite recent attempts using model-based methods. Our conclusions are that the SLM should generally be used rather than k-NN if the goal is accurate mapping or estimation of population totals or averages.

Haul-Out Behavior of Harbor Seals (Phoca vitulina) in Hood Canal, Washington

The goal of this study was to model haul-out behavior of harbor seals (Phoca vitulina) in the Hood Canal region of Washington State with respect to changes in physiological, environmental, and temporal covariates. Previous research has provided a solid understanding of seal haul-out behavior. Here, we expand on that work using a generalized linear mixed model (GLMM) with temporal autocorrelation and a large dataset. Our dataset included behavioral haul-out records from archival and VHF radio tag deployments on 25 individual seals representing 61,430 seal hours. A novel application for increased computational efficiency allowed us to examine this large dataset with a GLMM that appropriately accounts for temporal autocorellation. We found significant relationships with the covariates hour of day, day of year, minutes from high tide and year. Additionally, there was a significant effect of the interaction term hour of day : day of year. This interaction term demonstrated that seals are more likely to haul out during nighttime hours in August and September, but then switch to predominantly daylight haul-out patterns in October and November. We attribute this change in behavior to an effect of human disturbance levels. This study also examined a unique ecological event to determine the role of increased killer whale (Orcinus orca) predation on haul-out behavior. In 2003 and 2005 these harbor seals were exposed to unprecedented levels of killer whale predation and results show an overall increase in haul-out probability after exposure to killer whales. The outcome of this study will be integral to understanding any changes in population abundance as a result of increased killer whale predation.

Using spatiotemporal statistical models to estimate animal abundance and infer ecological dynamics from survey counts

Ecologists often fit models to survey data to estimate and explain variation in animal abundance. Such models typically require that animal density remains constant across the landscape where sampling is being conducted, a potentially problematic assumption for animals inhabiting dynamic landscapes or otherwise exhibiting considerable spatiotemporal variation in density. We review several concepts from the burgeoning literature on spatiotemporal statistical models, including the nature of the temporal structure (i.e., descriptive or dynamical) and strategies for dimension reduction to promote computational tractability. We also review several features as they specifically relate to abundance estimation, including boundary conditions, population closure, choice of link function, and extrapolation of predicted relationships to unsampled areas. We then compare a suite of novel and existing spatiotemporal hierarchical models for animal count data that permit animal density to vary over space and time, including formulations motivated by resource selection and allowing for closed populations. We gauge the relative performance (bias, precision, computational demands) of alternative spatiotemporal models when confronted with simulated and real data sets from dynamic animal populations. For the latter, we analyze spotted seal (Phoca largha) counts from an aerial survey of the Bering Sea where the quantity and quality of suitable habitat (sea ice) changed dramatically while surveys were being conducted. Simulation analyses suggested that multiple types of spatiotemporal models provide reasonable inference (low positive bias, high precision) about animal abundance, but have potential for overestimating precision. Analysis of spotted seal data indicated that several model formulations, including those based on a log-Gaussian Cox process, had a tendency to overestimate abundance. By contrast, a model that included a population closure assumption and a scale prior on total abundance produced estimates that largely conformed to our a priori expectation. Although care must be taken to tailor models to match the study population and survey data available, we argue that hierarchical spatiotemporal statistical models represent a powerful way forward for estimating abundance and explaining variation in the distribution of dynamical populations.

Passive acoustic monitoring of the decline of Mexico's critically endangered vaquita.

The vaquita (Phocoena sinus) is the worlds most endangered marine mammal with approximately 245 individuals remaining in 2008. This species of porpoise is endemic to the northern Gulf of California, Mexico, and historically the population has declined because of unsustainable bycatch in gillnets. An illegal gillnet fishery for an endangered fish, the totoaba (Totoaba macdonaldi), has recently resurged throughout the vaquitas range. The secretive but lucrative wildlife trade with China for totoaba swim bladders has probably increased vaquita bycatch mortality by an unknown amount. Precise population monitoring by visual surveys is difficult because vaquitas are inherently hard to see and have now become so rare that sighting rates are very low. However, their echolocation clicks can be identified readily on specialized acoustic detectors. Acoustic detections on an array of 46 moored detectors indicated vaquita acoustic activity declined by 80% between 2011 and 2015 in the central part of the species range. Statistical models estimated an annual rate of decline of 34% (95% Bayesian credible interval -48% to -21%). Based on results from 2011 to 2014, the government of Mexico enacted and is enforcing an emergency 2-year ban on gillnets throughout the species range to prevent extinction, at a cost of US

A Bayesian hierarchical model of Antarctic fur seal foraging and pup growth related to sea ice and prey abundance

74 million to compensate fishers. Developing precise acoustic monitoring methods proved critical to exposing the severity of vaquitas decline and emphasizes the need for continual monitoring to effectively manage critically endangered species.

Discretized and Aggregated: Modeling Dive Depth of Harbor Seals from Ordered Categorical Data with Temporal Autocorrelation

We created a Bayesian hierarchical model (BHM) to investigate ecosystem relationships between the physical ecosystem (sea ice extent), a prey measure (krill density), predator behaviors (diving and foraging effort of female Antarctic fur seals, Arctocephalus gazella, with pups) and predator characteristics (mass of maternal fur seals and pups). We collected data on Antarctic fur seals from 1987/1988 to 1994/1995 at Seal Island, Antarctica. The BHM allowed us to link together predators and prey into a model that uses all the data efficiently and accounts for major sources of uncertainty. Based on the literature, we made hypotheses about the relationships in the model, which we compared with the model outcome after fitting the BHM. For each BHM parameter, we calculated the mean of the posterior density and the 95% credible interval. Our model confirmed others findings that increased sea ice was related to increased krill density. Higher krill density led to reduced dive intensity of maternal fur seals, as measured by dive depth and duration, and to less time spent foraging by maternal fur seals. Heavier maternal fur seals and lower maternal foraging effort resulted in heavier pups at 22 d. No relationship was found between krill density and maternal mass, or between maternal mass and foraging effort on pup growth rates between 22 and 85 days of age. Maternal mass may have reflected environmental conditions prior to the pup provisioning season, rather than summer prey densities. Maternal mass and foraging effort were not related to pup growth rates between 22 and 85 d, possibly indicating that food was not limiting, food sources other than krill were being used, or differences occurred before pups reached age 22 d.