Devin S. Johnson

CONTINUOUS‐TIME CORRELATED RANDOM WALK MODEL FOR ANIMAL TELEMETRY DATA

We propose a continuous-time version of the correlated random walk model for animal telemetry data. The continuous-time formulation allows data that have been nonuniformly collected over time to be modeled without subsampling, interpolation, or aggregation to obtain a set of locations uniformly spaced in time. The model is derived from a continuous-time Ornstein-Uhlenbeck velocity process that is integrated to form a location process. The continuous-time model was placed into a state-space framework to allow parameter estimation and location predictions from observed animal locations. Two previously unpublished marine mammal telemetry data sets were analyzed to illustrate use of the model, by-products available from the analysis, and different modifications which are possible. A harbor seal data set was analyzed with a model that incorporates the proportion of each hour spent on land. Also, a northern fur seal pup data set was analyzed with a random drift component to account for directed travel and ocean currents.

Spatial occupancy models for large data sets

Since its development, occupancy modeling has become a popular and useful tool for ecologists wishing to learn about the dynamics of species occurrence over time and space. Such models require presence–absence data to be collected at spatially indexed survey units. However, only recently have researchers recognized the need to correct for spatially induced overdisperison by explicitly accounting for spatial autocorrelation in occupancy probability. Previous efforts to incorporate such autocorrelation have largely focused on logit-normal formulations for occupancy, with spatial autocorrelation induced by a random effect within a hierarchical modeling framework. Although useful, computational time generally limits such an approach to relatively small data sets, and there are often problems with algorithm instability, yielding unsatisfactory results. Further, recent research has revealed a hidden form of multicollinearity in such applications, which may lead to parameter bias if not explicitly addressed. Com...

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.

Velocity-Based Movement Modeling for Individual and Population Level Inference

Understanding animal movement and resource selection provides important information about the ecology of the animal, but an animals movement and behavior are not typically constant in time. We present a velocity-based approach for modeling animal movement in space and time that allows for temporal heterogeneity in an animals response to the environment, allows for temporal irregularity in telemetry data, and accounts for the uncertainty in the location information. Population-level inference on movement patterns and resource selection can then be made through cluster analysis of the parameters related to movement and behavior. We illustrate this approach through a study of northern fur seal (Callorhinus ursinus) movement in the Bering Sea, Alaska, USA. Results show sex differentiation, with female northern fur seals exhibiting stronger response to environmental variables.

Modeling Wolverine Occurrence Using Aerial Surveys of Tracks in Snow

Abstract We designed a novel approach to determining extent of distribution and area of occupancy for wolverines (Gulo gulo) by using aerial surveys of tracks in snow and hierarchical spatial modeling. In 2005 we used a small, fixed-wing aircraft with pilot and one observer to search 575 of 588 survey units for wolverine tracks in approximately 60,000 km2 of boreal forest in northwestern Ontario, Canada. We used sinuous flight paths to scan open areas in the forest in the 100-km2 survey units. We detected tracks in 138 (24%) of the 575 sampled units. There was strong evidence of occurrence (probability of occurrence >0.80) in 30% of the 588 survey units, weak evidence of occurrence (0.50–0.80) in 12%, weak evidence of absence (0.20–0.50) in 15%, and strong evidence of absence (<0.20) in 43%. Wolverine range comprised 59% of the study area and area of occupancy was 33,400 km2. With information on probability of occurrence and core areas of occupation for wolverines in our study area, resource managers and others can examine factors that influence wolverine distribution patterns and use this information to formulate best management practices that will maintain wolverines on the landscape in the face of increasing resource development. Comparing future survey results with those of our 2005 survey will provide an objective way to assess the efficacy of management practices.

When to be discrete: the importance of time formulation in understanding animal movement

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal (Callorhinus ursinus) biotelemetry data.

Extreme weather events influence dispersal of naive northern fur seals

Since 1975, northern fur seal (Callorhinus ursinus) numbers at the Pribilof Islands (PI) in the Bering Sea have declined rapidly for unknown reasons. Migratory dispersal and habitat choice may affect first-year survivorship, thereby contributing to this decline. We compared migratory behaviour of 166 naive pups during 2 years from islands with disparate population trends (increasing: Bogoslof and San Miguel Islands; declining: PI), hypothesizing that climatic conditions at weaning may differentially affect dispersal and survival. Atmospheric conditions (Bering Sea) in autumn 2005–2006 were anomalously cold, while 2006–2007 was considerably warmer and less stormy. In 2005, pups departed earlier at all sites, and the majority of PI pups (68–85%) departed within 1 day of Arctic storms and dispersed quickly, travelling southwards through the Aleutian Islands. Tailwinds enabled faster rates of travel than headwinds, a trend not previously shown for marine mammals. Weather effects were less pronounced at Bogoslof Island (approx. 400 km further south), and, at San Miguel Island, (California) departures were more gradual, and only influenced by wind and air pressure in 2005. We suggest that increasingly variable climatic conditions at weaning, particularly timing, frequency and intensity of autumnal storms in the Bering Sea, may alter timing, direction of dispersal and potentially survival of pups.

Estimating animal resource selection from telemetry data using point process models

1. Analyses of animal resource selection functions (RSF) using data collected from relocations of individuals via remote telemetry devices have become commonplace. Increasing technological advances, however, have produced statistical challenges in analysing such highly autocorrelated data. Weighted distribution methods have been proposed for analysing RSFs with telemetry data. However, they can be computationally challenging due to an intractable normalizing constant and cannot be aggregated (i.e. collapsed) over time to make space-only inference. 2. In this study, we take a conceptually different approach to modelling animal telemetry data for making RSF inference. We consider the telemetry data to be a realization of a space-time point process. Under the point process paradigm, the times of the relocations are also considered to be random rather than fixed. 3. We show the point process models we propose are a generalization of the weighted distribution telemetry models. By generalizing the weighted model, we can access several numerical techniques for evaluating point process likelihoods that make use of common statistical software. Thus, the analysis methods can be readily implemented by animal ecologists. 4. In addition to ease of computation, the point process models can be aggregated over time by marginalizing over the temporal component of the model. This allows a full range of models to be constructed for RSF analysis at the individual movement level up to the study area level. 5. To demonstrate the analysis of telemetry data with the point process approach, we analysed a data set of telemetry locations from northern fur seals (Callorhinus ursinus) in the Pribilof Islands, Alaska. Both a space-time and an aggregated space-only model were fitted. At the individual level, the space-time analysis showed little selection relative to the habitat covariates. However, at the study area level, the space-only model showed strong selection relative to the covariates.

marked: an R package for maximum likelihood and Markov Chain Monte Carlo analysis of capture–recapture data

Summary We describe an open-source r package, marked, for analysis of mark–recapture data to estimate survival and animal abundance. Currently, marked is capable of fitting Cormack–Jolly–Seber (CJS) and Jolly–Seber models with maximum likelihood estimation (MLE) and CJS models with Bayesian Markov Chain Monte Carlo methods. The CJS models can be fitted with MLE using optimization code in R or with Automatic Differentiation Model Builder. The latter allows incorporation of random effects. Some package features include: (i) individual-specific time intervals between sampling occasions, (ii) generation of optimization starting values from generalized linear model approximations and (iii) prediction of demographic parameters associated with unique combinations of individual and time-specific covariates. We demonstrate marked with a commonly analysed European dipper (Cinclus cinclus) data set. The package will be most useful to ecologists with large mark–recapture data sets and many individual covariates.

A General Bayesian Hierarchical Model for Estimating Survival of Nests and Young

ABSTRACT. Models for estimating survival probability of nests and young have changed dramatically since the development of the Mayfield method. Improvements in software and a steady increase in computing power have allowed more complexity and realism in these models, allowing researchers to provide better estimates of survival and to relate survival rates to relevant covariates. However, many current analysis methods utilize fixed-effects models with the implicit assumption that the covariates explain all of the variation in the data, other than random variation within a specified family of distributions. This is generally a strong assumption, and, in the presence of heterogeneity and lack of independence, these estimates have been shown to be negatively biased. Others have begun to explore random-effects models for these situations, but a readily applicable Bayesian approach has been lacking. We present a general Bayesian modeling framework appropriate for survival of both nests and young that simultaneously allows for the inclusion of individual covariates and random effects and provides a measure of goodness-of-fit. We used previously published data on survival of Common Goldeneye (Bucephala clangula) ducklings in interior Alaska and on nest survival in three species of prairie-nesting ducks that nested in the Missouri Coteau region of North Dakota to demonstrate this approach. The inclusion of a brood-level random effect in the Common Goldeneye example increased point estimates and credible interval [CI] coverage from 0.62 (95% CI: 0.49–0.73) and 0.66 (95% CI: 0.58–0.74) for 2002 and 2003, respectively, to 0.69 (95% CI: 0.42–0.88) and 0.74 (95% CI: 0.57–0.88) for 2002 and 2003, respectively.