1. Evaluating Animal Space Use: New Developments to Estimate Animal Movements, Home Range, and Habitat Selection Dr. Jon S. Horne, University of Idaho

2. Central question: “Where do animals live… and why?” Space Use is Non-uniform Quantitative Description of Space Use “Utilization Distribution” The relative amount of time spent in an area

3. Biotelemetry Cannot Monitor Animals Continuously –Have locations at discrete intervals (e.g., telemetry)

4. Describing and Understanding Animal Space Use is Important We Want an Estimate of the Utilization Distribution Obtain This Estimate Using Discrete Locations

5. New Developments 1)Objective Method for Choosing Among Home Range Models 2)Improve the Kernel – Likelihood-based smoothing parameter 3)Correct Home Range Models for Observation Bias 4)The Brownian Bridge Movement Model 5)Incorporate Other Variables (e.g., habitat, other organisms) Into Home Range Models

6. 1) Selecting the Best Home Range Model How do we choose the best home range model? –Popularity –Evaluate using simulated data Shouldn’t we “Let the data speak”? –Information-theoretic model selection

7. Selecting the Best Model Selection Criteria –Akaike’s Information Criteria (AIC) Adjusts model likelihood for overfitting –Likelihood Cross-validation Criteria (CVC) Evaluates the predictive ability Stone (1977) Showed Asymptotic Equivalence

8. Applying Selection Criteria to Home Range Models Can we calculate likelihood? –Yes, if home range models estimate the utilization distribution –No for minimum convex polygon (MCP) New model based on uniform distribution

9. Ecologically Based Shapes for Territories ( from Covich 1976 )

10. Exponential Power Model c = 1 c = 0.5 c = 0.1 Circular Uniform is a Particular Case 3 parameters: location, scale, shape ( c )

11. Application: Home Range Model Selection Used location data from a variety of species Evaluated 6 home range models: –Bivariate normal –Exponential power –2-mode circular normal mix –2-mode bivariate normal mix –Fixed and adaptive kernels Calculated AIC and CVC

12. Adaptive kernel 2-mode circular normal mix 2-mode bivariate mix Bivariate normal

13. Conclusions AIC or CVC –No strong arguments favoring one over the other –Must use CVC with kernel models No Single Model Was Always Best –Kernels performed quite well Goal of Model Selection –Find model closest to truth –“Test” hypotheses Use model selection to understand home range

14. New Approaches 1)Develop Objective Method for Choosing Among Home Range Models 2)Improve the Kernel – Likelihood-based smoothing parameter 3)Correct Home Range Models for Observation Bias 4)The Brownian Bridge Movement Model 5)Incorporate Other Variables (e.g., habitat, other organisms) Into Home Range Models

15. Influence of smoothing parameter (h) on kernel density Smoothing parameter (h) kernels Kernel estimate

16. Influence of smoothing parameter (h) on kernel density

17. Previously Recommended for Home Range Estimation Fixed Kernel Density –Least Squares Cross-validation (LSCVh) Drawbacks to LSCVh –High variablility –Tendency to undersmooth –Multiple minima in the LSCVh function

18. An Alternative Likelihood cross-validation (CVh) M inimizes Kullback-Leibler Distance CVh outperforms LSCVh –Especially at smaller sample sizes (i.e., <~50) –Especially if you enjoy Kullback-Leibler

19. Influence of Smoothing Parameter CVh LSCVh

20. Beware of Your Home Range Program 4 Programs All with LSCVh? KERNELHR (Seaman) HOMERANGE (Carr) My Program (Horne) AnimalMovement (Hooge)

21. New Approaches 1)Develop Objective Method for Choosing Among Home Range Models 2)Improve the Kernel – Likelihood-based smoothing parameter 3)Correct Home Range Models for Observation Bias 4)The Brownian Bridge Movement Model 5)Incorporate Other Variables (e.g., habitat, other organisms) Into Home Range Models

22. 3) Observation Bias of Locations Home range models traditionally assumed locations were obtained with equal probability Documented Unequal Observation Rates –Mostly for satellite telemetry –Can be modeled across a study site Corrections Based on Probability Sampling –Weight locations by 1/probability of inclusion

23. Difference between corrected and uncorrected models Bivariate normal 2-mode BVN Mix Location weights Fixed Kernel Underestimate ~18% Overestimate ~19%

24. Contributors to Magnitude of Bias Magnitude of differences in observation rates Aggregation of observation rates Home range model Sample size Intentional Differences (i.e., sampling design) –Diurnal vs. nocturnal locations

25. New Approaches 1)Develop Objective Method for Choosing Among Home Range Models 2)Improve the Kernel – Likelihood-based smoothing parameter 3)Correct Home Range Models for Observation Bias 4)The Brownian Bridge Movement Model 5)Incorporate Other Variables (e.g., habitat, other organisms) Into Home Range Models

26. 0.5 Kilometer

27. From: Stokes, D. L., P. D. Boersma, and L. S. Davis. 1998. Satellite tracking of Megellanic Penguin migration. Condor 100:376-381. Probabilistic model of the movement path? “Brownian Bridge”

28. Brownian Bridge Movement Model Can we model the probability of occurrence? Given: –Known locations –Time interval between locations

29. 2-location Brownian Bridge Shape dependent on: 1.Distance 2.Time interval 3.Animal mobility

30. Brownian Bridge Applications Estimate movement paths –Home range –Migration routes –Resource utilization/selection

31. Kilometer Black bear Satellite telemetry 1470 locations 20-min. intervals ~1 month

32. Home range of a male black bear Brownian bridge Fixed Kernel

33. Advantages of Brownian Bridge Home Range ASSUMES serially correlated data Models the movement path Location error explicitly incorporated

34. Caribou Migration Fall migration in southwestern Alaska 11 female caribou with GPS collars Locations every 7 hours

35. Probability Low High

36. Fine-scale Resource Selection Why did the bear cross the road… where it did?

37. Probability of crossing

38. Probability of Crossing

39. New Approaches 1)Develop Objective Method for Choosing Among Home Range Models 2)Improve the Kernel – Likelihood-based smoothing parameter 3)Correct Home Range Models for Sampling Bias 4)The Brownian Bridge Movement Model 5)Incorporate Other Variables (e.g., habitat, other organisms) Into Home Range Models

40. Ecological Factors Affecting Space Use –Site Fidelity (i.e., home range) –Habitat Selection –Interrelations with Other Organisms

41. 5) A Synoptic Model of Space Use Space Use Generally Estimated Using Discrete Locations (x-y coordinates) Can we get a better model and learn more by incorporating additional variables? –Distribution of… Important resources Avoided areas Other animals

42. Synoptic Approach… Multiple Competing Models Initial/Null Model (site fidelity) Habitat Inter/Intraspecific Relationships Model Assessment “Best” Model(s) Prediction and Inference

43. Example: Space Use of Male White Rhinos Location Data: 3 Adult Males, Matobo National Park, Zimbabwe

44. Candidate Models… Covariates Park boundary 3 Environmental Covariates H(x) Percent slope Grassland/open woodland Female Density

45. Candidate Models… Hypotheses Null model: no environmental covariates –Exponential Power + Park boundary Habitat model: –Null + open covertype + percent slope Social model: –Null + female density Combined model: –Null + habitat + social AIC Model Selection Best Model

46. slope OPEN female slope

47. Interpretation of Best Model Best Model Can Be Used to: –Estimate space use –Define home range –Determine factors affecting space use –Infer importance of these factors Answers not only “Where?” but “Why?” M05 was 3 times more likely to be in an area: 2% slope, 0.5 relative female density, and open covertype 10% slope, 0.7 relative female density, and not open

48. To Summarize Information theoretic criteria for choosing among home range models Use likelihood cross-validation choice of smoothing parameter Home range models can be corrected for observation bias Brownian bridge for serially correlated data Synoptic models answer “where?” and “why?”

49. Publications Horne, J. S. and E. O. Garton. 2006. Likelihood Cross-validation vs. Least Squares Cross-validation for Choosing the Smoothing Parameter in Kernel Home Range Analysis. Journal of Wildlife Management 70:641-648 Horne, J. S., E. O. Garton, and K. A. Sager. 2007. Correcting Home Range Models For Sample Bias. Journal of Wildlife Management 71:996-1001 Horne, J. S. and E. O. Garton. 2006. Selecting the Best Home Range Model: An Information Theoretic Approach. Ecology 87:1146-1152 Horne, J. S., E. O. Garton, and J. L. Rachlow. 2008. A Synoptic Model of Animal Space Use: Simultaneous Analysis of Home Range, Habitat Selection, and Inter/Intra-specific Relationships. Ecological Modelling 214:338-348. Horne, J. S., E. O. Garton, S. M. Krone, and J. S. Lewis. 2008. Analyzing Animal Movements using Brownian Bridges. Ecology 88:2351-2363