Improving stock assessments in Hawaiʻi

Objectives

  • Estimate abundance of rough-toothed dolphins in Kauaʻi
  • Estimate stock-level space use

Main Hawaiian Islands

Improving stock assessments in Hawaiʻi

Challenges

  • Sampling restricted by conditions
  • Dolphin movement appears less restricted
  • Non-systematic surveys, variable effort

Non-systematic photo-ID surveys

Telemetry data

Space-use covariate

Modeling Framework

  • Spatial capture-recapture (SCR) for photo-ID data
  • Resource selection function (RSF) for “geolocator data”
  • Integrate the two via Royle et al. (2013)

Spatial capture-recapture model

Density model \[ \mathbf{s}_i \sim \text{Uniform}(\mathcal{S}) \]

Photo-ID data

\[ y_{ij} \sim \text{Binomial}\left(T_j, \; 1 - \exp\left(-\lambda_{ij}\right)\right) \\ \]

Detection model

\[ \lambda_{ij} = \exp\left(\alpha_0 - \color{red}{\alpha_1} d_{ij}^2 + \color{orange}{\alpha_2} \text{depth}_j + \color{green}{\alpha_3} \text{depth}_j ^2 + \color{blue}{\alpha_4} \text{channel} \right) \\ ~ \\ d_{ij} = ||\mathbf{s}_i - \mathbf{r}_j|| \quad \alpha_1 = 1 / (2\sigma^2) \\ \]

Resource selection function

Telemetry data

\[ x_{mk} \sim \text{Multinomial}(R_m, \; \pi_{mk}) \]

Selection model

\[ \pi_{mk} = \frac{\exp\left(- \color{red}{\alpha_1} d_{mk}^2 + \color{orange}{\alpha_2} \text{depth}_k + \color{green}{\alpha_3} \text{depth}_k ^2 + \color{blue}{\alpha_4} \text{channel}\right)} {\sum_{k=1}^K \exp\left(- \color{red}{\alpha_1} d_{mk}^2 + \color{orange}{\alpha_2} \text{depth}_k + \color{green}{\alpha_3} \text{depth}_k ^2 + \color{blue}{\alpha_4} \text{channel}\right)} \\ ~ \\ d_{mk} = ||\mathbf{s}_m - \mathbf{z}_k|| \]

Sampling

Priors

\[\begin{equation} M = 2000 \\ \psi \sim \text{Uniform}(0, 1) \\ \alpha_0 \sim \text{Uniform}(-10, 10) \\ \sigma \sim \text{HalfNormal}(10) \\ \alpha_2 \sim \text{Normal}(0, 2) \\ \alpha_3 \sim \text{Normal}(0, 2) \\ \alpha_4 \sim \text{Normal}(0, 2) \\ \end{equation}\]

PyMC Settings

  • No U-turn Sampler
  • 8 chains
  • 2000 tuning samples (discarded)
  • 1000 post-tune samples

Results: Parameter estimates



Coefficients

Parameter Median 90% CI
\(\alpha_2\) 0.38 (0.29, 0.74)
\(\alpha_3\) -0.27 (-0.33, -0.21)
\(\alpha_4\) -0.56 (-0.65, -0.46)
\(\alpha_0\) -6.62 (-6.78, -6.46)
\(\sigma\) 25.8 (24.5, 27.2)
\(\psi\) 0.68 (0.60, 0.75)

Results: Space-use

Results: Space-use

Results: Abundance

Next steps


  1. Location data
  2. More mechanistic covariates
  3. Second order selection (acitivity center density)
  4. Calculate PMRF exposure

Thank You

Questions?


Contact Information
pattonp@hawaii.edu
philpatton.github.io

References

Royle, J Andrew, Richard B Chandler, Catherine C Sun, and Angela K Fuller. 2013. “Integrating Resource Selection Information with Spatial Capture–Recapture.” Methods in Ecology and Evolution 4 (6): 520–30.