Closed models data doubts

[AzucenaUgalde]

Hello. I study whales and I have tried to estimate abundance, the problem is that in every year the amount of data is low. I have read that I require at least five capture occasions to apply these models.?

I made an exercise using the sightings in a whale season (January – May), five capture occasions withing the season with 18, 36, 30, 43, and 34 individual sightings in the different occasions. The total number of different individuals was 107.

I tried to estimate abundance with Full Closed Captures with Heterogeneity, but there were some “errors”. First as the MARK book says, the time dependent model is not identifiable without constraints; but what I was waiting for was, after to test different models (section 14.26 Mark book), the full time dependent model be the last in the Results browser. But in the exercise the full time dependent model appears as the best model, although the abundance estimate is wrong, as it must be.

I could not verify with the example file because this and other file did not appear in the examples files, I have downloaded the program two times, but some examples files in the Mark Book are still missing.

So, I am not sure if it is the amount of data which is causing problems with the estimation. I am pretty sure to follow the instructions in Mark to construct the design matrix.

Is there a minimum number of individual captures in every encounter occasion? And are five encounter occasions required to apply any closed population models?

That is all for now, thanks for your attention.

[cooch]

I could not verify with the example file because this and other file did not appear in the examples files, I have downloaded the program two times, but some examples files in the Mark Book are still missing.

See the MARK FAQ, item 7(c)

viewtopic.php?f=39&t=9

[abreton]

I made an exercise using the sightings in a whale season (January – May), five capture occasions withing the season with 18, 36, 30, 43, and 34 individual sightings in the different occasions. The total number of different individuals was 107.

The 'minimum' data requirements will depend on (in particular) probabilities of detection. If these were close to 1 (animals that are alive and in the study area are never missed, they are always seen) then data requirements would be much lower than scenarios where detection probability is very low, ca. less than 0.3. Data requirements will also depend on the model, e.g., your data will be more than sufficient to fit a model with only an intercept (p=c).

I suggest you proceed with the simplest model possible, i.e., the intercept only or "dot" model, a model without any effects except an intercept. To accomplish this, I suggest you start with a closed model parameterization (different model parameterizations are refereed to as 'data types' in MARK) that only includes the parameters p, c and N. When importing your data into MARK choose Closed Captures and then Closed Captures from the list of 'Data Types'. See 14.2 and 14.5 in the MARK book for more details.

From here, specify the intercept only model, model M0 in the table on page 14.13 in the MARK book. If you're estimating abundance (N) for more than one group, then you will want to allow group variation in this parameter. Model M0 can easily be constructed using the PIM Chart, see section 14.5 for details. However, eventually you will want to construct your models in the design matrix to achieve the greatest model building options/flexibility in MARK.

If you specify the dot model correctly, I suspect you'll get estimates of real and beta parameters that are "error" free. But of course, this may be a biologically unreasonable (to simple) model for your system/data. Nonetheless, it's a very good place to start, especially given sparse data. From the dot model, I suggest that you gradually add complexity to the model, e.g., p=c with group variation (if your dataset includes groups) or p<>c. As you build these more complex models, look the betas over carefully for problems and keep in mind section 14.3.1. Use estimates of the betas from models in your results browser as starting values when building more complex models (more details on page 10-38 and elsewhere I suspect in the MARK book, "There are several approaches...").

If your dataset can accommodate complexity in p, c and N, then you can try adding the mixture parameter. From the MARK Menu, click on PIM and choose Change Data Type. This will allow you to switch from 'Closed Captures' to 'Full Closed Captures with Heterogeneity'.

Based on your post, it seems that you've tried to initially fit a very complex model (perhaps the most complex model you'll consider in your analysis) relative to the intercept-only model that I propose starting with. You may not be able to fit the complex model given your data. However, your chances of fitting this model will increase if you use 'starting values' from a progression of less complex models.

andre

[AzucenaUgalde]

Hello,
Actually, I used the simplest model (closed captures) first, and the same “errors” occurred. Now I could download the exercise samples and noticed that, even {N, p(t), c(t)} model is not useful, is the first model in the results browser.
Now, my best model was {N, p(.) c(t)} but the estimations does not appear plausible based on the knowledge of this specie (N=886, CI 149-14,409) and de M0 was the last model (Delta AICc= 15.2; N=155, CI 135-188), a more plausible result but not the best model.
Besides, I noticed that the ‘p’ and ‘c’ values in every model are lower than 0.3 (most of the times), sometimes the value is lower than 0.1. So, I guess the data are not enough to apply such models, since in my data set the 60% of the individuals were seen only once.
What is your opinion?
Thanks

[abreton]

Actually, I used the simplest model (closed captures) first, and the same errors occurred.

Likely because you ran the default N, p(t) c (t) model without constraining the last p. And even if you constrained the last p, this model likely has more parameters than you can estimate given your data. That may have caused the errors you're referring to as well.

even {N, p(t), c(t)} model is not useful

Did you put a constraint on the last p? Abundance estimates from this model will not be valid unless a constraint is applied to the last p. See section 14.3.1 in the MARK book.

Consider model N, p=c(t). Use a common intercept across c and p, and the time offsets in the usual way. See the SECOND design matrix on page 14-19 in the MARK book, columns B1-B7. B1 is the common intercept across both p and c parameters (see parm column). B2 is the offset that allows p to be different from c. B3-B7 are time effects. Note c has fewer rows because no animals can be 'recaptured' on the first occasion.

From this model, drop columns B8-B11 and B2 to get model (N, p=c(t)). Or drop just columns B8-B11 to get model (N,p(t) c(t)). Drop columns B3-B11 to get model (N,p(.),c(.)). To get model (N,p=c(.)) drop columns B2-B11.

Models (N, p=c(t)) and (N,p=c(.)) assume recapture was not affected by previous capture history. If whales are unaffected by initial capture, which we might expect if 'capture' was by a photo-ID, then model (N, p=c(t)) is a plausible and parsimonious alternative to model N, p(t) c (t) and model (N,p=c(.)) is the same for model (N,p(.),c(.)).

Consider adding the following models to your set,
N,p(.),c(.)
N,p=c(.)
N, p=c(t)

I assume you already have,
N,p=c(.)

...in your model set. And consider building model N, p(t) c (t) - as well as all other models - using the design matrix. Label your columns carefully to aide interpretation of the effects.

I can't say whether you do or do not have 'enough' data. Nonetheless, my impression is that you can do better than you've done so far. Consider re-reading the linear models and closed-capture chapters in the MARK book. And also, keep asking questions!

andre