Correlation and studies of habitat selection: problem, red herring or opportunity?

With the advent of new technologies, animal locations are being collected at ever finer spatio-temporal scales. We review analytical methods for dealing with correlated data in the context of resource selection, including post hoc variance inflation techniques, ‘two-stage’ approaches based on models fit to each individual, generalized estimating equations and hierarchical mixed-effects models. These methods are applicable to a wide range of correlated data problems, but can be difficult to apply and remain especially challenging for use–availability sampling designs because the correlation structure for combinations of used and available points are not likely to follow common parametric forms. We also review emerging approaches to studying habitat selection that use fine-scale temporal data to arrive at biologically based definitions of available habitat, while naturally accounting for autocorrelation by modelling animal movement between telemetry locations. Sophisticated analyses that explicitly model correlation rather than consider it a nuisance, like mixed effects and state-space models, offer potentially novel insights into the process of resource selection, but additional work is needed to make them more generally applicable to large datasets based on the use–availability designs. Until then, variance inflation techniques and two-stage approaches should offer pragmatic and flexible approaches to modelling correlated data.

[1]  Jason Matthiopoulos,et al.  The interpretation of habitat preference metrics under use–availability designs , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[2]  O. Ovaskainen,et al.  State-space models of individual animal movement. , 2008, Trends in ecology & evolution.

[3]  Stan Lipovetsky,et al.  Generalized Latent Variable Modeling: Multilevel,Longitudinal, and Structural Equation Models , 2005, Technometrics.

[4]  John Fieberg,et al.  Understanding variation in autumn migration of northern white-tailed deer by long-term study , 2008 .

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

[6]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[7]  Benjamin D. Dalziel,et al.  Fitting Probability Distributions to Animal Movement Trajectories: Using Artificial Neural Networks to Link Distance, Resources, and Memory , 2008, The American Naturalist.

[8]  Samuel A. Cushman,et al.  Elephants in space and time , 2005 .

[9]  M. Hebblewhite,et al.  Distinguishing technology from biology: a critical review of the use of GPS telemetry data in ecology , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[10]  Helene Lair,et al.  Estimating the Location of the Focal Center in Red Squirrel Home Ranges , 1987 .

[11]  Gordon B. Stenhouse,et al.  Temporal autocorrelation functions for movement rates from global positioning system radiotelemetry data , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[12]  M. Boyce,et al.  WOLVES INFLUENCE ELK MOVEMENTS: BEHAVIOR SHAPES A TROPHIC CASCADE IN YELLOWSTONE NATIONAL PARK , 2005 .

[13]  P. Albert,et al.  Models for longitudinal data: a generalized estimating equation approach. , 1988, Biometrics.

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

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

[16]  ELIZABETH M. GLENN,et al.  SPOTTED OWL HOME-RANGE AND HABITAT USE IN YOUNG FORESTS OF WESTERN OREGON , 2004 .

[17]  Paul R Moorcroft,et al.  Mechanistic home range models and resource selection analysis: a reconciliation and unification. , 2006, Ecology.

[18]  G. Stenhouse,et al.  Modeling grizzly bear habitats in the Yellowhead ecosystem of Alberta: taking autocorrelation seriously , 2002 .

[19]  L. Skovgaard NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. , 1996 .

[20]  Devin S Johnson,et al.  A General Framework for the Analysis of Animal Resource Selection from Telemetry Data , 2008, Biometrics.

[21]  Hugh P. Possingham,et al.  A SPATIALLY EXPLICIT HABITAT SELECTION MODEL INCORPORATING HOME RANGE BEHAVIOR , 2005 .

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

[23]  Paul A Murtaugh,et al.  Simplicity and complexity in ecological data analysis. , 2007, Ecology.

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

[25]  W. Pan Akaike's Information Criterion in Generalized Estimating Equations , 2001, Biometrics.

[26]  Juan M. Morales,et al.  EXTRACTING MORE OUT OF RELOCATION DATA: BUILDING MOVEMENT MODELS AS MIXTURES OF RANDOM WALKS , 2004 .

[27]  V. Carey,et al.  Mixed-Effects Models in S and S-Plus , 2001 .

[28]  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.

[29]  Gary C. White,et al.  Analysis of Wildlife Radio-Tracking Data , 1990 .

[30]  Cameron L. Aldridge,et al.  Application of random effects to the study of resource selection by animals. , 2006, The Journal of animal ecology.

[31]  R. Clark,et al.  Design and analysis of clustered, unmatched resource selection studies , 2008 .

[32]  C. Bennington,et al.  Use and Misuse of Mixed Model Analysis of Variance in Ecological Studies , 1994 .

[33]  James E. Dunn,et al.  Analysis of Radio Telemetry Data in Studies of Home Range , 1977 .

[34]  Gary C. White,et al.  Autocorrelation of location estimates and the analysis of radiotracking data , 1999 .

[35]  Mark Hebblewhite,et al.  Modelling wildlife–human relationships for social species with mixed‐effects resource selection models , 2007 .

[36]  Mollie E. Brooks,et al.  Generalized linear mixed models: a practical guide for ecology and evolution. , 2009, Trends in ecology & evolution.

[37]  Nairanjana Dasgupta,et al.  A Multivariate χ 2 Analysis of Resource Selection Data , 1998 .

[38]  H. Beyer,et al.  Group-size-mediated habitat selection and group fusion-fission dynamics of bison under predation risk. , 2009, Ecology.

[39]  F. Bunnell,et al.  Characterizing independence of observations in movements of columbian black-tailed deer , 1994 .

[40]  Devin L. Johnson,et al.  A Bayesian Random Effects Discrete-Choice Model for Resource Selection: Population-Level Selection Inference , 2006 .

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

[42]  Atle Mysterud,et al.  Temporal scales, trade-offs, and functional responses in red deer habitat selection. , 2009, Ecology.

[43]  Trent L McDonald,et al.  Estimating habitat selection when GPS fix success is less than 100%. , 2009, Ecology.

[44]  J. Fieberg,et al.  Regression modelling of correlated data in ecology: subject‐specific and population averaged response patterns , 2009 .

[45]  F. Cagnacci,et al.  Animal ecology meets GPS-based radiotelemetry: a perfect storm of opportunities and challenges , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[46]  G Molenberghs,et al.  The impact of a misspecified random‐effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models , 2008, Statistics in medicine.

[47]  Leo Polansky,et al.  Disentangling the effects of forage, social rank, and risk on movement autocorrelation of elephants using Fourier and wavelet analyses , 2008, Proceedings of the National Academy of Sciences.

[48]  Chris J. Johnson,et al.  Movement parameters of ungulates and scale‐specific responses to the environment , 2002 .

[49]  G. Molenberghs,et al.  Models for Discrete Longitudinal Data , 2005 .

[50]  Thomas Kneib,et al.  A general approach to the analysis of habitat selection , 2009, Environmental and Ecological Statistics.

[51]  John Fieberg,et al.  Kernel density estimators of home range: smoothing and the autocorrelation red herring. , 2007, Ecology.

[52]  Salvatori,et al.  Estimating temporal independence of radio-telemetry data on animal activity , 1999, Journal of theoretical biology.

[53]  Mark S. Boyce,et al.  Scale for resource selection functions , 2006 .

[54]  Tim Coulson,et al.  An Integrated Approach to Identify Spatiotemporal and Individual‐Level Determinants of Animal Home Range Size , 2006, The American Naturalist.

[55]  J. Rhymer,et al.  HABITAT SELECTION BY WOOD TURTLES (CLEMMYS INSCULPTA): AN APPLICATION OF PAIRED LOGISTIC REGRESSION , 2002 .

[56]  S. Cherry,et al.  USE AND INTERPRETATION OF LOGISTIC REGRESSION IN HABITAT-SELECTION STUDIES , 2004 .

[57]  DANA L. THOMAS,et al.  Study Designs and Tests for Comparing Resource Use and Availability II , 2006 .

[58]  Lennart Persson,et al.  Comparative support for the niche variation hypothesis that more generalized populations also are more heterogeneous , 2007, Proceedings of the National Academy of Sciences.

[59]  RYAN M. NIELSON,et al.  Winter Habitat Selection of Mule Deer Before and During Development of a Natural Gas Field , 2006 .

[60]  Subhash R Lele,et al.  Weighted distributions and estimation of resource selection probability functions. , 2006, Ecology.

[61]  P. Moorcroft,et al.  Analytic steady-state space use patterns and rapid computations in mechanistic home range analysis , 2007, Journal of mathematical biology.

[62]  J M Neuhaus,et al.  The effect of retrospective sampling on binary regression models for clustered data. , 1990, Biometrics.

[63]  Dale L. Zimmerman,et al.  An animal movement model incorporating home range and habitat selection , 2008, Environmental and Ecological Statistics.

[64]  Atle Mysterud,et al.  FUNCTIONAL RESPONSES IN HABITAT USE: AVAILABILITY INFLUENCES RELATIVE USE IN TRADE-OFF SITUATIONS , 1998 .

[65]  Nicola Koper,et al.  Generalized estimating equations and generalized linear mixed-effects models for modelling resource selection , 2009 .

[66]  T. Hayden,et al.  Autocorrelated data in telemetry studies: time to independence and the problem of behavioural effects , 1998 .

[67]  Bryan F. J. Manly,et al.  Resource Selection by Animals , 1993, Springer Netherlands.

[68]  Paul J Rathouz,et al.  Accounting for animal movement in estimation of resource selection functions: sampling and data analysis. , 2009, Ecology.

[69]  J. Diniz‐Filho,et al.  Spatial autocorrelation and red herrings in geographical ecology , 2003 .

[70]  Douglas H. Johnson THE COMPARISON OF USAGE AND AVAILABILITY MEASUREMENTS FOR EVALUATING RESOURCE PREFERENCE , 1980 .

[71]  Dag Ø. Hjermann,et al.  Analyzing habitat selection in animals without well-defined home ranges , 2000 .

[72]  Nicholas J. Aebischer,et al.  Compositional Analysis of Habitat Use From Animal Radio-Tracking Data , 1993 .

[73]  D. Haydon,et al.  Multiple movement modes by large herbivores at multiple spatiotemporal scales , 2008, Proceedings of the National Academy of Sciences.

[74]  A. Dufour,et al.  Eigenanalysis of selection ratios from animal radio-tracking data. , 2006, Ecology.

[75]  P. Diggle Analysis of Longitudinal Data , 1995 .

[76]  S. Lele A New Method for Estimation of Resource Selection Probability Function , 2009 .

[77]  Deborah A. Jenkins,et al.  Socially informed random walks: incorporating group dynamics into models of population spread and growth , 2008, Proceedings of the Royal Society B: Biological Sciences.

[78]  Donald N. McCloskey The Insignificance of Statistical Significance , 1995 .

[79]  Bryan F. J. Manly,et al.  Assessing habitat selection when availability changes , 1996 .

[80]  Joshua J. Millspaugh,et al.  THE APPLICATION OF DISCRETE CHOICE MODELS TO WILDLIFE RESOURCE SELECTION STUDIES , 1999 .

[81]  Raoul Van Damme,et al.  Foraging mode and locomotor capacities in Lacertidae , 2008 .

[82]  P. Heagerty Marginally Specified Logistic‐Normal Models for Longitudinal Binary Data , 1999, Biometrics.

[83]  Radu V. Craiu,et al.  Inference Methods for the Conditional Logistic Regression Model with Longitudinal Data , 2008, Biometrical journal. Biometrische Zeitschrift.

[84]  R. White,et al.  Energy expenditures for locomotion by barren-ground caribou , 1987 .

[85]  Yongdai Kim,et al.  Analysis of longitudinal data in case-control studies , 2004 .

[86]  P. Burridge,et al.  A Very Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix , 1991 .

[87]  Chris J. Johnson,et al.  Resource Selection Functions Based on Use–Availability Data: Theoretical Motivation and Evaluation Methods , 2006 .

[88]  Douglas H. Johnson The Insignificance of Statistical Significance Testing , 1999 .

[89]  J. Kalbfleisch,et al.  A Comparison of Cluster-Specific and Population-Averaged Approaches for Analyzing Correlated Binary Data , 1991 .

[90]  J. Gaillard,et al.  Habitat–performance relationships: finding the right metric at a given spatial scale , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[91]  M. Boyce,et al.  Evaluating resource selection functions , 2002 .

[92]  Bernie J. McConnell,et al.  Estimating space‐use and habitat preference from wildlife telemetry data , 2008 .

[93]  R L Williams,et al.  A Note on Robust Variance Estimation for Cluster‐Correlated Data , 2000, Biometrics.

[94]  Jason Matthiopoulos,et al.  The use of space by animals as a function of accessibility and preference , 2003 .

[95]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[96]  B. Manly,et al.  Resource selection by animals: statistical design and analysis for field studies. , 1994 .

[97]  Jean Chesson,et al.  MEASURING PREFERENCE IN SELECTIVE PREDATION , 1978 .

[98]  S. Rabe-Hesketh,et al.  Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects , 2005 .