(2015), who propose the autocorrelated kernel density estimator (AKDE). One further generalization of the KDE home range to the time-dependent context is given by Fleming et al. The main difference with MKDE is that the smoothing parameter of the SLKDE is selected in such a way that it “inflates” the home range estimator on the observed relocations and thins it in the lines connecting them: the rasters have what Steiniger and Hunter (2013) call a “bone-like” shape. Then all the rasters are pooled to construct an unnormalized estimator of the UD (it does not integrate to 1). This estimator is called the raster r i, i+1. Each line segment connecting two consecutive relocations, x i and x i+1, is divided into subsegments and a KDE is constructed on the line segment based on observed and interpolated relocations. Steiniger and Hunter (2013) propose the scaled line kernel home range estimator (SLKDE), which is similar to the MKDE of Benhamou and Cornelis (2010). (2014) use the MKDE on 3-dimensional location data. For instance, to incorporate knowledge of boundaries that the animal does not go through (rivers, cliffs, etc.), Benhamou and Cornelis (2010) suggest to reset to 0 beyond the boundary and reflect with respect to the boundary the resulting estimate of the utilization density. There have been extensions to the original MKDE proposal. MKDE home range with h min = 1 ( solid line) and h min = 4000 ( dashed line).

(2019) analyze the influence of fix rate and tracking duration on the home ranges obtained with MKDE and KDE, thus providing also a comparison between the performance of the two methods on a specific set of locations.įig. Optimal simultaneous selection of all the parameters of MKDE with respect to some criterion seems computationally unfeasible even for moderate sample sizes. 13 we have plotted the MKDE home ranges for two very different values of h min but equal values of the rest of parameters: clearly, the choice of this smoothing parameter can substantially alter the resulting home range. For instance, using package adehabitatHR, in Fig. A drawback of MKDE is that it depends, thus, on the choice of several parameters, such as h min, h max and the length of the subintervals. For each time interval h i is a smooth function of the time lapse from t i and to t i+1, taking its smallest value h min at the end points and the largest (at most h max) at the midpoint. Then KDE is carried out on the known and the interpolated relocations with a variable one-dimensional smoothing parameter h i( t). MKDE consists in dividing each step or time interval into several substeps, that is, adding new points at regular intervals on each step. In the context of estimating the active utilization distribution (describing space frequency use in the active moments of the animal), Benhamou and Cornelis (2010) developed the movement-based kernel density estimation (MKDE) method. This approach does not seem appropriate, since time is not a random variable whose frequency we want to analyze, as we noted at the beginning of Section 2.2. Keating and Cherry (2009) suggested a product kernel density estimator where time was incorporated as an extra variable to the two-dimensional location vector, thus yielding three-dimensional observations. This means that, to design methods to estimate the utilization distribution density, we can proceed exactly the same as for independent data. Nevertheless, there are two important issues that should be remarked: first, the definition of the kernel density estimator for dependent data is exactly the same as for independent data, and second, regarding the fundamental problem of bandwidth selection, the data can be treated as if they were independent, since the asymptotically optimal bandwidth for independent data is also optimal under quite general conditions of dependence, as shown in Hall et al. There have been various attempts to generalize the kernel home range estimator to incorporate the time dependence between the observed locations. Amparo Baíllo, José Enrique Chacón, in Handbook of Statistics, 2021 2.2.1.2 Kernel density estimation