Elliptical Time-Density Model (Wall et al. 2014) African Elephant Dataset (Source-Save the Elephants)

Wall J, Wittemyer G, LeMay V, Douglas-Hamilton I, Klinkenberg B (2014) Elliptical Time-Density model to estimate wildlife utilization distributions: Methods in Ecology and Evolution. doi:10.1111/2041-210X.12218 We present a new animal space-use model (Elliptical Time-Density - ETD) that uses discrete-time tracking data collected in wildlife movement studies. The ETD model provides a trajectory-based, non-parametric approach to estimate the utilization distribution (UD) of an animal, using model parameters derived directly from the movement behavior of the species. The model builds on the theory of ‘time-geography’ whereby elliptical constraining regions are established between temporally-adjacent recorded locations. Using a Weibull speed distribution fitted for an animal's movement data, a time-density value (i.e., time per unit landscape) is determined from the expectation of all elliptical regions equal to, or greater-than, the minimum bounding ellipse for a given landscape point. We tested the ETD model using a tracking dataset for an African elephant (Loxodonta africana) and compared the resulting UDs for regularly sampled, frequently recorded locations, as well as irregular random time intervals between locations and also infrequent temporal-sampling regimes, providing insight to the method's performance with different resolution data. We compared the performance of the ETD model, the Brownian Bridge Movement Model (BBMM), the Time-Geography Density Estimator (TGDE) and the Kernel Density Estimator (KDE) by calculating omission/commission errors from the predicted space-use distribution of each model relative to the true known UD of our elephant test data. The comparison was made for the 10% to 99% percentile UD model areas. The ETD90 model (i.e., ETD model parameterized using the 90% percentile value of the Weibull speed distribution) resulted in the fewest errors of commission and omission with regards to locating the true movement path at the 99% percentile UD area. The ETD model provides an improved approach for estimating animal UDs since: i) parameters are derived directly from the tracking data rather than assumed; ii) parameter values are biologically interpretable; iii) the Weibull speed distribution is adaptable to various temporal-sampling regimes; and iv) the ETD model handles the case of degenerate ellipses thus preserving landscape connectivity in the UD. Software (freeware) for calculating the ETD and a Bayesian framework for estimating the Weibull distribution speed parameters are also introduced in the paper.