Correcting for missing and irregular data in home-range estimation.

Home-range estimation is an important application of animal tracking data that is frequently complicated by autocorrelation, sampling irregularity, and small effective sample sizes. We introduce a novel, optimal weighting method that accounts for temporal sampling bias in autocorrelated tracking data. This method corrects for irregular and missing data, such that oversampled times are downweighted and undersampled times are upweighted to minimize error in the home-range estimate. We also introduce computationally efficient algorithms that make this method feasible with large data sets. Generally speaking, there are three situations where weight optimization improves the accuracy of home-range estimates: with marine data, where the sampling schedule is highly irregular, with duty cycled data, where the sampling schedule changes during the observation period, and when a small number of home-range crossings are observed, making the beginning and end times more independent and informative than the intermediate times. Using both simulated data and empirical examples including reef manta ray, Mongolian gazelle, and African buffalo, optimal weighting is shown to reduce the error and increase the spatial resolution of home-range estimates. With a conveniently packaged and computationally efficient software implementation, this method broadens the array of data sets with which accurate space-use assessments can be made.

[1]  A. Izenman.  Recent Developments in Nonparametric Density Estimation , 1991 .

[2]  Borger Luca,et al.  Animal Home Ranges: Concepts, Uses and Estimation , 2020 .

[3]  Tremaine Gregory.  Home Range Estimation , 2017 .

[4]  Rolf A. Ims,et al.  Effects of spatiotemporal scale on autocorrelation and home range estimators , 1997 .

[5]  C H Fleming,et al.  Estimating where and how animals travel: an optimal framework for path reconstruction from autocorrelated tracking data. , 2015, Ecology.

[6]  MARK S. LINDBERG,et al.  Satellite Telemetry in Avian Research and Management: Sample Size Considerations , 2007 .

[7]  Peter Leimgruber,et al.  From Fine-Scale Foraging to Home Ranges: A Semivariance Approach to Identifying Movement Modes across Spatiotemporal Scales , 2014, The American Naturalist.

[8]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[9]  Francesca Cagnacci,et al.  Resolving issues of imprecise and habitat-biased locations in ecological analyses using GPS telemetry data , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[10]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[11]  C H Fleming,et al.  Rigorous home range estimation with movement data: a new autocorrelated kernel density estimator. , 2015, Ecology.

[12]  R. Powell,et al.  What is a home range? , 2012 .

[13]  Norman A. Slade,et al.  Testing For Independence of Observations in Animal Movements , 1985 .

[14]  Don W. Hayne,et al.  Calculation of Size of Home Range , 1949 .

[15]  Niki Trigoni,et al.  A new Magneto‐Inductive tracking technique to uncover subterranean activity: what do animals do underground? , 2015 .

[16]  Sandro Lovari,et al.  Effects of sampling regime on the mean and variance of home range size estimates. , 2006, The Journal of animal ecology.

[17]  W. H. Burt.  Territoriality and Home Range Concepts as Applied to Mammals , 1943 .

[18]  Wolfgang Heidrich,et al.  Accelerometer-informed GPS telemetry : Reducing the trade-off between resolution and longevity , 2012 .

[19]  Mark S Boyce,et al.  Correlation and studies of habitat selection: problem, red herring or opportunity? , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[20]  Bruce A. Pond,et al.  Allowing for redundancy and environmental effects in estimates of home range utilization distributions , 2005 .

[21]  Greg A Breed,et al.  Predicting animal home-range structure and transitions using a multistate Ornstein-Uhlenbeck biased random walk. , 2017, Ecology.

[22]  Atte Moilanen,et al.  Kernel-based home range method for data with irregular sampling intervals , 2006 .

[23]  Edy Setyawan,et al.  Data from: Correcting for missing and irregular data in home-range estimation , 2018 .

[24]  Lee A. Vierling,et al.  Effects of habitat on GPS collar performance: using data screening to reduce location error , 2007 .

[25]  R. Mazo.  On the theory of brownian motion , 1973 .

[26]  Peter Leimgruber,et al.  Non‐Markovian maximum likelihood estimation of autocorrelated movement processes , 2014 .

[27]  A. Izenman.  Review Papers: Recent Developments in Nonparametric Density Estimation , 1991 .

[28]  W. V. Winkle.  COMPARISON OF SEVERAL PROBABILISTIC HOME-RANGE MODELS' , 1975 .

[29]  Justin M. Calabrese,et al.  ctmm: an r package for analyzing animal relocation data as a continuous‐time stochastic process , 2016 .

[30]  J. Squires,et al.  Effect of forest canopy on GPS-based movement data , 2005 .

[31]  Paul G. Blackwell,et al.  Exact Bayesian inference for animal movement in continuous time , 2016 .

[32]  Devin S Johnson,et al.  Continuous-time correlated random walk model for animal telemetry data. , 2008, Ecology.

[33]  Gary C. White,et al.  Effects of biotelemetry triangulation error on detecting habitat selection , 1986 .

[34]  R. Kays,et al.  Terrestrial animal tracking as an eye on life and planet , 2015, Science.

[35]  H. Kile,et al.  Bandwidth Selection in Kernel Density Estimation , 2010 .

[36]  Gordon B. Stenhouse,et al.  Removing GPS collar bias in habitat selection studies , 2004 .

[37]  Guillaume Péron,et al.  Uncovering periodic patterns of space use in animal tracking data with periodograms, including a new algorithm for the Lomb-Scargle periodogram and improved randomization tests , 2016, Movement ecology.

[38]  JOHN FIEBERG,et al.  Utilization Distribution Estimation Using Weighted Kernel Density Estimators , 2007 .

[39]  Jon S. Horne,et al.  Correcting Home-Range Models for Observation Bias , 2007 .

[40]  Christen H. Fleming,et al.  A new kernel density estimator for accurate home‐range and species‐range area estimation , 2017 .