Multi-Season closure assumptions

[NicolaG]

Hi!
TL;DR: In multi-season models, is the closure assumption violated if the population isn’t closed across all transects/units within a season, or does closure only need to apply to individual transects/units within each season?

I’m seeking advice on handling the closure assumption in my occupancy modelling study of a mouse lemur species. My study involved two detection methods (Sherman traps and camera traps) deployed across 69 transects between April 2018 and August 2019. Transects were far enough apart that no individuals were ever detected on more than one transect.

Context
I conducted:
- Sherman trapping: 2 weeks per transect, 13 traps (25m apart along 300m transects).
- Camera trapping: Up to 12 nights per transect, 1 camera at the 150m marker.

The lag time between the methods ranged from 40 to 236 days, with Sherman trapping conducted from April 2018 to July 2019 and camera trapping from November 2018 to August 2019. We did a sweep over the landscape, so each transect was only surveyed once with Sherman traps and once with camera traps (no repeat visits).

Likelihood Ratio Tests from multi-method models suggested no difference in detection probabilities between methods. So, I’m now deciding between a single-season or multi-season approach.

Options and Concerns
1. Multi-season Model
I initially planned to treat each method as a “season” due to the lag time. However, the Occupancy Estimation and Modelling book (p452) it says, “We stress that the estimate of occupancy applies to the entire population of units, and consideration of the closure assumption not only applies at the time-frame during which surveys are conducted at a single unit, but to the timeframe during which all units within the population are surveyed.”
- If I define seasons by method, each season spans over a year.
- Alternatively, splitting by actual seasons (dry vs wet) creates ~6-month-long seasons but results in significant missing data (as some transects were surveyed by only one method per season). Additionally, my occupancy covariates (e.g., forest proportion) are not season-specific. I'm more interested in what influences their occupancy in general, not over seasons.

2. Single-season Model
I could:
- Use all the data and report probability of use rather than occupancy, acknowledging closure violations.
- Restrict the lag time between methods to ≤3 months (removing camera trapping data for transects with longer lags), as individuals were detected up to 3 months apart on the same transect. If I do this, could I then use the term occupancy instead of use?

The mouse lemurs have stable home ranges with overlapping individual ranges. Despite some variability (e.g., male dispersal, seasonal movement during mating), the population likely uses the same areas consistently.

Questions:

1. In multi-season models, does the closure assumption need to hold across all transects within a season, or is it only required within each transect?
2. If I choose a single-season model and keep the lag ≤3 months, is it valid to use the term occupancy, or should I still use “use”?
3. Can anyone recommend studies where probability of use was used instead of occupancy due to closure violations?

Thanks in advance for your advice!

Nicola

[jhines]

From your description, it sounds like there are areas between transects where the species can permanently emigrate/immigrate, so the closure assumption would be violated if the occupancy status of a transect changes from occupied to not occupied or not occupied to occupied. It does not mean the assumption is violated if single individuals emigrate/immigrate, just whether the occupancy state changed. If the population in a transect is relatively large, then a few individuals leaving/entering probably won’t change the occupancy state.

If the closure assumption is violated on one of the 69 transects, then estimates could be biased. The bias would be relatively small if it’s only one transect. If half of the transects have emigration/immigration, then the bias will be larger. Bias will be proportional to the degree of emigration/immigration across all transects.

To minimize the probability of violating the closure assumption, you could treat each transect as a “site” and keep the survey period short. For example, for transect 1, make each day of the 2-week period for Sherman trapping a “survey”. This means the population for the transect only has to be closed for 2 weeks. Each day of camera trapping could be a survey for season 2. The fact that you have different methods doesn’t matter as each “season” could have a different detection probability. Transect 2 would have the same structure with the only difference being that it started on a different day. A site covariate could be used to indicate day of first survey if you think detection might change later in the year. The detection histories would all start with survey 1, even though survey 1 for transect 2 is 2 weeks later than survey 1 for transect 1.

This could allow you to estimate “occupancy” as opposed to “use”, if the transects are closed for the short survey periods.

I’ve seen a good number of papers where they estimate “site use” due to violating the closure assumption. A quick Google search for “occupancy site use” produced this reference:
Matthew J. Gould, William R. Gould, James W. Cain, Gary W. Roemer,
Validating the performance of occupancy models for estimating habitat use and predicting the distribution of highly-mobile species: A case study using the American black bear,
Biological Conservation,
Volume 234,
2019,
Pages 28-36,
ISSN 0006-3207,
https://doi.org/10.1016/j.biocon.2019.03.010.
(https://www.sciencedirect.com/science/a ... 071831214X)

[NicolaG]

Thank you for your response! I really appreciate it.

I have treated each transect as a site. For Sherman traps, I have up to 7 surveys (conducted every other day). For camera trapping, I pooled the data into 4 survey occasions (each representing 3 consecutive days of trapping) because running the camera trap data as 12 separate survey days resulted in poor model fit in a single-season model.

Given this setup, if I use a multi-season model where season 1 corresponds to the 7 Sherman trap surveys and season 2 corresponds to the 4 camera trap surveys, am I correct in understanding that I wouldn’t be violating the closure assumption as closure would only apply to the 7 survey days for Sherman trapping and to the 4 survey occasions for camera trapping within each transect? My interpretation of your response is that the closure assumption applies separately to each season for a given site, rather than requiring closure across each “season” on the whole for all sites combined. Is that correct?

I also have a question about model parameterization. If my primary interest is understanding whether the proportion of forest cover (measured in a buffer around the transect) influences occupancy, do you have a recommendation for which of the four options for model parameterization in the multi-season model in PRESENCE I should select? Should I keep colonization and/or extinction constant in the model since they aren’t of primary interest? Give I only have 69 sites, I'm worried about using too many parameters and overfitting the model. Ideally I'd like to be able to include at least 1 occupancy and 1 detection covariate per model.

Additionally, if I wanted to explore how the proportion of forest cover might influence colonization or extinction, would that even be possible in this case? Since each “season” in my model represents a different method rather than an actual time period, and I only have one value for forest cover per transect.

Thanks,

Nicola

[jhines]

You are correct that closure applies to each season and with short survey periods within each season, closure seems likely to be true. The only time sites can change status (from occupied to not occupied or vice-versa) is between seasons. Since you indicated that animals do not move from transect to transect, closure means each transect must be closed to changes in occupancy status. Most often, occupancy studies are carried out on an area with many sites within the area. For animals to emigrate, they would have to leave the area enclosed by all sites. If sites are so far apart that animals can leave the site to an area where they can never be detected, then that is the same as animals leaving the entire study area.

If you only have 2 seasons (Sherman traps, camera traps), there will only be one estimate of colonization and one estimate of extinction. Any of the 4 parameterizations will produce the same number of estimates. The first one, psi/gamma/epsilon will produce 1 estimate of initial occupancy, 1 estimate of colonization, and 1 estimate of extinction. The psi/gamma parameterization will produce 2 estimates of occupancy (1 per season) and 1 estimate of colonization. The psi/epsilon will also produce 2 estimates of occupancy and 1 estimate of extinction. Since you’re interested in how forest cover might influence colonization and/or extinction, I’d suggest the 1st parameterization. Whether you can model colonization or extinction as a function of a covariate will depend on the data. I’d give it a try to see if that sort of model converges on sensible values.

Each season estimates occupancy using a different method, resulting in potentially different detection probabilities. This should not affect the occupancy estimates, other than the method with higher detection will probably yield more precise estimates of occupancy. It’s possible that detection could be similar between the two methods, but I’d definitely recommend including models which allow the two seasons to have different detection probabilities in your model-set.

[NicolaG]

Thank you so much for all your help! I really appreciate it.

I ran the multi-season model (using the first parameterization option), and the 95% confidence intervals for both gamma and epsilon included zero, so they weren't significant. From my understanding, this suggests no significant colonisation or extinction is happening between the seasons. I also ran the likelihood ratio test comparing the multi-season model and single-season model with the same data, and the p-value was 0.07, suggesting I shouldn't reject the null hypothesis and could use the simpler model. Given both these results, I've decided to go with a single-season model with the lag time between the methods reduced to less than 3 months, and I can use the results from the multi-season model and LRT to justify presuming closure. Does that sound reasonable?

Thanks,

Nicola