Search

1. Movement is the primary means by which animals obtain resources and avoid hazards. Most movement exhibits directional bias that is related to environmental features (taxis), such as the location of food patches, predators, ocean currents, or wind. Numerous behaviours with directional bias can be characterized by maintaining orientation at an angle relative to the environmental stimuli (menotaxis), including navigation relative to sunlight or magnetic fields and energy-conserving flight across wind. However, no statistical methods exist to flexibly classify and characterise such directional bias. 2. We propose a biased correlated random walk model that can identify menotactic behaviours by predicting turning angle as a trade-off between directional persistence and directional bias relative to environmental stimuli without making a priori assumptions about the angle of bias. We apply the model within the framework of a multi-state hidden Markov model (HMM) and describe methods to remedy information loss associated with coarse environmental data to improve the classification and parameterization of directional bias. 3. Using simulation studies, we illustrate how our method more accurately classifies behavioural states compared to conventional correlated random walk HMMs that do not incorporate directional bias. We illustrate the application of these methods by identifying cross wind olfactory foraging and drifting behaviour mediated by wind-driven sea ice drift in polar bears (Ursus maritimus) from movement data collected by satellite telemetry. 4. The extensions we propose can be readily applied to movement data to identify and characterize behaviours with directional bias toward any angle, and open up new avenues to investigate more mechanistic relationships between animal movement and the environment.

1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in their environments allows for an increased understanding of animal cognition. 2. Here we describe a model that accounts for the memory of seasonal or ephemeral qualities of an animal's environment. The model captures multiple behaviors at once by allowing for resource selection in the present time as well as long-distance navigations to previously visited locations within an animal's home range. 3. We performed a set of analyses on simulated data to test our model, determining that it can provide informative results from as little as one year of discrete-time location data. We also show that the accuracy of model selection and parameter estimation increases with more location data. 4. This model has potential to identify a specific mechanism in which animals use memory to optimize their foraging, by revisiting temporally and predictably variable resources at consistent time lags., Comment: 23 pages, including title and abstract; 4 tables; 3 figures; one Appendix containing 2 additional tables and 1 additional figure

State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (\textit{Ursus maritimus}) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.

1. Understanding how to find targets with very limited information is a topic of interest in many disciplines. In ecology, such research has often focused on the development of two movement models: i) the L\'evy walk and; ii) the composite correlated random walk and its associated area-restricted search behaviour. Although the processes underlying these models differ, they can produce similar movement patterns. Due to this similarity and because of their disparate formulation, current methods cannot reliably differentiate between these two models. 2. Here, we present a method that differentiates between the two models. It consists of likelihood functions, including one for a hidden Markov model, and associated statistical measures that assess the relative support for and absolute fit of each model. 3. Using a simulation study, we show that our method can differentiate between the two search models over a range of parameter values. Using the movement data of two polar bears (\textit{Ursus maritimus}), we show that the method can be applied to complex, real-world movement paths. 4. By providing the means to differentiate between the two most prominent search models in the literature, and a framework that could be extended to include other models, we facilitate further research into the strategies animals use to find resources.