1. Occupancy Models when misclassification occurs

2. Detection Errors and Occupancy Estimation  Occupancy estimation accounts for issues of detection when estimating species occurrence  Generally focus on false negative detections – individuals are present but not detected  False positive detections – individuals are not present but are recorded as detected

3. False Positives  When false positive detections go unaccounted estimators will be biased VisitsTrue positive detection rate True occupancy False positive probability Estimated occupancy 30.250.030.0100.16 30.250.030.0020.05

4. False Positives  May arise due to: recording errors, misidentification, auditory or visual miscues, inexperienced observers, lab error, etc.

5. Dealing with false positives  Design phase of studies should emphasize costs associated with making false positive errors  In many cases even small probabilities of false positives can bias results – analytical solutions will be important

6. Binomial Mixture Model  Royle and Link (2005) devised a simple mixture model to account for false positives  Detections possible at all sites  True positive detection recorded with probability p 11 for occupied sites  False positive detection recorded with probability p 10 for unoccupied sites

7. Incorporating Auxilliary Information  Detections can vary in their degree of certainty – exploit this to improve estimates.  Focus on models where detections are classified as either “certain” or “uncertain” Single detection method where both types possible Two detection methods corresponding to each type

8. Multiple Detection States  Single detection method used  Detection divided based on criteria into certain and uncertain detections  Potential criteria: calling intensity, auditory versus visual cues, quality of cue, observer discretion, etc.

9. Multiple Detection Methods  Two detection methods used during unique occasions  First method detections are uncertain, second detections are certain  Examples: auditory versus direct sampling, expert versus novice observer, etc.

10. Standard Occupancy Model – Detection Rates Observed State unoccupiedoccupied True State unoccupied10 occupied1-pp

12. Royle-Link Model Observed State unoccupiedoccupied True State unoccupied1-p 10 p 10 occupied 1-p 11 p 11

13. Royle - Link

14. Multiple Detection States Observed State unoccupieduncertaincertain True State unoccupied1- p 10 p 10 0 occupied1- p 11 p 11 (1-b 1 ) p 11 *b 1

15. MDSM

16. Multiple Detection Methods Observed State uncertain methodcertain method unoccupiedoccupied unoccupiedoccupied True unoccupied1- p 10 p 10 10 State occupied1- p 11 p 11 1-r 11 r 11

17. MDMM

18. Example  Combined both models to estimate occupancy for 3 frog species in Maryland  Detection method 1: auditory call survey Calls divided into high intensity (certain) and low-intensity (uncertain)  Detection method 2: dip-net surveys for tadpoles and eggs – assumed all detections certain

19. Analysis  124 site where auditory survey occurred, 14 where dip-net survey occurred also  Temperature covariate for true positive detection rate for auditory survey AuditoryDip-net none Low- intensity High- intensity Not foundfound unoccupied1-p 10 p 10 010 occupied1-p 1 p 1 (1-b)p 1 *b1-rr

20. Results SpeciesModelAIC p 10 ψ1 ψ1 LCLUCL American bullfrog unconstrained295.20.030.490.430.55 constrained294.4------0.580.520.64 green frog unconstrained320.50.0080.520.490.55 constrained323.7------0.550.520.58 pickerel frog unconstrained262.80.0270.140.080.24 constrained263.1------0.30.250.35

21. Misclassification for Multistate Models  Need to specify different f(y|z) (i.e., probability of observing a state given the true state) f(y = 0|z)f(y = 1|z)f(y = 2|z)f(y = 3|z) z = 0π 00 π 10 π 20 π 30 z = 1π 01 π 11 π 21 π 31 z = 2π 02 π 12 π 22 π 32 z = 3π 03 π 13 π 23 π 33

22. Other extensions  Covariates for detection, independent estimates of false positive rates  Two-species model where misclassification occurs between species.  Extensions for multiseason dynamics