A review of hierarchical occupancy modeling
The authors propose a novel modeling framework capable of estimating site-level occupancy when detection probabilities are less than 1. The authors provide a likelihood based method for estimation by marginalizing out the latent occupancy states. Using simulation, the authors show that their model provides reasonably unbiased estimates of occupancy when detection probabilities are at least 0.3. For low detection probabilities, occupancy probabilities tend to be overestimated. The authors apply their model to a field study involving American toads.
Assume that \(i\) sites are visited \(j\) times each. Let
Then, \[ \begin{split} Z_i &\sim \text{Bernoulli}(\psi_i) \\ y_{ij} &\sim \text{Bernoulli}(p_{ij}) \end{split} \]
The authors extend the model of MacKenzie et al. (2002) to accommodate longitudinal survey designs in which \(i\) sites are visited \(j\) times each over \(t\) seasons. The authors provide a likelihood based method for estimation by marginalizing out the latent occupancy states. Using simulation, the authors show that parameter estimates are generally unbiased, except when both the number of visits to each site during a season is small and the detection probability is small. The authors apply their model to two field studies, involving spotted owls and tiger salamanders, respectively.
Assume that \(i\) sites are visited \(j\) times each across \(t\) seasons. Let
Then, \[ \begin{split} Z_{i, 1} &\sim \text{Bernoulli}(\psi_{i, 1}) \\ Z_{i,t} | Z_{i, t-1} &\sim \text{Bernoulli}(\pi_{i,t}) \text{ for } t \geq 2 \\ \pi_{i,t} &= \begin{cases} 1 - \epsilon_{t-1} & \text{for } z_{t-1} = 1 \\ \gamma_{t-1} & \text{for } z_{t-1} = 0 \end{cases} \\ \\ y_{ij,t} &\sim \text{Bernoulli}(z_{i,t}p_{ij, t}) \end{split} \]
The authors provide a Bayesian state-space representation of the dynamic occupancy model developed by MacKenzie et al. (2003) and provide WINBugs code to fit their model. The authors apply their model to two field studies, concerning the European crossbill and Cerulean warbler, respectively.
Assume that \(i\) sites are visited \(j\) times each across \(t\) seasons. Let
Then, \[ \begin{split} Z_{i, 1} &\sim \text{Bernoulli}(\psi_{i, 1}) \\ Z_{i,t} | Z_{i, t-1} &\sim \text{Bernoulli}(\pi_{i,t}) \text{ for } t \geq 2 \\ \pi_{i,t} &= \begin{cases} \phi_{t-1} & \text{for } z_{t-1} = 1 \\ \gamma_{t-1} & \text{for } z_{t-1} = 0 \end{cases} \\ y_{ij, t} &\sim \text{Bernoulli}(z_{i,t}p_{ij,t}) \end{split} \]
Note that this model is equivalent to that of MacKenzie et al. (2003), with \(\phi_{t-1} = 1 - \epsilon_{t-1}\).
The authors describe development and implementation of a novel
R package, dynOccuPow, capable of conducting
simulation-based power analyses for dynamic occupancy models. Leveraging
the Bayesian state-space representation of the explicit dynamic
occupancy model (Royle and Kéry,
2007), the package allows users to assess the power to
identify average annual trends in occupancy or net changes in occupancy
for sampling designs with varying number of sites, visits, and years.
The package includes tools to simulate data, fit models, conduct
simulation-based power analyses, and summarize and visualize the
results. The package is implemented on a subset of the North American
Bat Monitoring Program master sample, located in United States Forest
Service Region 9.