An Enhanced Spatial Capture Model for Population Analysis Using Unidentified Counts through Camera Encounters
Abstract
:1. Introduction
- (1)
- Employs a prior distribution for the essential parameter of the zero-inflated population;
- (2)
- Regularizes the Markov chain Monte Carlo (MCMC) by controlling the effective sample size;
- (3)
2. Methods
2.1. Hierarchical Spatial Capture–Recapture Model
2.2. Proposed Method
2.3. Sensitivity of the Model to
2.4. Autocorrelation Plot
2.5. Effective Sample Size
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
MCMC | Markov chain Monte Carlo |
HSCR | Hierarchical spatial capture–recapture |
Population size | |
Estimated population size | |
Sampling occasion | |
Camera encounter history for individual , at camera , on occasion | |
The encounter rate for individual at camera | |
The baseline encounter rate | |
Home range radius. | |
The Euclidean distance between activity center and the camera location | |
The number of camera encounters at camera on occasion | |
The augmented parameter (the total number of hypothetical individuals) | |
Probability of success, i.e., the probability that an individual in the occupancy model of size is a member of the original model of size | |
and | Parameters of Beta probability distribution |
ESS | The effective sample size |
The number of zeros added to the model (data augmentation size) | |
The autocorrelation between the current sample and kth preceding sample |
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100 | 0.00–1.00 | 0.437 | 0.589 | 0.313 | 0.046 | 25.200 | 30.887 | 2.577 | 1113.2 | 1297.6 | 0.668 | 0.625 |
0.00–0.50 | 0.451 | 0.606 | 0.274 | 0.045 | 9.600 | 27.107 | 2.322 | 1850.8 | 2180.9 | 0.482 | 0.412 | |
0.10–0.40 | 0.465 | 0.585 | 0.253 | 0.043 | 1.200 | 25.255 | 2.185 | 2679.4 | 3232.7 | 0.403 | 0.324 | |
0.05–0.35 | 0.479 | 0.584 | 0.231 | 0.042 | 7.600 | 23.326 | 2.036 | 2505.5 | 3145.0 | 0.395 | 0.309 | |
0.10–0.35 | 0.471 | 0.589 | 0.237 | 0.043 | 5.200 | 23.862 | 2.077 | 2738.4 | 3681.9 | 0.352 | 0.260 | |
200 | 0.00–1.00 | 0.416 | 0.596 | 0.199 | 0.028 | 59.200 | 39.231 | 2.501 | 250.6 | 263.3 | 0.909 | 0.894 |
0.00–0.50 | 0.443 | 0.579 | 0.158 | 0.026 | 26.400 | 30.979 | 2.030 | 1066.8 | 1140.4 | 0.674 | 0.623 | |
0.10–0.40 | 0.415 | 0.579 | 0.174 | 0.027 | 39.200 | 33.433 | 2.192 | 2340.8 | 2727.2 | 0.496 | 0.431 | |
0.05–0.35 | 0.443 | 0.579 | 0.153 | 0.025 | 22.400 | 29.922 | 1.969 | 2082.8 | 2203.2 | 0.547 | 0.486 | |
0.10–0.35 | 0.411 | 0.592 | 0.173 | 0.027 | 38.400 | 33.340 | 2.184 | 3017.5 | 3701.7 | 0.446 | 0.375 |
100 | 0.00–1.00 | 0.560 | 0.497 | 0.323 | 29.200 | 31.943 | 1674.3 | 1862.4 | 0.635 | 0.593 |
0.00–0.50 | 0.563 | 0.546 | 0.273 | 9.200 | 27.173 | 3661.7 | 4368.0 | 0.393 | 0.334 | |
0.10–0.40 | 0.516 | 0.557 | 0.261 | 4.400 | 26.251 | 5987.0 | 7677.7 | 0.270 | 0.205 | |
200 | 0.00–1.00 | 0.546 | 0.527 | 0.170 | 36.000 | 33.321 | 1490.3 | 1778.8 | 0.670 | 0.620 |
0.00–0.50 | 0.527 | 0.564 | 0.158 | 26.400 | 31.026 | 2647.5 | 3152.3 | 0.528 | 0.473 | |
0.10–0.40 | 0.496 | 0.545 | 0.165 | 32.00 | 31.168 | 3880.0 | 4606.6 | 0.412 | 0.355 |
95% CI | 95% CI | |||||
---|---|---|---|---|---|---|
= 100 | 30.887 | 25.733 | 36.041 | 0.313 | 0.220 | 0.406 |
27.107 | 22.463 | 31.751 | 0.274 | 0.185 | 0.363 | |
25.255 | 20.886 | 29.624 | 0.253 | 0.166 | 0.340 | |
23.326 | 19.255 | 27.397 | 0.231 | 0.147 | 0.315 | |
23.862 | 19.707 | 28.017 | 0.237 | 0.152 | 0.322 | |
= 200 | 39.231 | 34.230 | 44.232 | 0.199 | 0.143 | 0.255 |
30.979 | 26.919 | 35.039 | 0.158 | 0.106 | 0.210 | |
33.433 | 29.049 | 37.817 | 0.174 | 0.120 | 0.228 | |
29.922 | 25.984 | 33.860 | 0.153 | 0.102 | 0.204 | |
33.340 | 28.972 | 37.708 | 0.173 | 0.120 | 0.226 |
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Jaber, M.; Hamad, F.; Breininger, R.D.; Kachouie, N.N. An Enhanced Spatial Capture Model for Population Analysis Using Unidentified Counts through Camera Encounters. Axioms 2023, 12, 1094. https://doi.org/10.3390/axioms12121094
Jaber M, Hamad F, Breininger RD, Kachouie NN. An Enhanced Spatial Capture Model for Population Analysis Using Unidentified Counts through Camera Encounters. Axioms. 2023; 12(12):1094. https://doi.org/10.3390/axioms12121094
Chicago/Turabian StyleJaber, Mohamed, Farag Hamad, Robert D. Breininger, and Nezamoddin N. Kachouie. 2023. "An Enhanced Spatial Capture Model for Population Analysis Using Unidentified Counts through Camera Encounters" Axioms 12, no. 12: 1094. https://doi.org/10.3390/axioms12121094