Robustness of movement models: can models bridge the gap between temporal scales of data sets and behavioural processes?

A random walk model that accounts for space occupation and movements of a large herbivore

Animal movement has been identified as a key feature in understanding animal behavior, distribution and habitat use and foraging strategies among others. Large datasets of invididual locations often remain unused or used only in part due to the lack of practical models that can directly infer the desired features from raw GPS locations and the complexity of existing approaches. Some of them being disputed for their lack of biological justifications in their design. We propose a simple model of individual movement with explicit parameters, based on a two-dimensional biased and correlated random walk with three forces related to advection (correlation), attraction (bias) and immobility of the animal. These forces can be directly estimated using individual data. We demonstrate the approach by using GPS data of 5 red deer with a high frequency sampling. The results show that a simple random walk template can account for the spatial complexity of wild animals. The practical design of the model is also verified for detecting spatial feature abnormalities and for providing estimates of density and abundance of wild animals. Integrating even more additional features of animal movement, such as individuals’ interactions or environmental repellents, could help to better understand the spatial behavior of wild animals.

Reptiles on the wrong track? Moving beyond traditional estimators with dynamic Brownian Bridge Movement Models

BACKGROUND

Animal movement expressed through home ranges or space-use can offer insights into spatial and habitat requirements. However, different classes of estimation methods are currently instinctively applied to answer home range, space-use or movement-based research questions regardless of their widely varying outputs, directly impacting conclusions. Recent technological advances in animal tracking (GPS and satellite tags), have enabled new methods to quantify animal space-use and movement pathways, but so far have primarily targeted mammal and avian species.

METHODS

Most reptile spatial ecology studies only make use of two older home range estimation methods: Minimum Convex Polygons (MCP) and Kernel Density Estimators (KDE), particularly with the Least Squares Cross Validation (LSCV) and reference (h _ref ) bandwidth selection algorithms. These methods are frequently applied to answer space-use and movement-based questions. Reptile movement patterns are unique (e.g., low movement frequency, long stop-over periods), prompting investigation into whether newer movement-based methods -such as dynamic Brownian Bridge Movement Models (dBBMMs)- apply to Very High Frequency (VHF) radio-telemetry tracking data. We simulated movement data for three archetypical reptile species: a highly mobile active hunter, an ambush predator with long-distance moves and long-term sheltering periods, and an ambush predator with short-distance moves and short-term sheltering periods. We compared traditionally used estimators, MCP and KDE, with dBBMMs, across eight feasible VHF field sampling regimes for reptiles, varying from one data point every four daylight hours, to once per month.

RESULTS

Although originally designed for GPS tracking studies, dBBMMs outperformed MCPs and KDE h _ref across all tracking regimes in accurately revealing movement pathways, with only KDE LSCV performing comparably at some higher frequency sampling regimes. However, the LSCV algorithm failed to converge with these high-frequency regimes due to high site fidelity, and was unstable across sampling regimes, making its use problematic for species exhibiting long-term sheltering behaviours. We found that dBBMMs minimized the effect of individual variation, maintained low error rates balanced between omission (false negative) and commission (false positive), and performed comparatively well even under low frequency sampling regimes (e.g., once a month).

CONCLUSIONS

We recommend dBBMMs as a valuable alternative to MCP and KDE methods for reptile VHF telemetry data, for research questions associated with space-use and movement behaviours within the study period: they work under contemporary tracking protocols and provide more stable estimates. We demonstrate for the first time that dBBMMs can be applied confidently to low-resolution tracking data, while improving comparisons across regimes, individuals, and species.

SUPPLEMENTARY INFORMATION

Supplementary information accompanies this paper at 10.1186/s40462-020-00229-3.

Territory surveillance and prey management: Wolves keep track of space and time

Identifying behavioral mechanisms that underlie observed movement patterns is difficult when animals employ sophisticated cognitive‐based strategies. Such strategies may arise when timing of return visits is important, for instance to allow for resource renewal or territorial patrolling. We fitted spatially explicit random‐walk models to GPS movement data of six wolves (Canis lupus; Linnaeus, 1758) from Alberta, Canada to investigate the importance of the following: (1) territorial surveillance likely related to renewal of scent marks along territorial edges, to reduce intraspecific risk among packs, and (2) delay in return to recently hunted areas, which may be related to anti‐predator responses of prey under varying prey densities. The movement models incorporated the spatiotemporal variable “time since last visit,” which acts as a wolf's memory index of its travel history and is integrated into the movement decision along with its position in relation to territory boundaries and information on local prey densities. We used a model selection framework to test hypotheses about the combined importance of these variables in wolf movement strategies. Time‐dependent movement for territory surveillance was supported by all wolf movement tracks. Wolves generally avoided territory edges, but this avoidance was reduced as time since last visit increased. Time‐dependent prey management was weak except in one wolf. This wolf selected locations with longer time since last visit and lower prey density, which led to a longer delay in revisiting high prey density sites. Our study shows that we can use spatially explicit random walks to identify behavioral strategies that merge environmental information and explicit spatiotemporal information on past movements (i.e., “when” and “where”) to make movement decisions. The approach allows us to better understand cognition‐based movement in relation to dynamic environments and resources.

A framework for analyzing the robustness of movement models to variable step discretization

When sampling animal movement paths, the frequency at which location measurements are attempted is a critical feature for data analysis. Important quantities derived from raw data, e.g. travel distance or sinuosity, can differ largely based on the temporal resolution of the data. Likewise, when movement models are fitted to data, parameter estimates have been demonstrated to vary with sampling rate. Thus, biological statements derived from such analyses can only be made with respect to the resolution of the underlying data, limiting extrapolation of results and comparison between studies. To address this problem, we investigate whether there are models that are robust against changes in temporal resolution. First, we propose a mathematically rigorous framework, in which we formally define robustness as a model property. We then use the framework for a thorough assessment of a range of basic random walk models, in which we also show how robustness relates to other probabilistic concepts. While we found robustness to be a strong condition met by few models only, we suggest a new method to extend models so as to make them robust. Our framework provides a new systematic, mathematically founded approach to the question if, and how, sampling rate of movement paths affects statistical inference.