Mixed conditional logistic regression for habitat selection studies.

1. Resource selection functions (RSFs) are becoming a dominant tool in habitat selection studies. RSF coefficients can be estimated with unconditional (standard) and conditional logistic regressions. While the advantage of mixed-effects models is recognized for standard logistic regression, mixed conditional logistic regression remains largely overlooked in ecological studies. 2. We demonstrate the significance of mixed conditional logistic regression for habitat selection studies. First, we use spatially explicit models to illustrate how mixed-effects RSFs can be useful in the presence of inter-individual heterogeneity in selection and when the assumption of independence from irrelevant alternatives (IIA) is violated. The IIA hypothesis states that the strength of preference for habitat type A over habitat type B does not depend on the other habitat types also available. Secondly, we demonstrate the significance of mixed-effects models to evaluate habitat selection of free-ranging bison Bison bison. 3. When movement rules were homogeneous among individuals and the IIA assumption was respected, fixed-effects RSFs adequately described habitat selection by simulated animals. In situations violating the inter-individual homogeneity and IIA assumptions, however, RSFs were best estimated with mixed-effects regressions, and fixed-effects models could even provide faulty conclusions. 4. Mixed-effects models indicate that bison did not select farmlands, but exhibited strong inter-individual variations in their response to farmlands. Less than half of the bison preferred farmlands over forests. Conversely, the fixed-effect model simply suggested an overall selection for farmlands. 5. Conditional logistic regression is recognized as a powerful approach to evaluate habitat selection when resource availability changes. This regression is increasingly used in ecological studies, but almost exclusively in the context of fixed-effects models. Fitness maximization can imply differences in trade-offs among individuals, which can yield inter-individual differences in selection and lead to departure from IIA. These situations are best modelled with mixed-effects models. Mixed-effects conditional logistic regression should become a valuable tool for ecological research.

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

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

[3]  Kenneth E. Train,et al.  Discrete Choice Methods with Simulation , 2016 .

[4]  Andrew Fall,et al.  A domain-specific language for models of landscape dynamics , 2001 .

[5]  D. Hik,et al.  Forage selection by collared pikas, Ochotona collaris, under varying degrees of predation risk , 2004 .

[6]  R. Courtois,et al.  Winter selection of landscapes by woodland caribou: behavioural response to geographical gradients in habitat attributes , 2008 .

[7]  M. Hay,et al.  Seed Escape from Heteromyid Rodents: The Importance of Microhabitat and Seed Preference , 1981 .

[8]  John M. Fryxell,et al.  THE TEMPORAL SCALE OF FORAGING DECISIONS IN BISON , 2002 .

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

[10]  Lynn Kuo,et al.  A Note on the Estimation of the Multinomial Logit Model With Random Effects , 2001 .

[11]  EVELYN H. MERRILL,et al.  HABITAT SELECTION BY ELK BEFORE AND AFTER WOLF REINTRODUCTION IN YELLOWSTONE NATIONAL PARK , 2005 .

[12]  R. Sukumar.  The management of large mammals in relation to male strategies and conflict with people , 1991 .

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

[14]  Henrik G. Smith,et al.  Landscape composition affects habitat use and foraging flight distances in breeding European starlings , 2003 .

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

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

[17]  TRENT L. McDONALD,et al.  Discrete-Choice Modeling in Wildlife Studies Exemplified by Northern Spotted Owl Nighttime Habitat Selection , 2006 .

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

[19]  Donald G. Whittaker,et al.  Habitat use patterns of sympatric deer species on Rocky Mountain Arsenal, Colorado , 2004 .

[20]  Sophia Rabe-Hesketh,et al.  Multilevel logistic regression for polytomous data and rankings , 2003 .

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

[22]  G. Molenberghs,et al.  Linear Mixed Models for Longitudinal Data , 2001 .

[23]  K. Train,et al.  Mixed Logit with Repeated Choices: Households' Choices of Appliance Efficiency Level , 1998, Review of Economics and Statistics.

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

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

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

[27]  Burt P. Kotler,et al.  Patch use, apprehension, and vigilance behavior of Nubian Ibex under perceived risk of predation , 2006, Behavioral Ecology.

[28]  Darryl N. Jones,et al.  Management of aggressive Australian magpies by translocation , 2003 .

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

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

[31]  Monica G. Turner,et al.  Scale and heterogeneity in habitat selection by elk in Yellowstone National Park , 2003 .

[32]  D. McFadden,et al.  MIXED MNL MODELS FOR DISCRETE RESPONSE , 2000 .

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

[34]  C. Bhat.  Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model , 2001 .

[35]  Daniel Fortin,et al.  Considering ecological dynamics in resource selection functions. , 2010, The Journal of animal ecology.

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

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