Density surface models

David L Miller (CREEM, University of St Andrews)

Duke University, 13 February 2014

Who is this guy?

Spatial modelling

What do we want to do?

Line transects

Data setup

Some “problems”

Density surface models

Detection

How do we deal with detectability?

 

 

Distance sampling

 

Distance sampling software

Generalized additive models

Two pages generalized additive models (I)

If we are modelling counts:

\[ \mathbb{E}(n_j) = \exp \left\{ \beta_0 + \sum_k f_k(z_{jk}) \right\} \]

Two pages generalized additive models (II)

Minimise distance between data and model while minimizing:

\[ \lambda_k \int_\Omega \frac{\partial^2 f_k(z_k)}{\partial z_k^2} \text{ d}z_k \]

“just wiggly enough”

Two options for response

\(n_j\) - raw counts per segment

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

 

\(\hat{n}_j\) - H-T estimate per segment

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

\[ \hat{n}_j = \sum_{i \text{ in segment } j} \frac{s_i}{\hat{p}_i} \]

The dsm package

Case study I - Seabirds in RI waters

Case study I - Seabirds in RI waters

RI seabirds - Aims

Photo by jackanapes on flickr (CC BY-NC-ND)

RI seabirds - Detection function modelling

RI seabirds - Spatial covariates

RI seabirds - The model

From Fig. 1 of Wood (2011)

RI seabirds - Covariate effects

RI seabirds - Results

RI seabirds - Uncertainty

Case study II - black bears in Alaska

Case study II - black bears in AK

1238 transects

Survey protocol

Black bears

Final model

 

Abundance estimate for GMU13E

Abundance map

CV map

Conclusions

References

 

Talk available at http://dill.github.com/talks/duke-dsm/talk.html

Thanks

Randomised quantile residuals

gam.check

rqgam.check