Population estimation

[cam]

Hello -

I'm relatively new to MARK, and I'm considering applying MARK to a wolverine dataset (all individuals known) such that we can identify actual population sizes.

The challenge is to model using a small number of individuals (approx 12 male and 12 female; 2 groups), and with only two occassions (see below).

Preliminary simulations indicate very hat c-hat estimates and large SEs associated with N when using the Huggins model; whereas the closed population estimation model produces c-hat estimates near but below 1 and relatively small SEs associated with N. In fact, for some of the closed popn models, the N estimates are exactly the same as the number of captured indviduals.

So my questions are first, whether this result makes 'sense' given the dataset below, and also, are there any tips for modelling (e.g., PIM) with small numbers of individuals when the primary goal is to estimate N??

Example dataset:
01 1 1;
10 4 6;
11 6 6;

Any comments would be useful. In the future I wish to explore the robust model using a similar dataset but with using two years of monitoring data.
Best, Cam

[hjunji21]

Hi,

I'm a new MARK user and I'm learning about capture-recapture to study stray dogs population.

I get data of this population related to 3 ocasions (3 days) and I ran it on Mark. I selected the standard closed capture models to analyze it.

However, I also had the N equal to total marked animals (=70) with the models:
- {p(t) c(.) N(.) PIM} (the smaller AIC value (=-185,6190)),
- {p(t) c(.) N(t) PIM},
- {p(t) c(t) N(.) PIM},
- {p(t) c(t) N(t) PIM}.

But, when I ran the:
- {p(.) c(.) N(.) PIM},
- {p(.) c(.) N(t) PIM},
- {p(.) c(t) N(.) PIM},
- {p(.) c(t) N(t) PIM} (the greater AIC value (=-180,9811)),
I had an another N (=79).

I wonder if you could tell me something that could help to understand my results.

Thank you for attention.

Kind Regards

[Fish_Boy]

I am having a similar problem using closed captures in robust design. The 'best' models make intuitive sense knowning the data and system, however, the N(t) estimates have no SE (only have two secondary occassions) and are essentially the same or slightly higher than the number of captured animals durng the primary session.

When the CJS models are used for annual data and population size calculated the values are significantly higher and closer to what one might expect.

[TGrant7]

Cam,

You're confusing statement is that all individuals are known, but that you want to identify the true size of the population.

You probably can't get much out that dataset with a closed pop model. You'll get nothing with robust design, which requires even more dense data. It's a very small dataset as far as mark-recapture datasets go.

c-hat with closed models? c-hat is only with open models, AFAIK.

The full likelihood (standard non-Huggins) closed capture models will give you a result of mt+1 (minimum known alive - in your case 12) when the numerical estimation can't work because there is no maximum to speak of. You can tell when the numerical estimation hasn't work, has failed to converge, because SEs are ridculously large or small. The Huggins results are your best bet and the large CIs are a reflection of your very small dataset.

hjunji21,

Usually the point of closed capture models is to estimate N, the point being you don't know N. Do you know N or not? I suspect not if you are dealing with free-roaming stray dogs, so you wouldn't want to fix N. In other words, it's saying there are probably about 9 dogs you never managed to mark.

Also the modeling of N varying over time - I'm not sure what you mean by that. But the closed capture model assumes N is constant or "closed" to change. So something is not right.

Fish_Boy,

If by no SE you mean 0.00 SE, that means it didn't converge. Try Huggins. Not clear what you mean by CJS, annual data, and population size. CJS doesn't do N. Jolly-Seber?

Tyler

[Fish_Boy]

Tyler,

I failed to get convergence. Yes, I meant Jolly-Seber. The data are collected annually at about the same time afor about the same period. A CJS model with constant survival and variable recapture was always the best model regardless of population. A Jolley-Seber estimate was calculated and provided reasonable estimates.

Because the annual sample period can be divided into two realistic periods each year, the spawning period and post-spawning period. I setup the encounter histories for a robust design. The simple closed captures models were failing to converge. However, closed captures with heterogeneity provided estimates I felt were reasonable (i.e. not over estimated). I did have a couple issues with pi for one population and gamma" for another population. I fixed pi for the one population to the average of the other two populations (they were practically identical to each other). The gamma" I am still having problems with, regardless of link function. That being said the datasets are perhaps a little light on data density given the needs of robust design ~300 and ~460. The last population has 1000's of encounters and has no convergence issues.

I have a dfeeling my convergence issues with the gamma" are from a longer time interval between two of the primary occassions. I am going to try and drop some of the early data out and see whether that fixes the problem. We have several reliability issues with that year of data. But because we are still recapturing the fish I wanted to keep them in the dataset.

I will post results once I am done.