I am interested in using the Pradel model to set up a monitoring program for bears using DNA hair data. One advantage that I see are that the method is robust to heterogeneity (bears are notorious for this). I am thinking that the method could be used to monitor a population of about 2600 bears and, after running some simulations in MARK, assuming a capture probability of 0.17 and phi of 0.9, we would be able to detect a 5% annual decline in lambda over a 5-year period 97% of the time (90% CI of lambda not overlapping 1). That effect level seems reasonable and only about 500 hair samples would have to be genotyped, which is feasible.
This simulation has several assumptions. First, I did not assume any capture heterogeneity. This was because the literature says that Pradel is robust to heterogeneity. Also, it would be advantageous if we could collect the samples at one time during an individual year (rather than weekly and using Robust Design for Pradel to estimate heterogeneity). Is this a reasonable assumption or just wishful thinking?
Also, the population consists of about 7 subpopulations, and I ran the simulation for the total. Can the data be pooled to estimate trend if the sampled populations are disjunct? The effect would be less detectable if the simulations were for the individual subpopulations of course.
Finally, does the Robust Design for Pradel simulation work in MARK? I could not seem to get it to run.
Sorry for the long-winded post. Any thoughts are welcome.
Joe
Pradel questions
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Pradel questions
by sixtystrat » Wed Jun 01, 2011 9:41 am
- sixtystrat
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Re: Pradel questions
by Eric Janney » Thu Jun 02, 2011 11:52 am
Joe,
Here are some thoughts to consider.
The temporal symmetry models described by Pradel are more robust to heterogeneity in capture because they are conditional on marked animals and thus do not make inference to the portion of the population that is never captured/detected. However, the recruitment parameters in the temporal symmetry models are susceptible to bias resulting from a permanent trap response (i.e., trap-happy, trap-shy). Check out Hines & Nichols (2002) in the Journal of Applied Statistics for more information.
“First, I did not assume any capture heterogeneity. This was because the literature says that Pradel is robust to heterogeneity.”
This is true to an extent. However, like the CJS model the Pradel models assume that all marked individuals have the same probability of survival and recapture. This assumption should be evaluated using GOF testing on your most general (i.e., global model). If GOF tests indicate some violation of this assumption (which they almost always do), then a variance inflation factor (c-hat) should used to compensate. So, if you do have heterogeneity in your data and you adjust for it by imposing a variance inflation factor, it could definitely influence your ability to detect increases/decreases in abundance over time.
“Also, it would be advantageous if we could collect the samples at one time during an individual year (rather than weekly and using Robust Design for Pradel to estimate heterogeneity). Is this a reasonable assumption or just wishful thinking?”
I think this it is certainly feasible to intensely sample during one time of the year. The trick is to maximize your releases and recaptures (recaptures even more so than release #) in a relatively short time period while meeting the model assumptions.
“Also, the population consists of about 7 subpopulations, and I ran the simulation for the total. Can the data be pooled to estimate trend if the sampled populations are disjunct? The effect would be less detectable if the simulations were for the individual subpopulations of course.”
This is a model selection question. In short, it will depend on how similar life history parameters are between these sub-populations. If sub-populations are subjected to very different environmental factors or hunting pressure, then you probably won’t be able to pool the data. On the other hand, it will be tough to estimate all of the model parameters for 7 subpopulations with annual releases of 500 individuals and p=.17.
Here are some thoughts to consider.
The temporal symmetry models described by Pradel are more robust to heterogeneity in capture because they are conditional on marked animals and thus do not make inference to the portion of the population that is never captured/detected. However, the recruitment parameters in the temporal symmetry models are susceptible to bias resulting from a permanent trap response (i.e., trap-happy, trap-shy). Check out Hines & Nichols (2002) in the Journal of Applied Statistics for more information.
“First, I did not assume any capture heterogeneity. This was because the literature says that Pradel is robust to heterogeneity.”
This is true to an extent. However, like the CJS model the Pradel models assume that all marked individuals have the same probability of survival and recapture. This assumption should be evaluated using GOF testing on your most general (i.e., global model). If GOF tests indicate some violation of this assumption (which they almost always do), then a variance inflation factor (c-hat) should used to compensate. So, if you do have heterogeneity in your data and you adjust for it by imposing a variance inflation factor, it could definitely influence your ability to detect increases/decreases in abundance over time.
“Also, it would be advantageous if we could collect the samples at one time during an individual year (rather than weekly and using Robust Design for Pradel to estimate heterogeneity). Is this a reasonable assumption or just wishful thinking?”
I think this it is certainly feasible to intensely sample during one time of the year. The trick is to maximize your releases and recaptures (recaptures even more so than release #) in a relatively short time period while meeting the model assumptions.
“Also, the population consists of about 7 subpopulations, and I ran the simulation for the total. Can the data be pooled to estimate trend if the sampled populations are disjunct? The effect would be less detectable if the simulations were for the individual subpopulations of course.”
This is a model selection question. In short, it will depend on how similar life history parameters are between these sub-populations. If sub-populations are subjected to very different environmental factors or hunting pressure, then you probably won’t be able to pool the data. On the other hand, it will be tough to estimate all of the model parameters for 7 subpopulations with annual releases of 500 individuals and p=.17.
- Eric Janney
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- Location: Klamath Falls, Oregon
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