Choosing a model that includes auxiliary observations

[vegemite]

Hi,

I have capture-mark-recapture data collected on surveys undertaken between May-October (animal's active season) over 4 years. The intervals between surveys vary between 2 days-1 month. I also have a dataset of animal resightings recorded opportunistically in between survey days that I would like to include as it's quite substantial.

Having trawled the literature, I cannot find an example or suitable model to fit the CMR and auxiliary data combined that incorporates primary sessions. Whilst the Barker robust design model might be a good fit, it only seems to consider auxiliary data that is collected between primary sampling periods (May-October), but for my study, the auxiliary data has been collected during the primary sampling periods.

Can the Barker robust design model be tweaked to include auxiliary data collected during the primary seasons? If not, does anyone have any alternative model suggestions?

Many thanks for your time.

[vegemite]

Replying to my own post here (but still seeking help!)

I think what is best would be to use a Barker joint model allowing for incidental sightings to be included. I will be able to estimate survival during the active seasons (May-October, 6 months)....but am unsure of how to estimate annual survival, from which I would like to derive overwinter survival.

How can I calculate annual survival, making use of the incidental sightings? If I modify the PIMs to reflect years, won't that just be the same as reflecting my 1-yearly active seasons?

Would it be valid to just pool data within May-Oct seasons to indicate whether an animal had been caught or incidentally resighted at least once during this period, and then analyzing the resulting yearly capture histories to gain the annual survival estimates?

[Bill Kendall]

Below is a response to your original note and refers to estimating annual survival. The question about the length of your primary period is a separate issue.

It sounds like these extra detections occur within the study area where the formal sampling is being conducted. If these detections between formal secondary sampling periods can be considered just extra effort (i.e., all individuals subject to detection during the sampling periods are also subject to these extra detections), it seems you could pool them with one of the secondary periods.

But the short answer is that yes, you should be able to include those detections as auxiliary detections. The first question is whether these detections denote the individual has survived for the entire time period. Since these are detections during the primary sampling period, I'm assuming the answer is 'yes'. In that case you would include the detections in the 'D' column after the 'L' columns for the primary period (i.e.. the individual has survived to period t and is then detected between t and t+1.

However, it also matters whether or not you are considering an unobservable state (temporary emigration). If not, then the Barker/RD model will work and you just set fidelity to 1. If there is an unobservable state, and the auxiliary observations are only from the observable state, then the Barker/RD model is not the right one to use. Instead one of the Multistate live and dead with resightings models in MARK would be more appropriate.

[B.K. Sandercock]

On handling of auxiliary data collected during primary sampling periods. I have had similar situations with field projects where live encounters within a sampling period can include systematic captures and opportunistic resightings. In this case, both sources of data were coming from within the same study area or plot, and at the same time. In the Barker joint model that you mention, the additional resightings are often coming from a different area and seasonal period, detections of migratory birds elsewhere in the flyway for example. For a relatively short 4-year period, you might just use CJS models but try it two different ways with building the encounter histories. You could evaluate the effect of your sampling decision by comparing model rankings, parameter estimates, and their precision.

Option 1 would be to build the encounter histories with detections from the systematic surveys in May-Oct. Any detection on any systematic survey gets a 1. Advantage here is you have better understanding of the detection process and could model the encounter rates as a function of effort, such as number of surveys in the 6-month sampling period.

Option 2 would be to build the encounter histories with any detection by any method in May-Oct. Any detection with systematic surveys or auxiliary sampling gets a 1. If your auxiliary data are coming from the same sampling area and time period as the systematic surveys, then this approach should be okay. You might expect that adding more information would increase the probability of encounter but if it creates more gaps in the encounter histories, you can get the opposite effect. Advantage here is that you are using all of the encounter data. One disadvantage is that you might be adding heterogeneity leading to overdispersion if the systematic surveys and auxiliary data are coming from different sampling procedures. Also it might be harder to devise an annual covariate for sampling effort if the auxiliary data are coming from opportunistic sightings or citizen science reports.

[vegemite]

Thanks both for your insightful answers.

I'm leaning towards pooling my data into two periods (e.g. May-June, Sept-Oct) so I can then estimate within-season survival (from period 1 to 2) and outside-season survival (period 2 to 1 the following year), and will test this with and without the opportunistic data included, in a similar way to what was suggested in the second response above.

Thanks for your time