Spatial models integrating two survey platforms

David L Miller

CREEM, University of St Andrews

converged.yt

National Oceanic and Atmospheric Administration

Visual and Passive Acoustic Data Integration Modeling Workshop

Woods Hole, Massachusetts

15 September 2015

- Some practical issues
- Rhode Island case study
- Not much model detail (but do ask me about this!)
- More about “model independent” checking
- Diagnostics etc

Case study:

Common loons in Rhode Island

Common loons in Rhode Island

- Ocean Special Area Management Plan
- Windfarm development nr. Block Island
- Part of state-wide EIA
- Potential pre-impact survey

- 2 platforms
- Ship-based surveys
- 8 grids of zig-zag randomly located
- 10 days – 2 December 2009 - 13 February 2010
- Single observer distance sampling

- Aerial surveys
- 24 transects
- 9 days – 2 December 2009 - 22 February 2010
- Strip transects

How do we integrate this data?

- Detectability
- Availability
- Effort
- Overlap (temporal and spatial)
- Variance estimation

Density surface models

(Spatial models that account for detectability)

(…and more)

Hedley and Buckland (2004). Miller et al (2013).

Detectability

Code for animation at https://gist.github.com/dill/2b0c120d5484d338d8ef

\(\mathbb{P} \left[ \text{animal detected } \vert \text{ animal at distance } y\right]\)

Integrate out distance: \[ \hat{p}_i = \frac{1}{w} \int_0^w g(y; \boldsymbol{\hat{\theta}}, z_i) \text{d}y \]

or…

\(p=1\)

Availability

- Simple correction
- Ford & Gieg (1995) quantified diving habits in RI waters

- More complicated stuff
- Borchers, Langrock & co have many solutions using Hidden Markov Models

- (Different for different platforms?)

Effort

- “Simple” here
- Strip transects == line transects w. \(p=1\) (nesting)
- Always surveying surface (effort equivalence)
- (More complex with different “types” of data)
- (Need to find equivalency?)

Overlap

- Ensure we’re not combining apples and oranges
- Are counts/unit effort reasonable?
- Compare overlapping & non-overlapping areas
- Quantile-quantile plots – Kolmogorov-Smirnov tests (Cramer-von Mises?)
- Sensitivity – leave-\(k\)-out cross-validation

Spatially explicit models

- Generalized Additive Models (GAMs)

\[ \mathbb{E}(\hat{n}_j) = A_j\exp \left\{ \beta_0 + \sum_k f_k(z_{jk}) \right\} \]

- \(\hat{n}_j \sim\) count distribution (raw or Horvtiz-Thompson estimate)
- \(f_k\) are
*smooth*functions (splines \(\Rightarrow f_k(x)=\sum_l \beta_l b_l(x)\)) - \(f_k\) can just be fixed effects \(\Rightarrow\) GLM
- Add-in random effects, correlation structures \(\Rightarrow\) GAMM
- \(A_j\) is area of segment
- R package
`dsm`

- Wood (2006) is a good intro to GAMs

Variance estimation

- Major criticism of \(\geq2\)-stage models
- Uncertainty from detection function AND spatial model (and…)
- Refit model with “extra” term – zero mean effect, variance contribution
- Williams et al (2011). Bravington, Hedley and Miller (in prep)

Conclusions

- Ensure that data are compatible
*before*modelling - Equivalency in effort tricky for non-trivial cases
- Two-stage models can be useful!
- Distribute tasks
- Modular model checking

- Existing statistical framework (GAM)
- Flexible spatial models
- Detectability
- GLMs + random effects + smooths + other extras
- autocorrelation can be modelled
- accounting for uncertainty

- St Andrews: Eric Rexstad, Louise Burt
- Rhode Island: Kris Winiarski (now UMass), Peter Paton, Scott McWilliams, Carol Trocki
- Funding State of Rhode Island for the Ocean Special Area Management Plan

- Borchers, DL, Zucchini, W, Heide-Jørgensen, MP, Cañadas, A, Langrock, R, Buckland, ST, & Marques, TA (2013). Using hidden Markov models to deal with availability bias on line transect surveys. Biometrics, 69(3), 703–713.
- Ford, T. B., and J. A. Gieg (1995). Winter behavior of the Common Loon. Journal of Field Ornithology 66:22–29.
- Miller, DL, ML Burt, EA Rexstad and L Thomas. Spatial Models for Distance Sampling Data: Recent Developments and Future Directions. Methods in Ecology and Evolution 4, no. 11 (2013): 1001–1010.
- Williams, R, SL Hedley, TA Branch, MV Bravington, AN Zerbini, & KP Findlay (2011). Chilean Blue Whales as a Case Study to Illustrate Methods to Estimate Abundance and Evaluate Conservation Status of Rare Species. Conservation Biology, 25(3), 526–535.
- Winiarski, KJ, ML Burt, Eric Rexstad, DL Miller, CL Trocki, PWC Paton, and SR McWilliams. Integrating Aerial and Ship Surveys of Marine Birds Into a Combined Density Surface Model: a Case Study of Wintering Common Loons. The Condor 116, no. 2 (2014): 149–161.
- Wood, S. (2006). Generalized Additive Models. CRC Press.