Recent advances in GPS and data transmission technologies have greatly increased the volume, accuracy, affordability, and ancillary variables integrated with movement data [1, 2], creating both opportunities and challenges for ecologists [3, 4].

One of the most common uses of location data has been the estimation of home ranges and utilization distributions (UDs) [5]. Minimum convex polygons (MCPs) were among the earliest home range construction techniques, and are still widely used [6] despite their well-known biases in range estimation, sensitivity to point geometry, and inability to differentiate internal space [7–9]. In the 1980s, kernel density estimators (KDE) for constructing UDs [10] were developed and became quickly popular. These methods, based on the superposition of Gaussian or compact (e.g. uniform or Epinechnikov) kernels, are more suitable for concave geometries, can construct probability contours, and are easy to use due to their implementation in a variety of software packages [6]. More recent methods combine the simplicity of polygon methods with the robustness of kernel methods by superimposing and then aggregating non-parametric shapes constructed around each point, including Voronoi polygons [11], Delaunay triangles [12], and local MCPs [13, 14].

These classic home range methods generally treat locations as independent, an assumption especially violated with regularly sampled GPS locations. Techniques to correct for serial correlation include resampling the data [15, 16] and applying weights based on temporal density [17]. However other methods have been developed that take advantage of the information contained in serial correlation by modelling the movement between known locations. Among these are the Brownian bridge movement model (BBMM) method that constructs kernel density surfaces above each movement segment based on a diffusion model and the spatial uncertainty of each end point [18]. Enhancements to BBMM refine the bridge model between known locations by dynamically adjusting diffusion rates based on an independent segmentation of the trajectory into discrete behaviour modes [19]. Similarly, movement based KDE (MKDE) incorporates serial correlation by interpolating additional points between known locations based on activity time [20], with options to detect and correct for boundary constraints [20], and incorporate an anisotropic advective component into the local kernel [21]. More recently, time geography methods, which model movement between known locations based on the animal's maximum theoretical velocity, have been extended to home range analysis. These include the construction and aggregation of elliptical spatiotemporal potential path areas (PPA) [22], as well as probabilistic geoellipse surfaces based on a probability decay function away from the center path [23]. The later approach, known as Time Geography Density Estimation (TGDE), produces a probability surface comparable to BBMM but with smoothing objectively specified based on the animal's movement velocity.

Such movement-based home range methods explicitly incorporate information contained in temporal auto-correlation, but are still essentially models of space-use. Other methods aim to infer behavioural clues from movement data based upon the temporal patterns in the data, including variations in the amount of time spent near each location [24, 25], periodicities in step length [26, 27], path recursions [28], fractal searching behaviour [29], and a partial sum analysis of movement properties [30]. To shed light on behavioural mechanisms, such temporally-sensitive characterizations of movement can be analysed in light of data on resource distribution using spatiotemporal statistical models [31], process-based stochastic state space models [32–34], agent-based models [35, 36], and cognitive models [37].

Although progress has been made in developing methods that quantify space-use and behavior [38], these advances have not, in general, been well-integrated [39]. Home range estimators commonly ignore time other than for time-interval windowing [6, 40], while spatiotemporal and space-state models are often divorced from a model of space-use. Far fewer techniques model space-use and time-use simultaneously, with important exceptions being joint space-time utilization distributions [41] and time weighted MKDE which combines movement KDE with an adaptation of the time-of-first passage method [42].

Here we present Time Local Convex Hull (T-LoCoH) which generalizes the non-parametric utilization construction method, LoCoH [13]. T-LoCoH integrates time with space in the construction of local hulls through a scaling that relates distance and time in reference to the individual's characteristic velocity. The resulting hulls are local in both space and time, enabling metrics for movement phase and multiple dimensions of time-use including revisitation and duration. By taking hulls, rather than individual points, as samples for analysis, T-LoCoH produces UDs with high fidelity to temporal partitions of space and can differentiate internal space either with a traditional density gradient or alternately various behavioral metrics, including time-use properties. This flexibility places T-LoCoH in a growing family of methods responding to the demand for more question-based home range methods [43]. In the discussion, we compare and contrast T-LoCoH with other home range methods.