This week’s lab provides you with an introduction to single-species occupancy modeling. You’ll work with data from multiple observers and two habitats to model occupancy and detection for an interesting creature from New Zealand: the Mahoenui giant weta (Deinacrida mahoenui). This species is one of the world’s largest insects; you can see photos of the weta and read more about it at New Zealand’s Department of Conservation website.

The data were collected by 3 different observers on 72 sites that differed in terms of browsing levels as part of a pilot study on the species that was conducted in 2004. You can read more about the study in the book on occupancy modeling by MacKenzie et al. (2018: pages 177-189).

Browsing level on the gorse bushes on the site was assessed on each site prior to the occupancy sampling. For the data analyzed here, information on browsing is provided by entering data with 2 groups where group 1 includes sites that showed evidence of sustained browsing (dense, compact bushes) and group 2 includes sites that did no show evidence of sustained browsing (open, less-compact bushes). A site’s browse status might have affected a site’s occupancy status.

Detection rates might have depended on a site’s browsing status (i.e., $$\hat{p}$$ might differ by group), varied by day, and been different for different observers. Each observer visited each site at least once. Most sites were not visited on all 5 occasions. If a site was not visited on a given occasion, a ‘.’ appears in the encounter history for that site on the relevant occasion.

The input file contains data for 2 groups (browsed sites [1st group] and unbrowsed sites [2nd group]) and 10 covariates: (1-5) obs11, obs12, …, obs15 are indicators for whether or not observer 1 surveyed the site on occasions 1-5, respectively; (6-10) obs21, obs22, …, obs25 are indicators for whether or not observer 2 surveyed the site on occasions 1-5, respectively. If observer 3 surveyed the site on a given occasion then the corresponding values for observers 1 and 2 will each be 0 for that occasion.

If no observer surveyed a given site on a given occasion, I put a ‘9’ in the relevant columns for obs1x and obs2x to make it easier to see which days a given site was or was not surveyed. Program MARK does not allow missing values for individual covariates, so you can’t put a ‘.’ in for the observer covariate values on those days. However, the 9’s are never used in estimation because they are only associated with days on which a given site was not surveyed.

For your homework, please run 16 models that include all-possible combinations of 2 models for $$\psi$$ and 8 models for $$p$$. The 2 model structures for $$\psi$$ are (1) $$\psi(.)$$ and (2) $$\psi({browse})$$. The 8 model structures for $$p$$ are: (1) $$p(.)$$, (2) $$p({browse})$$, (3) $$p({day})$$, (4) $$p({obs})$$, (5) $$p({day + browse})$$, (6) $$p({day + obs})$$, (7) $$p({obs + browse})$$, and (8) $$p({day + browse + obs})$$.

To run these models in MARK, use the ‘Occupancy Estimation’ Data type and fill in the relevant details (5 occasions, 2 groups, 10 covariates). Set up each of the models using the design matrix and either the default PIM, which has 10 $$p’s$$ (5 for each group) and 2 $$\psi's$$ (1 for each group), or simplified PIMs if you prefer that approach for some models. Note: in a single-season design, $$\psi$$ is constant through the season but can vary by group (or by individual site covariates); $$p$$ can vary by occasion and/or by site. A design matrix for model $$\psi({browse}), p({day + browse + obs})$$ can be set up as follows.

There are certainly other ways that you could build the design matrix to achieve this model. But, with this version, you can drop various columns to achieve other models that are nested inside this most general model. For example, if you delete the columns for B2-B5 you drop the daily variation in $$p$$. If you delete the columns for B6-B7, you remove observer differences on $$p$$. If you delete the column for B8, $$p$$ is no longer allowed to differ between browsed and unbrowsed sites. And, If you drop the column for B10, $$\psi$$ is no longer allowed to differ between browsed and unbrowsed sites.

### Assignment

1. Run each model in the table above and provide the table of model-selection results.

2. What factors seem to be associated with variation in $$p$$ and how large are the differences in estimated $$p$$ among sampling conditions?

3. Provide your estimates of $$p_j$$ for each observer and day $$(j = 1, 2, \ldots, 5)$$ from the best model.

4. What are some reasons that you think might explain why $$p$$ might differ among observers?

5. Based on estimates from the best-supported model, does $$\psi$$ seem to differ between sites with browse values of 0 versus 1?

6. When you consider model-selection uncertainty and uncertainty in estimates, does $$\psi$$ seem to differ between sites with browse values of 0 versus 1? [Note: the researchers provide an interesting discussion of the fact that there was an a priori prediction that browsed sites would have higher occupancy. Thus, they noted that it might well be most appropriate to construct 1-tailed confidence intervals for the beta-hat associated with the effect of browsing on $$\psi$$. They also concluded with the following quote on page 181: “Unfortunately, we cannot make any firm recommendations at this time for how one might objectively incorporate this idea into an information-theoretic framework”.]

7. How do the estimates of $$\psi$$ from occupancy modeling compare to the naive estimates obtained by simply calculating how many plots had the species detected on them?

8. Spend a bit of time using a search engine like Google Scholar to search on “single season occupancy models”. Filter your search results down to just the results for 2015 to present. Does it appear that this method is being used in ecology? Does it appear that there is much active development in this type of modeling? How diverse are the types of problems on which this approach is being used?

### References

MacKenzie, D.I., J.D. Nichols, J.A. Royle, K.H. Pollock, L.L. Bailey, and J.E. Hines. 2018. Occupancy Estimation and Modeling (Second Edition). Academic Press.