Ecological Archives E084-015-A1

J. Andrew Royle and James D. Nichols. 2003. Estimating abundance from repeated presence–absence data or point counts. Ecology 84:777–790.

Appendix B. Simulation results.

Table 1: Summaries of the sampling distribution of estimators for $\lambda $ and $\psi $ for T = 5 sampling occasions and R = 500 sample locations, while varying $\lambda $ and r.

Scenario $\psi $
$\lambda $ r $r$ mean median   mean median constant p
4.61 0.1 0.37 0.13 4.87 4.66 0.99 0.99 0.99 0.92
4.61 0.2 0.61 0.17 4.72 4.64 0.99 0.99 0.99 0.96
2.30 0.1 0.23 0.10 2.39 2.30 0.90 0.90 0.90 0.78
2.30 0.2 0.41 0.16 2.33 2.31 0.90 0.90 0.90 0.83
1.61 0.1 0.19 0.09 1.67 1.62 0.80 0.80 0.80 0.68
1.61 0.2 0.34 0.14 1.63 1.62 0.80 0.80 0.80 0.73
1.20 0.1 0.16 0.08 1.26 1.22 0.70 0.71 0.70 0.60
1.20 0.2 0.31 0.12 1.22 1.21 0.70 0.70 0.70 0.64
0.92 0.1 0.15 0.06 0.96 0.92 0.60 0.61 0.60 0.52
0.92 0.2 0.28 0.11 0.93 0.92 0.60 0.60 0.60 0.55
0.69 0.1 0.13 0.06 0.73 0.69 0.50 0.51 0.50 0.44
0.69 0.2 0.26 0.10 0.70 0.70 0.50 0.50 0.50 0.46
0.51 0.1 0.12 0.05 0.54 0.51 0.40 0.41 0.40 0.37
0.51 0.2 0.24 0.08 0.52 0.51 0.40 0.40 0.40 0.38

   Notes: Mean and median are given. For $\psi $ we also provide the mean "constant p" estimate obtained using the approach of MacKenzie et al. (2002) which ignores heterogeneity in pi. Each summary is based on 2000 simulated data sets.

Table 2: Summaries of the sampling distribution of estimators for $\lambda $ and $\psi $ for T = 5 sampling occasions and R = 200 sample locations, while varying $\lambda $ and r.

Scenario $\psi $
$\lambda $ r mean median   mean median constant p
4.61 0.1 0.37 0.13 5.30 4.64 0.99 0.98 0.99 0.92
4.61 0.2 0.61 0.17 4.88 4.66 0.99 0.99 0.99 0.96
2.30 0.1 0.23 0.10 2.62 2.34 0.90 0.90 0.90 0.78
2.30 0.2 0.41 0.16 2.39 2.33 0.90 0.90 0.90 0.83
1.61 0.1 0.19 0.09 1.82 1.63 0.80 0.80 0.80 0.69
1.61 0.2 0.34 0.14 1.65 1.61 0.80 0.80 0.80 0.73
1.20 0.1 0.16 0.08 1.40 1.24 0.70 0.72 0.71 0.61
1.20 0.2 0.31 0.12 1.24 1.21 0.70 0.70 0.70 0.64
0.92 0.1 0.15 0.06 1.06 0.93 0.60 0.62 0.61 0.53
0.92 0.2 0.28 0.11 0.94 0.92 0.60 0.60 0.60 0.55
0.69 0.1 0.13 0.06 0.80 0.70 0.50 0.52 0.50 0.45
0.69 0.2 0.26 0.10 0.71 0.70 0.50 0.50 0.50 0.46
0.51 0.1 0.12 0.05 0.64 0.54 0.40 0.44 0.42 0.39
0.51 0.2 0.24 0.08 0.53 0.52 0.40 0.41 0.40 0.38

   Notes: Mean and median are given. For $\psi $ we also provide the mean "constant p" estimate obtained using the approach of MacKenzie et al. (2002) which ignores heterogeneity in pi. Each summary is based on 2000 simulated data sets.

Table 3: Summaries of the sampling distribution of estimators of negative binomial model parameters and the estimator of $\lambda $ and $\psi $ when the Poisson model is fit to the data for T = 5 sampling occasions and R = 200 sample locations.

Scenario Negative Binomial Poisson constant p
a $\psi $
0.69 3.45 0.467 0.740 0.487 0.622 0.463 0.433
0.69 0.69 0.380 0.700 0.382 0.439 0.356 0.339
0.69 0.23 0.273 0.669 0.279 0.285 0.248 0.238
1.61 8.05 0.770 1.695 0.782 1.432 0.761 0.702
1.61 1.61 0.672 1.650 0.681 1.024 0.641 0.602
1.61 0.54 0.526 1.624 0.528 0.677 0.492 0.471

   Notes: Summaries are medians of the sampling distribution. The "constant p" estimator of is that given by MacKenzie et al. (2002) which ignores heterogeneity in pi.

Literature cited

MacKenzie, D. I., J. D. Nichols, G. B. Lachman, S. Droege, J. A. Royle, and C. A. Langtimm. 2002. Estimating site occupancy rates when detection probabilities are less than one. Ecology 83:2248–2255.


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