v.adehabitat.kernelUD is used to estimate the utilization distribution (UD) of animals monitored by radio-tracking, with the classical kernel method.
The Utilization Distribution (UD) is the bivariate function giving the probability density that an animal is found at a point according to its geographical coordinates. Using this model, one can define the home range as the minimum area in which an animal has some specified probability of being located. The module v.adehabitat.kernelUD correspond to the approach described in Worton (1995).
The kernel method has been recommended by many authors for the estimation of the utilization distribution (e.g. Worton, 1989, 1995). The default method for the estimation of the smoothing parameter is the ad hoc method, i.e. for a bivariate normal kernel: h = Sigma*n^(-1/6), where Sigma = 0.5*(sd(x)+sd(y)), which supposes that the UD is bivariate normal.
Alternatively, the smoothing parameter h may be computed by Least Square Cross Validation (LSCV). The estimated value then minimizes the Mean Integrated Square Error (MISE), i.e. the difference in volume between the true UD and the estimated UD. Note that the cross-validation criterion cannot be minimized in some cases (indicated by "convergence: no" by the module). According to Seaman and Powell (1998) "This is a difficult problem that has not been worked out by statistical theoreticians, so no definitive response is available at this time" (see Seaman and Powell, 1998 for further details and tricky solutions).
The flag -r returns the UD so that the contour of the equal value of the UD displayed by the module r.contour corresponds to the different percentage levels of home-range estimation.
The results returned by this module are roughly identical to the results of the function kernelUD of the adehabitat package for the R software. The only difference is related to the LSCV method: because the minimization of the MISE requires numerical methods, the smoothing parameter found by v.adehabitat.kernelUD differ slightly from those returned by the function kernelUD in adehabitat (the correlation between the two is often greater than 0.99, pers.obs.).
This module heavily relies on the code written by Stefano Menegon for his module v.kernel. It has just been extended to allow the LSCV and ad hoc estimation of the smoothing parameter, and the computation of the volume under the UD for home range estimation.
Estimation of the home range with the LSCV smoothing parameter:
v.adehabitat.kernelUD input=localisations output=ud -o
Estimation of the UD with the ad hoc smoothing parameter:
v.adehabitat.kernelUD input=localisations output=ud
Estimation of the volume under the UD with a LSCV smmoothing parameter:
v.adehabitat.kernelUD input=localisations output=ud -o -r
Worton, B.J. (1995) Using Monte Carlo simulation to evaluate kernel-based home range estimators. Journal of Wildlife Management, 59, 794-800.
Calenge, C. (2006) The package adehabitat for the R software: a tool for the analysis of space and habitat use by animals. Ecological Modelling, 197, 516-519.
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