Appendix E. Additional example application for experimental data with known occupancy probability.
McClintock et al. (2010a, b) previously presented results from an anuran occupancy study in which observers recorded detections from repeated electronic broadcast of calls in field conditions. Even in these controlled conditions with trained and experienced observers, false positive detections occurred at low but significant probabilities. Because known calls were broadcast, the true state of each “site” was known as well as the false positive detection rate, allowing us to test the efficacy of our approach for field data. When the data were used to estimate occupancy and occupancy dynamics using both the MacKenzie Model and the RoyleLink Model, the low levels of false positive detections created biases in estimates of occupancy, extinction, and colonization probabilities (McClintock et al. 2010b).
We investigated whether estimates from these data could be improved when augmented with a small number of certain detections and analyzed using our models. To apply the Multiple Detection State Model, we assumed that all detections were gathered using the same method, and we treated a portion of the detections where the species was actually present as certain, leaving the rest as uncertain. Similarly, to apply the Multiple Detection Method Model we treated the data collected by observers as the first uncertain detection method and then simulated data to represent a second certain detection method for a single occasion, based on the true, known occupancy state for each site. Simulations of a hypothetical second survey allowed us to confirm whether or not independent data of the type suggested for utilizing multiple detection methods could be used to reduce bias in occupancy estimates resulting from false positive detections.
We focus on data collected for southern leopard frog (Lithobates sphenocephala), one of the species in the study for which false positive detections were most frequent and for which estimates of occupancy probabilities and dynamics were most biased. Complete description of the study methods are found in McClintock et al. (2010a, b). We compiled encounter histories for 220 “sites” which were used in the analyses. The southern leopard frog was present at 40 of these sites; that is calls of an individual southern leopard frog were broadcast at one of 10 speakers that varied in distance at regularly spaced intervals from the observers. The other 180 sites were unoccupied by the southern leopard frog, and calls for 1 of 4 other species were played or no call was played. Each site was sampled on a total of 10 occasions, where detections were combined from observations during 3 sessions by 4, 4, and 2 observers during each session.
We analyzed the data set (220 sites with 10 occasions each) using both the MacKenzie Model and our Multiple Detection Method Model (Eq. 6 and 7 in text). Distance (m) to the broadcast site was shown by McClintock et al. (2010a) to be an important predictor of detection probabilities, so true detection probabilities were modeled as a function of distance using the logitlink function,
logit(p_{1}) = β_{0} + β_{1} × distance
Distance ranged from 10 to 55 m in 5 m increments and was standardized when estimating parameters ([distance in m – 30] / 25). For the Multiple Detection State Model we randomly selected 6 of the 248 true positive observations in the data set and reclassified them as certain (b = 0.024). For the Multiple Detection Method Model we simulated an additional occasion using a certain detection method where the species was detected at 6 of the 40 sites where it was present (r_{11} = 0.15). We simulated 1000 independent iterations of the sampling occasion using the second detection method. Results were consistent across the iterations, and therefore we only present the mean parameter estimates across all simulations.
The true proportion of occupied sites (ψ_{1}) for the data set was 0.182 (40 / 220) and false positive detections occurred at 37 of the 1800 observations in which frogs were not present (p_{10} = 0.021). Both the Multiple Detection State Model and the Multiple Detection Method Model successfully accounted for false positives that occurred in the detection data while accurately estimating the true occupancy probability (Table E1). Using the Mackenzie Model, the average occupancy estimate was almost twice the true value. Even with a low detection probability for the certain detection method, the estimated occupancy probability differed by < 2% from the true proportion of occupied sites using both of our model.
TABLE E1. Comparison of parameter estimates from different occupancy estimators for electronically broadcast southern leopard frog calls. Actual values for occupancy probability (ψ_{1}), false positive detection probability (p_{10}), and secondsurvey detection probability are given, along with parameter estimates using the MacKenzie Model where false positive detection probability is 0 and our Multiple Detection State Model and Multiple Detection Method Model. β_{0} and β_{1} are the intercept and slope parameters from the logitlinear model describing the relationship between the true positive detection probability (p_{11}) and distance from observer to the broadcast speaker.
Actual Values 
MacKenzie Model 
Multiple Detection State Model 
Multiple Detection Method Model 

ψ_{1}  0.18  0.33 (0.30, 0.37)  0.20 (0.18, 0.23)  0.18 (0.13, 0.25) 
p_{10}  0.021    0.018 (0.00, 0.024)  0.024 (0.017, 0.033) 
r_{11}  0.15      0.15 (0.07, 0.31) 
b  0.024    0.024 (0.009, 0.034)   
β_{0}    0.44 (0.61, 0.26)  1.50 (1.31, 1.69)  1.92 (1.33, 2.52) 
β_{1}    1.43 (1.78, 1.09)  4.22 (4.95, 3.49)  5.12 (6.24, 4.01) 
LITERATURE CITED
McClintock, B.T., L.L. Bailey, K.H. Pollock, and T.R. Simons. 2010a. Experimental investigation of observation error in anuran call surveys. Journal of Wildlife Management 74: 1882–1893.
McClintock, B.T., L.L. Bailey, K.H. Pollock, and T.R. Simons. 2010b. Unmodeled observation error induces bias when inferring patterns and dynamics of species occurrence via aural detections. Ecology 91:2446–2454.