2.1. Path-level analyses

Path-level analyses rely on several straightforward metrics that can be easily extracted from consecutive relocations in a time series of geographical points. These metrics are broadly referred to to as stepwise characteristics and can be split into primary and secondary metrics. Primary metrics, such as step length and turning angle (Table 1) are directly derived from relocations at each time step. However, they are highly sensitive to the spatial and temporal resolution at which the data were collected (Codling and Hill 2005, Gautestad 2012). Secondary metrics may be summary statistics derived from primary metrics (Edelhoff et al. 2016) or they may be computed from the trajectory at coarser spatio-temporal scales than represented by the raw data. These coarser scale metrics include net squared displacement (NSD) (Bunnefeld et al. 2011), which under a pure diffusive movement process scales linearly with time (Börger and Fryxell 2012), and residence time (Table 1). They may used, as in the case of NSD, to characterize the functional mode of a movement path (i.e., migratory vs. territorial; Bastille-Rousseau et al. 2016). The coarser-scale at which they are calculated makes them less sensitive to the spatio-temporal resolution of the data, provided the scale of the raw data is sufficiently fine (i.e., an order of magnitude finer than these secondary measures).

Metrics have been developed to describe structural aspects of movement trajectories that include many twists and turns. Two of these are the straightness index and tortuosity: both measure the degree to which movement trajectories deviate from straight lines (Table 1). A third is a trajectory’s fractal dimension: informally, it has a value between one and two, and is a measure of the extent to which a one-dimensional trajectory fills two-dimensional space, as an individual meanders around the landscape (values close to 2 represent trajectories that are more “space filling” than those with dimensions close to 1). These three structure-characterizing metrics are calculated across a series of steps (i.e. consecutive locations in space), typically using computer algorithms, although the fractal dimensions of earthworms moving in vegetated versus unvegetated landscapes have been computed by hand (Rice et al. 1998)!

2.2. Path Segmentation Analyses

One of the most active areas of research within movement ecology (see Edelhoff et al. 2016) is the development of methods to infer the behavioral state of individuals from relocation data. Some of these methods seek to segment movement paths into different behavioral phases (also known as canonical activity modes—see Getz and Saltz 2008), such as distinguishing between active and resting phases (van Beest and Milner 2013) or between foraging and traveling phases (Dzialak et al. 2015). Segmentation methods may be based on threshold concepts (Gutenkunst et al. 2007, Sur et al. 2014) or clustering methods (Van Moorter et al. 2010); or they may be based on geometric or periodic properties of the trajectory, as in recursion (Bar-David et al. 2009) and wavelet (Wittemyer et al. 2008) analyses, respectively (Table 1).

One set of methods—change point analyses (Table 1)—are designed to detect changes in the movement behavior of individuals, and then relate these to environmental covariates (Garstang et al. 2014) as possible causes for the behavioral shifts. These methods frequently use time-series analyses to identify notable shifts in the autocorrelations of the sequential values of primary or secondary metrics (Gurarie et al. 2009, 2016). Another set of methods—state space modeling approaches (Table 1)—are designed to identify a set of states (hopefully with a behavioral interpretation) underlying variations in movement behavior and, within the same analysis, determine the probabilities of switching among states. These methods attempt to assign “hidden behavioral states” to each location point, as well as a probability transition matrix that specifies the probability of an individual switching from one state to any other as the individual moves to the next location point. Essentially, the method produces a stochastic walk model, called a Hidden Markov Model (HMM; Patterson et al. 2009). HMM movement trajectory models are complicated generalizations of random walks (Morales et al. 2004), where movement elements (step size and turning angle) depend on the current behavioral state, as does the probability of changing behavioral state when reaching the next location. To demonstrate the HMM method, we have analyzed the trajectory of a zebra using the moveHMM package (Michelot et al. 2016) in the statistical analysis program R (version 3.4.3; R Core Team 2017). The results obtained constitute the most probable decomposition of all of the 10,600 steps into a “two-state no-covariate model”. The distributions of step lengths and turning angles associated with this model are depicted in Fig. 1.

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Figure 1.

Results of a “2-state, no-covariate” behavioral model of zebra “AG256” using the moveHMM package in R (see supplementary files for data and code). This analysis assumed 2 distinct behavioral states and included only an intercept term, no environmental or other physiological covariates were included. Panels (a) & (b) show the empirical distributions of step lengths and turning angles respectively, using yellow and blue lines to depict the estimated distributions in each behavioral state. Panel (c) displays the particular trajectory used to produce distributions (a) and (b), with each color-coded with respect to their predicted behavioral state: yellow for state 1 and blue for state 2. Data exploration and biological knowledge of the observed individual is necessary to determine whether a model with more than two states clarifies or muddies interpretation of what each state is likely to represent. In our example, it seems probable, given the relatively uniform distribution of turning angles and the high density of short steps, that State 1 represents bouts of foraging while State 2 represents more directed movement behavior (e.g., travel; notice the apparently unbiased distribution of turning angles and larger step sizes).

Path or trajectory segmentation methods are one area of research common to both GIScience and movement ecology, with the GIS community supporting significant research on pattern-oriented, cross-scale, and cross-type segmentation methods (Dodge et al. 2009, Ahearn and Dodge 2018). In a study designed to explore the role of uncertainty in trajectory and segmentation analyses, Laube and Purves (2011) fitted 10 cows with GPS collars taking sub-second fixes to investigate questions of scale, granularity, and uncertainty when working with GPS data to assess movement parameters. The results of this work should be of great interest to ecologists, who typically collect much coarser fix data and then either invoke a straight-line assumption about the nature of paths between any two consecutive points in their data or assume Gaussian diffusion, often relying on a Brownian Bridge method for constructing likely trajectories between such points (Horne et al. 2007).

Often limitations regarding the temporal resolution of movement data may require analysis at somewhat broader scales. Even at this higher level of abstraction, however, behavioral classification may still be powerful. Indeed, Abrahms et al. (2017) identified “movement syndromes” across 13 diverse taxa (marine and terrestrial) using five standard metrics (mean turning angle correlation, mean residence time, mean time-to-return, volume of intersection, and mean net squared displacement) and a principle components analysis. Although the trajectories studied varied in movement mode (e.g. flying, walking, swimming) and taxon, the analysis successfully differentiated among migratory, nomadic, central place foraging, and territorial behaviors from GPS data alone.

Alongside the development of analyses to derive behavioral states from GPS data, new tags and collars fitted with tri-axial accelerometers (and, often, additional sensors for light, barometric pressure, temperature, etc.—see Wilson et al. 2008) increasingly allow for direct observation of the dynamic behavioral states of free-ranging animals (Shepard et al. 2008, Wang et al. 2015). Using various machine learning algorithms, accelerometer data (in the form of three-dimensional movement generally at a 20–40Hz resolution) can be processed to classify basic behaviors (e.g. sitting, walking, diving, running, resting, foraging) across multiple taxa with high accuracy (Nathan et al. 2012, Bidder et al. 2014, Fehlmann et al. 2017). Although these algorithms require high resolution training data, often relying upon intensive observation of captive animals, this technology used in combination with GPS relocations can aid in the exploration of links among the biomechanical, behavioral, and ecological processes that influence whole-animal movement and contribute to a unified field of movement ecology (Nathan et al. 2012).

3.1. Feature-independent analyses

Metrics analyzing the frequency of relocations across space regardless of environmental covariates broadly include the various methods for home-range estimation. These simple measures of animal space use (see Table 2) are applied widely, even with low-resolution data: though daily fix rates may prohibit fine-scale analyses such as behavioral state extraction, the aggregation of points at this resolution (over appropriate temporal spans) can easily inform the general size and shape of an animal’s home range (Worton 1989, Fieberg and Kochanny 2005, Fieberg and Börger 2012).

Several alternative methods for describing the home range of an animal exist, ranging in complexity from the construction of the minimum convex polygon containing the movement trajectory to a construction of a utilization distribution (Van Winkle 1975) that can be used to estimate the probability of finding an individual in selected areas inside the home range; see Fig. 2 for a comparison across three common methods for home-range construction. Most commonly, utilization distributions (UDs) are derived using kernel density estimators, now widely incorporated in many spatial analysis packages (Worton 1989). Subsequent development of other methods, based on Brownian movement models (Horne et al. 2007) and Local Convex Hull unions (Getz and Wilmers 2004, Getz et al. 2007, Lyons et al. 2013, Dougherty et al. 2017), as well as autocorrelated kernel methods (Fleming and Calabrese 2017) have enabled more realistic or robust estimates of the utilization distribution. In order to delineate areas of most consistent use or offer conservative estimates of an animal’s typical home range, researchers often include isopleths on maps of utilization distributions to identify the areas associated with a given percentage of relocations (e.g., 50%, 80%, or 95%). Utilization distributions can be calculated over any time interval of interest to delineate the space use of an animal over that time (e.g. a single month, a particular season, an entire year, etc.). By assessing the volume of intersection or overlap of successive short-term UDs for a particular individual, researchers can evaluate broad-scale site fidelity and ultimately the stability of an animal’s home range (Fieberg and Kochanny 2005, Millspaugh et al. 2004, Clapp and Beck 2015; Table 2). Additionally, these same metrics can be used across individuals to estimate concurrent or shared space use, which can be important for understanding social structure, disease transmission, or competition for resources.

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Figure 2.

Comparative home range estimates for zebra “AG256” (using only the data that pertains to the western part of its total range—cf. Panel (c) in Fig. 1) across 3 static (i.e., time-integrated) techniques. The simplest technique, a minimum convex polygon (MCP), displayed in Panel (a), defines the extent of a home range as the smallest convex polygon fitting a given percentage of points. Though still used widely, MCPs are criticized as poor estimators of an animal’s true home range because they often contain large areas unused, and potentially unavailable, to the observed individual, as evident in the upper-center of our trajectory. Panel (b) displays a common alternative: the 95% kernel utilization distribution. This method was developed to more rigorously quantify an animals actual space use and ultimately defines an animal’s home range as a bivariate probability density function, calculating the probability of relocating an animal in any given location (Worton 1989). Panel (c) offers a non-parametric approach, calculating the home range of the zebra using a-LoCoH, the adaptive local convex hull method developed by Getz et al. (2007) that constructs kernels at each relocation using all points within a total distance a such that the distances of all neighboring points to the reference point sum to a value less than or equal to a. In our example, we used a = 75000 m, which provided a contiguous range that trades-off fewer false positives at the expense of more false negatives than the other two methods. There is much debate and continued development in the area of home-range estimation and researchers must be conscious of the differences across metrics, because results often vary widely and may offer different biological interpretations (e.g., defining the extent of the habitat available to the animal for selection versus the area traversed in daily activity; see Fieberg and B¨orger 2012). For more detail on the construction of these three home range measures, see Appendix B.

Within the utilization distribution, ecologists often define a “core area” of use. Core area methods refer to any one of a group of analyses that seek to identify the most intensely used areas from individuals’ relocations histories. In their simplest form, these areas are defined as the smallest area incorporating some subjective percentage of relocations, generally 30–50%. Although widely used, the selection of the 30% or 50% isopleth is ad-hoc. In an attempt to make this selection more rigorous, Vander Wal and Rodgers (2012) propose researchers fit an exponential model to the rate at which home-range area increases for each percent increase in isopleth value; they define the core area as the point at which the slope of this exponential curve is 1. Other approaches involve integrating time-use patterns into the spatial analysis of movement data. In the simplest time-use metrics, researchers evaluate the time to return and the return rate (frequency of returns) to pre-defined areas in the home range, given some prescribed minimum time between “returns” (Seidel and Boyce 2015, Van Moorter et al.2016). More elaborate methods incorporate time-use into the construction of the utilization distributions themselves (Benhamou and Riotte-Lambert 2012). The T-LoCoH method (implemented in R through the tlocoh package; (Lyons et al. 2013)), for example, allows users to evaluate revisitation (a measure of separate visits) and average duration of visits (Table 1) to all local hulls within an animal’s home range. These analyses can help elucidate spatial patterns in time strategies: teasing out not only what habitats animals are using, but also separating those they used in repeated short visits from those used for infrequent but extended visits.

In the GIS community, the competition in and for space and time that ecologists study as habitat selection or home range analysis, has often been considered as an extension of classic time geography (Demšar et al. 2015, Long 2016). Various methods for illuminating space-time prisms, which map the potential movements of an object in both geographic space and time given information about its movement capabilities (e.g. travel velocity), can account for the time and sequentiality of measurements along movement paths. Extensions of these space-time prisms has resulted in methods for constructing 3-dimensional elements used to estimate the probability that an object was located at some location at some particular time. This approach offers a sophisticated technique for understanding the movements and activities (and potentially interactions) of animals at fine temporal and spatial scales (Downs et al. 2014).

All simple home-range estimators that ignore the temporal autocorrelation inherent in movement trajectories may be applied either to a single animal’s trajectory or to a combined dataset across multiple individuals. Estimation methods that use the temporal nature of movement trajectories (e.g., autocorrelated kernel density methods, Brownian bridges, T-LoCoH), however, must be applied first to individual trajectories independently and subsequently combined if population space use is of interest.

The authors wish to thank the Getz and Brashares labs at UC Berkeley for their careful consideration of early manuscript drafts and helpful comments towards the shaping of this review. This research was supported by grants NIH-GM 083863 and NSF-EEID 1617982. The impetus for this review arose from a presentation given by WMG at Ohio State University, at an NSF Workshop on Advancing Movement and Mobility Science by Bridging Research on Human Mobility and Animal Movement Ecology, organized by Harvey J. Miller, Jennifer A. Miller and Gil Bohrer.