Abstract:  Choosing an appropriate home range model is important for describing space use by animals and understanding the ecological processes affecting animal movement. Traditional approaches for choosing among home range models have not resulted in general, consistent, and unambiguous criteria that can be applied to individual data sets. We present a new application of information-theoretic model selection that overcomes many of the limitations of traditional approaches, as follows. (1) It alleviates the need to know the true home range to assess home range models, thus allowing performance to be evaluated with data on individual animals. (2) The best model can be chosen from a set of candidate models with the proper balance between fit and complexity. (3) If candidate home range models are based on underlying ecological processes, researchers can use the selected model not only to describe the home range, but also to infer the importance of various ecological processes affecting animal movements within the home range.

Horne, J. S. and E. O. Garton.  2006.  Likelihood Cross-validation versus Least Squares Cross-validation for Choosing the Smoothing Parameter in Kernel Home Range Analysis. Journal of Wildlife Management 70:641-648.

Abstract:  Fixed kernel density analysis with least squares cross-validation (LSCVh) choice of the smoothing parameter is currently recommended for home-range estimation. However, LSCVh has several drawbacks, including high variability, a tendency to undersmooth data, and multiple local minima in the LSCVh function. An alternative to LSCVh is likelihood cross-validation (CVh). We used computer simulations to compare estimated home ranges using fixed kernel density with CVh and LSCVh to true underlying distributions. Likelihood cross-validation generally performed better than LSCVh, producing estimates with better fit and less variability, and it was especially beneficial at sample sizes <50. Because CVh is based on minimizing the Kullback-Leibler distance and LSCVh the integrated squared error, for each of these measures of discrepancy, we discussed their foundation and general use, statistical properties as they relate to home-range analysis, and the biological or practical interpretation of these statistical properties. We found 2 important problems related to computation of kernel home-range estimates, including multiple minima in the LSCVh and CVh functions and discrepancies among estimates from current home-range software. Choosing an appropriate smoothing parameter is critical when using kernel methods to estimate animal home ranges, and our study provides useful guidelines when making this decision.

Horne, J. S., E. O. Garton, and K. A. Sager.  2007.  Correcting Home Range Models For Observation  Bias. Journal of Wildlife Management: 71:996-1001.

Abstract:  Home-range models implicitly assume equal observation rates across the study area. Because this assumption is frequently violated, we describe methods for correcting home-range models for observation bias. We suggest corrections for 3 general types of home-range models including those for which parameters are estimated using least-squares theory, models utilizing maximum likelihood for parameter estimation, and models based on kernel smoothing techniques. When applied to mule deer (Odocoileus hemionus) location data, we found that uncorrected estimates of the utilization distribution were biased low by as much as 18.4% and biased high by 19.2% when compared to corrected estimates. Because the magnitude of bias is related to several factors, future research should determine the relative influence of each of these factors on home-range bias.

Horne, Jon S., Edward O. Garton, Stephen S. Krone, and Jesse L. Lewis.  2007.  Analyzing animal movements using Brownian bridges.  Ecology 88:2354-2363.

    Abstract: By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal’s mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal’s probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluatingthe influence of fine-scale resource selection on animal movement patterns.