A within-lake occupancy model for starry stonewort, Nitellopsis obtusa, to support early detection and monitoring.

To efficiently detect aquatic invasive species early in an invasion when control may still be possible, predictions about which locations are likeliest to be occupied are needed at fine scales but are rarely available. Occupancy modeling could provide such predictions given data of sufficient quality and quantity. We assembled a data set for the macroalga starry stonewort (Nitellopsis obtusa) across Minnesota and Wisconsin, USA, where it is a new and high-priority invader. We used these data to construct a multi-season, single-species spatial occupancy model that included biotic, abiotic, and movement-related predictors. Distance to the nearest access was an important occurrence predictor, highlighting the likely role boats play in spreading starry stonewort. Fetch and water depth also predicted occupancy. We estimated an average detection probability of 63% at sites with mean non-N. obtusa plant cover, declining to ~ 38% at sites with abundant plant cover, especially that of other Characeae. We recommend that surveyors preferentially search for starry stonewort in areas of shallow depth and high fetch close to boat accesses. We also recommend searching during late summer/early fall when detection is likelier. This study illustrates the utility of fine-scale occupancy modeling for predicting the locations of nascent populations of difficult-to-detect species.

A comparison of survey method efficiencies for estimating densities of zebra mussels (Dreissena polymorpha).

Abundance surveys are commonly used to estimate plant or animal densities and frequently require estimating detection probabilities to account for imperfect detection. The estimation of detection probabilities requires additional measurements that take time, potentially reducing the efficiency of the survey when applied to high-density populations. We conducted quadrat, removal, and distance surveys of zebra mussels (Dreissena polymorpha) in three central Minnesota lakes and determined how much survey effort would be required to achieve a pre-specified level of precision for each abundance estimator, allowing us to directly compare survey design efficiencies across a range of conditions. We found that the required sampling effort needed to achieve our precision goal depended on both the survey design and population density. At low densities, survey designs that could cover large areas but with lower detection probabilities, such as distance surveys, were more efficient (i.e., required less sampling effort to achieve the same level of precision). However, at high densities, quadrat surveys, which tend to cover less area but with high detection rates, were more efficient. These results demonstrate that the best survey design is likely to be context-specific, requiring some prior knowledge of the underlying population density and the cost/time needed to collect additional information for estimating detection probabilities.

Circular-linear copulae for animal movement data.

Animal movement is often modelled in discrete time, formulated in terms of steps taken between successive locations at regular time intervals. Steps are characterized by the distance between successive locations (step lengths) and changes in direction (turn angles). Animals commonly exhibit a mix of directed movements with large step lengths and turn angles near 0 when travelling between habitat patches and more wandering movements with small step lengths and uniform turn angles when foraging. Thus, step lengths and turn angles will typically be cross-correlated.Most models of animal movement assume that step lengths and turn angles are independent, likely due to a lack of available alternatives. Here, we show how the method of copulae can be used to fit multivariate distributions that allow for correlated step lengths and turn angles.We describe several newly developed copulae appropriate for modelling animal movement data and fit these distributions to data collected on fishers (Pekania pennanti). The copulae are able to capture the inherent correlation in the data and provide a better fit than a model that assumes independence. Further, we demonstrate via simulation that this correlation can impact movement patterns (e.g. rates of dispersion overtime).We see many opportunities to extend this framework (e.g. to consider autocorrelation in step attributes) and to integrate it into existing frameworks for modelling animal movement and habitat selection. For example, copulae could be used to more accurately sample available locations when conducting habitat-selection analyses.

Using piecewise regression to identify biological phenomena in biotelemetry datasets.

Technological advances in the field of animal tracking have greatly expanded the potential to remotely monitor animals, opening the door to exploring how animals shift their behaviour over time or respond to external stimuli. A wide variety of animal-borne sensors can provide information on an animal's location, movement characteristics, external environmental conditions and internal physiological status. Here, we demonstrate how piecewise regression can be used to identify the presence and timing of potential shifts in a variety of biological responses using multiple biotelemetry data streams. Different biological latent states can be inferred by partitioning a time-series into multiple segments based on changes in modelled responses (e.g. their mean, variance, trend, degree of autocorrelation) and specifying a unique model structure for each interval. We provide six example applications highlighting a variety of taxonomic species, data streams, timescales and biological phenomena. These examples include a short-term behavioural response (flee and return) by a trumpeter swan Cygnus buccinator following a GPS collar deployment; remote identification of parturition based on movements by a pregnant moose Alces alces; a physiological response (spike in heart-rate) in a black bear Ursus americanus to a stressful stimulus (presence of a drone); a mortality event of a trumpeter swan signalled by changes in collar temperature and overall dynamic body acceleration; an unsupervised method for identifying the onset, return, duration and staging use of sandhill crane Antigone canadensis migration; and estimation of the transition between incubation and brood-rearing (i.e. hatching) for a breeding trumpeter swan. We implement analyses using the mcp package in R, which provides functionality for specifying and fitting a wide variety of user-defined model structures in a Bayesian framework and methods for assessing and comparing models using information criteria and cross-validation measures. These simple modelling approaches are accessible to a wide audience and offer a straightforward means of assessing a variety of biologically relevant changes in animal behaviour.

A fresh look at an old concept: home-range estimation in a tidy world.

A rich set of statistical techniques has been developed over the last several decades to estimate the spatial extent of animal home ranges from telemetry data, and new methods to estimate home ranges continue to be developed. Here we investigate home-range estimation from a computational point of view and aim to provide a general framework for computing home ranges, independent of specific estimators. We show how such a workflow can help to make home-range estimation easier and more intuitive, and we provide a series of examples illustrating how different estimators can be compared easily. This allows one to perform a sensitivity analysis to determine the degree to which the choice of estimator influences qualitative and quantitative conclusions. By providing a standardized implementation of home-range estimators, we hope to equip researchers with the tools needed to explore how estimator choice influences answers to biologically meaningful questions.

Resampling-based methods for biologists.

Ecological data often violate common assumptions of traditional parametric statistics (e.g., that residuals are Normally distributed, have constant variance, and cases are independent). Modern statistical methods are well equipped to handle these complications, but they can be challenging for non-statisticians to understand and implement. Rather than default to increasingly complex statistical methods, resampling-based methods can sometimes provide an alternative method for performing statistical inference, while also facilitating a deeper understanding of foundational concepts in frequentist statistics (e.g., sampling distributions, confidence intervals, p-values). Using simple examples and case studies, we demonstrate how resampling-based methods can help elucidate core statistical concepts and provide alternative methods for tackling challenging problems across a broad range of ecological applications.

Moose movement rates are altered by wolf presence in two ecosystems.

Predators directly impact prey populations through lethal encounters, but understanding nonlethal, indirect effects is also critical because foraging animals often face trade-offs between predator avoidance and energy intake. Quantifying these indirect effects can be difficult even when it is possible to monitor individuals that regularly interact. Our goal was to understand how movement and resource selection of a predator (wolves; Canis lupus) influence the movement behavior of a prey species (moose; Alces alces). We tested whether moose avoided areas with high predicted wolf resource use in two study areas with differing prey compositions, whether avoidance patterns varied seasonally, and whether daily activity budgets of moose and wolves aligned temporally. We deployed GPS collars on both species at two sites in northern Minnesota. We created seasonal resource selection functions (RSF) for wolves and modeled the relationship between moose first-passage time (FPT), a method that discerns alterations in movement rates, and wolf RSF values. Larger FPT values suggest rest/foraging, whereas shorter FPT values indicate travel/fleeing. We found that the movements of moose and wolves peaked at similar times of day in both study areas. Moose FPTs were 45% lower in areas most selected for by wolves relative to those avoided. The relationship between wolf RSF and moose FPT was nonlinear and varied seasonally. Differences in FPT between low and high RSF values were greatest in winter (-82.1%) and spring (-57.6%) in northeastern Minnesota and similar for all seasons in the Voyageurs National Park ecosystem. In northeastern Minnesota, where moose comprise a larger percentage of wolf diet, the relationship between moose FPT and wolf RSF was more pronounced (ave. across seasons: -60.1%) than the Voyageurs National Park ecosystem (-30.4%). These findings highlight the role wolves can play in determining moose behavior, whereby moose spend less time in areas with higher predicted likelihood of wolf resource selection.

Time series sightability modeling of animal populations.

Logistic regression models-or "sightability models"-fit to detection/non-detection data from marked individuals are often used to adjust for visibility bias in later detection-only surveys, with population abundance estimated using a modified Horvitz-Thompson (mHT) estimator. More recently, a model-based alternative for analyzing combined detection/non-detection and detection-only data was developed. This approach seemed promising, since it resulted in similar estimates as the mHT when applied to data from moose (Alces alces) surveys in Minnesota. More importantly, it provided a framework for developing flexible models for analyzing multiyear detection-only survey data in combination with detection/non-detection data. During initial attempts to extend the model-based approach to multiple years of detection-only data, we found that estimates of detection probabilities and population abundance were sensitive to the amount of detection-only data included in the combined (detection/non-detection and detection-only) analysis. Subsequently, we developed a robust hierarchical modeling approach where sightability model parameters are informed only by the detection/non-detection data, and we used this approach to fit a fixed-effects model (FE model) with year-specific parameters and a temporally-smoothed model (TS model) that shares information across years via random effects and a temporal spline. The abundance estimates from the TS model were more precise, with decreased interannual variability relative to the FE model and mHT abundance estimates, illustrating the potential benefits from model-based approaches that allow information to be shared across years.

Bears Show a Physiological but Limited Behavioral Response to Unmanned Aerial Vehicles.

Unmanned aerial vehicles (UAVs) have the potential to revolutionize the way research is conducted in many scientific fields. UAVs can access remote or difficult terrain, collect large amounts of data for lower cost than traditional aerial methods, and facilitate observations of species that are wary of human presence. Currently, despite large regulatory hurdles, UAVs are being deployed by researchers and conservationists to monitor threats to biodiversity, collect frequent aerial imagery, estimate population abundance, and deter poaching. Studies have examined the behavioral responses of wildlife to aircraft (including UAVs), but with the widespread increase in UAV flights, it is critical to understand whether UAVs act as stressors to wildlife and to quantify that impact. Biologger technology allows for the remote monitoring of stress responses in free-roaming individuals, and when linked to locational information, it can be used to determine events or components of an animal's environment that elicit a physiological response not apparent based on behavior alone. We assessed effects of UAV flights on movements and heart rate responses of free-roaming American black bears. We observed consistently strong physiological responses but infrequent behavioral changes. All bears, including an individual denned for hibernation, responded to UAV flights with elevated heart rates, rising as much as 123 beats per minute above the pre-flight baseline. It is important to consider the additional stress on wildlife from UAV flights when developing regulations and best scientific practices.

A hidden Markov model to identify and adjust for selection bias: an example involving mixed migration strategies.

An important assumption in observational studies is that sampled individuals are representative of some larger study population. Yet, this assumption is often unrealistic. Notable examples include online public-opinion polls, publication biases associated with statistically significant results, and in ecology, telemetry studies with significant habitat-induced probabilities of missed locations. This problem can be overcome by modeling selection probabilities simultaneously with other predictor-response relationships or by weighting observations by inverse selection probabilities. We illustrate the problem and a solution when modeling mixed migration strategies of northern white-tailed deer (Odocoileus virginianus). Captures occur on winter yards where deer migrate in response to changing environmental conditions. Yet, not all deer migrate in all years, and captures during mild years are more likely to target deer that migrate every year (i.e., obligate migrators). Characterizing deer as conditional or obligate migrators is also challenging unless deer are observed for many years and under a variety of winter conditions. We developed a hidden Markov model where the probability of capture depends on each individual's migration strategy (conditional versus obligate migrator), a partially latent variable that depends on winter severity in the year of capture. In a 15-year study, involving 168 white-tailed deer, the estimated probability of migrating for conditional migrators increased nonlinearly with an index of winter severity. We estimated a higher proportion of obligates in the study cohort than in the population, except during a span of 3 years surrounding back-to-back severe winters. These results support the hypothesis that selection biases occur as a result of capturing deer on winter yards, with the magnitude of bias depending on the severity of winter weather. Hidden Markov models offer an attractive framework for addressing selection biases due to their ability to incorporate latent variables and model direct and indirect links between state variables and capture probabilities.

A long-term assessment of the variability in winter use of dense conifer cover by female white-tailed deer.

BACKGROUND: Long-term studies allow capture of a wide breadth of environmental variability and a broader context within which to maximize our understanding of relationships to specific aspects of wildlife behavior. The goal of our study was to improve our understanding of the biological value of dense conifer cover to deer on winter range relative to snow depth and ambient temperature. METHODOLOGY/PRINCIPAL FINDINGS: We examined variation among deer in their use of dense conifer cover during a 12-year study period as potentially influenced by winter severity and cover availability. Female deer were fitted with a mixture of very high frequency (VHF, n = 267) and Global Positioning System (GPS, n = 24) collars for monitoring use of specific cover types at the population and individual levels, respectively. We developed habitat composites for four study sites. We fit multinomial response models to VHF (daytime) data to describe population-level use patterns as a function of snow depth, ambient temperature, and cover availability. To develop alternative hypotheses regarding expected spatio-temporal patterns in the use of dense conifer cover, we considered two sets of competing sub-hypotheses. The first set addressed whether or not dense conifer cover was limiting on the four study sites. The second set considered four alternative sub-hypotheses regarding the potential influence of snow depth and ambient temperature on space use patterns. Deer use of dense conifer cover increased the most with increasing snow depth and most abruptly on the two sites where it was most available, suggestive of an energy conservation strategy. Deer use of dense cover decreased the most with decreasing temperatures on the sites where it was most available. At all four sites deer made greater daytime use (55 to >80% probability of use) of open vegetation types at the lowest daily minimum temperatures indicating the importance of thermal benefits afforded from increased exposure to solar radiation. Date-time plots of GPS data (24 hr) allowed us to explore individual diurnal and seasonal patterns of habitat use relative to changes in snow depth. There was significant among-animal variability in their propensity to be found in three density classes of conifer cover and other open types, but little difference between diurnal and nocturnal patterns of habitat use. CONCLUSIONS/SIGNIFICANCE: Consistent with our findings reported elsewhere that snow depth has a greater impact on deer survival than ambient temperature, herein our population-level results highlight the importance of dense conifer cover as snow shelter rather than thermal cover. Collectively, our findings suggest that maximizing availability of dense conifer cover in an energetically beneficial arrangement with quality feeding sites should be a prominent component of habitat management for deer.

Integrated population modeling of black bears in Minnesota: implications for monitoring and management.

BACKGROUND: Wildlife populations are difficult to monitor directly because of costs and logistical challenges associated with collecting informative abundance data from live animals. By contrast, data on harvested individuals (e.g., age and sex) are often readily available. Increasingly, integrated population models are used for natural resource management because they synthesize various relevant data into a single analysis. METHODOLOGY/PRINCIPAL FINDINGS: We investigated the performance of integrated population models applied to black bears (Ursus americanus) in Minnesota, USA. Models were constructed using sex-specific age-at-harvest matrices (1980-2008), data on hunting effort and natural food supplies (which affects hunting success), and statewide mark-recapture estimates of abundance (1991, 1997, 2002). We compared this approach to Downing reconstruction, a commonly used population monitoring method that utilizes only age-at-harvest data. We first conducted a large-scale simulation study, in which our integrated models provided more accurate estimates of population trends than did Downing reconstruction. Estimates of trends were robust to various forms of model misspecification, including incorrectly specified cub and yearling survival parameters, age-related reporting biases in harvest data, and unmodeled temporal variability in survival and harvest rates. When applied to actual data on Minnesota black bears, the model predicted that harvest rates were negatively correlated with food availability and positively correlated with hunting effort, consistent with independent telemetry data. With no direct data on fertility, the model also correctly predicted 2-point cycles in cub production. Model-derived estimates of abundance for the most recent years provided a reasonable match to an empirical population estimate obtained after modeling efforts were completed. CONCLUSIONS/SIGNIFICANCE: Integrated population modeling provided a reasonable framework for synthesizing age-at-harvest data, periodic large-scale abundance estimates, and measured covariates thought to affect harvest rates of black bears in Minnesota. Collection and analysis of these data appear to form the basis of a robust and viable population monitoring program.