Peter L. Boveng

QUASI‐POISSON VS. NEGATIVE BINOMIAL REGRESSION: HOW SHOULD WE MODEL OVERDISPERSED COUNT DATA?

Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. While they often give similar results, there can be striking differences in estimating the effects of covariates. We explain when and why such differences occur. The variance of a quasi-Poisson model is a linear function of the mean while the variance of a negative binomial model is a quadratic function of the mean. These variance relationships affect the weights in the iteratively weighted least-squares algorithm of fitting models to data. Because the variance is a function of the mean, large and small counts get weighted differently in quasi-Poisson and negative binomial regression. We provide an example using harbor seal counts from aerial surveys. These counts are affected by date, time of day, and time relative to low tide. We present results on a data set that showed a dramatic difference on estimating abundance of harbor seals when using quasi-Poisson vs. negative binomial regression. This difference is described and explained in light of the different weighting used in each regression method. A general understanding of weighting can help ecologists choose between these two methods.

Arctic marine mammal population status, sea ice habitat loss, and conservation recommendations for the 21st century

Abstract Arctic marine mammals (AMMs) are icons of climate change, largely because of their close association with sea ice. However, neither a circumpolar assessment of AMM status nor a standardized metric of sea ice habitat change is available. We summarized available data on abundance and trend for each AMM species and recognized subpopulation. We also examined species diversity, the extent of human use, and temporal trends in sea ice habitat for 12 regions of the Arctic by calculating the dates of spring sea ice retreat and fall sea ice advance from satellite data (1979–2013). Estimates of AMM abundance varied greatly in quality, and few studies were long enough for trend analysis. Of the AMM subpopulations, 78% (61 of 78) are legally harvested for subsistence purposes. Changes in sea ice phenology have been profound. In all regions except the Bering Sea, the duration of the summer (i.e., reduced ice) period increased by 5–10 weeks and by >20 weeks in the Barents Sea between 1979 and 2013. In light of generally poor data, the importance of human use, and forecasted environmental changes in the 21st century, we recommend the following for effective AMM conservation: maintain and improve comanagement by local, federal, and international partners; recognize spatial and temporal variability in AMM subpopulation response to climate change; implement monitoring programs with clear goals; mitigate cumulative impacts of increased human activity; and recognize the limits of current protected species legislation.

Population growth of Antarctic fur seals : Limitation by a top predator, the leopard seal?

Antarctic fur seals (Arctocephalus gazella) in the South Shetland Islands are recovering from 19th-century exploitation more slowly than the main population at South Georgia. To document demographic changes associated with the recovery in the South Shetlands, we monitored fur seal abundance and reproduction in the vicinity of Elephant Island during austral summers from 1986/1987 through 1994/1995. Total births, mean and variance of birth dates, and average daily mortality rates were estimated from daily live pup counts at North Cove (NC) and North Annex (NA) colonies on Seal Island. Sightings of leopard seals (Hydrurga leptonyx) and incidents of leopard seal predation on fur seal pups were recorded opportunistically during daily fur seal research at both sites. High mortality of fur seal pups, attributed to predation by leopard seals frequently observed at NC, caused pup numbers to decline rapidly between January and March (i.e., prior to weaning) each year and probably caused a long-term decline in the size of that colony. The NA colony, where leopard seals were never observed, increased in size during the study. Pup mortality from causes other than leopard seal predation appeared to be similar at the two sites. The number of pups counted at four locations in the Elephant Island vicinity increased slowly, at an annual rate of 3.8%, compared to rates as high as 11% at other locations in the South Shetland Islands. Several lines of circumstantial evidence are con- sistent with the hypothesis that leopard seal predators limit the growth of the fur seal population in the Elephant Island area and perhaps in the broader population in the South Shetland Islands. The sustained growth of this fur seal population over many decades rules out certain predator-prey models, allowing inference about the interaction between leopard seals and fur seals even though it is less thoroughly studied than predator-prey systems of terrestrial vertebrates of the northern hemisphere. Top-down forces should be included in hypotheses for future research on the factors shaping the recovery of the fur seal population in the South Shetland Islands.

Evaluation of Age- and Sex-Dependent Rates of Tag Loss in Southern Elephant Seals

Rates of tag loss were estimated in a long-term tagging study of southern elephant seals (Mirounga leonina) to assess the potential for bias in estimates of survival rates. Dalton Jumbo Rototags® were applied to each hind flipper of 5,743 recently weaned elephant seal pups on Marion Island from 1983 to 1993. We adapted and developed a method based on the resighting times of seals retaining 1 or 2 tags to estimate tag loss and test for effects of age and sex of the seals. Tag loss by young seals was low, but there was a strong increase in tag loss with seal age, especially for males. Annual single tag loss at age 14 was 10% for males and 5.6% for females. Although these are relatively modest rates of tag loss, substantial fractions of seals (35% of males and 17% of females) would lose both tags by age 15, requiring corrections to avoid bias in demographic studies based on these tagging data. The method we used to estimate tag loss has significant advantages over a ratio estimator that has been used for most previous studies of tag loss in pinnipeds.

Estimating multispecies abundance using automated detection systems: ice‐associated seals in the Bering Sea

Summary Automated detection systems employing advanced technology (e.g. infrared imagery, auditory recording systems, pattern recognition software) are compelling tools for gathering animal abundance and distribution data since investigators can often collect data more efficiently and reduce animal disturbance relative to surveys using human observers. Even with these improvements, analysing animal abundance with advanced technology can be challenging because of potential for incomplete detection, false positives and species misidentification. We argue that double sampling with an independent sampling method can provide the critical information needed to account for such errors. We present a hierarchical modelling framework for jointly analysing automated detection and double sampling data obtained during animal population surveys. Under our framework, observed counts in different sampling units are conceptualized as having arisen from a thinned log-Gaussian Cox process subject to spatial autocorrelation (where thinning accounts for incomplete detection). For multispecies surveys, our approach handles incomplete species observations owing to (i) structural uncertainties (e.g. in cases where the automatic detection data do not provide species observations) and (ii) species misclassification; the latter requires auxiliary information on the misclassification process. As an example of combining an automated detection system and a double sampling procedure, we consider the problem of estimating animal abundance from aerial surveys that use infrared imagery to detect animals, and independent, high-resolution digital photography to provide information on species composition and thermal detection accuracy. We illustrate our approach by analysing simulated data and data from a survey of four ice-associated seal species in the eastern Bering Sea. Our analysis indicated reasonable performance of our hierarchical modelling approach, but suggested a need to balance model complexity with the richness of the data set. For example, highly parameterized models can lead to spuriously high predictions of abundance in areas that are not sampled, especially when there are large gaps in spatial coverage. We recommend that ecologists employ double sampling when enumerating animal populations with automated detection systems to estimate and correct for detection errors. Combining multiple data sets within a hierarchical modelling framework provides a powerful approach for analysing animal abundance over large spatial domains.

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.

Modelling animal movement using the Argos satellite telemetry location error ellipse

Summary The Argos satellite telemetry system is popular for studying the movement and space use of marine animals. The life histories of marine mammals, in particular, result in a relatively large proportion of inaccurate locations, thus making analysis methods that do not account for location measurement error inappropriate for these data. Using a new Kalman filtering algorithm, Argos now provides locations and estimated error ellipses associated with each satellite fix, but to our knowledge, the location error ellipse has yet to be incorporated into analyses of animal movement or space use. We first present an observation model utilizing the Argos error ellipse and then demonstrate how this observation model can be combined with a simple three-dimensional movement model in a state-space formulation to infer activity budgets and movement characteristics from location and dive data of two species of seal, the bearded seal (Erignathus barbatus) and the Hawaiian monk seal (Monachus schauinslandi). These example data sets are of variable quality and represent species that differ in both space use and latitudinal range relative to the polar orbits of Argos satellites. We also compare the results from our error ellipse model with those from an approximate (isotropic) error circle model. We found the error circle to be a crude approximation of the actual anisotropic error ellipse for the higher quality bearded seal data, but inferences from the lower quality Hawaiian monk seal data were more robust to the choice of observation model. In both examples, we found the theoretical bivariate normal distribution corresponding to the error ellipse often failed to adequately explain the most extreme location outliers. In practice, we suspect the inferential consequences of using traditional isotropic location quality classes or other crude approximations in lieu of the error ellipse will be largely case-dependent. We support the Argos recommendation that practitioners wishing to more properly account for location measurement error utilize the error ellipse in analyses. However, the continued presence of outliers using the new algorithm suggests practitioners should consider using a fat-tailed distribution derived from the error ellipse (e.g. bivariate t-distribution) or filtering extreme outliers during data pre-processing.

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.

Estimating population status under conditions of uncertainty: the Ross seal in East Antarctica

Abstract The Ross seal (Ommatophoca rossii) is the least studied of the Antarctic ice-breeding phocids. In particular, estimating the population status of the Ross seal has proved extremely difficult. The Protocol on Environmental Protection to the Antarctic Treaty currently designates the Ross seal as a ‘Specially Protected Species’, contrasting with the IUCNs classification of ‘Least Concern’. As part of a review of the Ross seals classification under the Protocol, a survey was undertaken in 1999/2000 to estimate the status of the Ross seal population in the pack ice off East Antarctica between 64–150°E. Shipboard and aerial sighting surveys were carried out along 9476 km of transect to estimate the density of Ross seals hauled out on the ice, and satellite dive recorders deployed on a sample of Ross seals to estimate the proportion of time spent on the ice. The survey design and analysis addressed the many sources of uncertainty in estimating the abundance of this species in an effort to provide a range of best and plausible estimates. Best estimates of abundance in the survey region ranged from 41 300–55 900 seals. Limits on plausible estimates ranged from 20 500 (lower 2.5 percentile) to 226 600 (upper 97.5 percentile).

On Extrapolating Past the Range of Observed Data When Making Statistical Predictions in Ecology

Ecologists are increasingly using statistical models to predict animal abundance and occurrence in unsampled locations. The reliability of such predictions depends on a number of factors, including sample size, how far prediction locations are from the observed data, and similarity of predictive covariates in locations where data are gathered to locations where predictions are desired. In this paper, we propose extending Cook’s notion of an independent variable hull (IVH), developed originally for application with linear regression models, to generalized regression models as a way to help assess the potential reliability of predictions in unsampled areas. Predictions occurring inside the generalized independent variable hull (gIVH) can be regarded as interpolations, while predictions occurring outside the gIVH can be regarded as extrapolations worthy of additional investigation or skepticism. We conduct a simulation study to demonstrate the usefulness of this metric for limiting the scope of spatial inference when conducting model-based abundance estimation from survey counts. In this case, limiting inference to the gIVH substantially reduces bias, especially when survey designs are spatially imbalanced. We also demonstrate the utility of the gIVH in diagnosing problematic extrapolations when estimating the relative abundance of ribbon seals in the Bering Sea as a function of predictive covariates. We suggest that ecologists routinely use diagnostics such as the gIVH to help gauge the reliability of predictions from statistical models (such as generalized linear, generalized additive, and spatio-temporal regression models).