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Hej all,

I'm interested in what people think is the best model for analyzing the following data set. I am currently using RDHet, but am getting very high survival rates and am wondering if it is because I'm not using the right model.

I did a mark-recapture study of rodents in 2005 in an area divided into 3 timber treatment regions, trapping for 4 consecutive nights each month for 6 months. I am using a robust design, assuming a closed population during the 4 nights and an open population between different months. Based on the size of the trapping area and the frequency with which individuals were recaptured in a treatment region other than the one they were captured in originally, I am assuming zero immigration and emigration. Essentially, I am interested in how survival rates between months vary as a function of treatment region.

Any suggestions are much appreciated.

To close the loop here, off-list we had a discussion and the concern about high survival rates was not warranted. It was due to a misunderstanding about the unit interval which was in days rather than months or years. Because there are no units associated with the estimate in MARK it is easy to forget what you chose for time intervals when you setup the MARK database.

We often call them survival probabilities but they are survival rates in that it is the probability of surviving per unit time and not the probability of surviving the interval between occasions, unless the unit of time between occasions is 1. If your unit is a day and 30 is the time interval then it is a daily rate. If your unit is a year, then your interval between occasions is 1/12 (approximately) for occasions separated by a mongth. If your annual survival rate is 0.1 then the monthly and daily rates are:
> .1^(1/12)
[1] 0.8254042
> .1^(1/365)
[1] 0.9937114

--jeff

jlaake wrote:To close the loop here, off-list we had a discussion and the concern about high survival rates was not warranted. It was due to a misunderstanding about the unit interval which was in days rather than months or years. Because there are no units associated with the estimate in MARK it is easy to forget what you chose for time intervals when you setup the MARK database.

We often call them survival probabilities but they are survival rates in that it is the probability of surviving per unit time and not the probability of surviving the interval between occasions, unless the unit of time between occasions is 1. If your unit is a day and 30 is the time interval then it is a daily rate. If your unit is a year, then your interval between occasions is 1/12 (approximately) for occasions separated by a mongth. If your annual survival rate is 0.1 then the monthly and daily rates are:
> .1^(1/12)
[1] 0.8254042
> .1^(1/365)
[1] 0.9937114

--jeff

I would submit that the issue between 'probability' and 'rate' is something of a semantic red-herring. What is the more relevant issue is the appropriateness of the time scale of sampling occasions, relative to the scale at which 'biologically meaningful' variation in some parameter occurs. For example, suppose the true annual probability of survival is 0.9 (say, your typical 'adult of any long-lived species'). However, suppose you sample this population every month. Then, if we assume the try underlying survival 'rate' (at an infinitesimal time step) is a constant, then your estimated survival over each month interval would be



In other words, so close to 1.0 that you're unlikely to be able to get a decent estimate.

The larger issue is that you need to think hard about the appropriate scale, both of sampling, and in terms of the interval over which you want to make inference.

Sure, the interval should make sense for the critter. I'm not particular whether you call it a probability or rate but it is a rate and the probability only makes sense if the unit time interval is known. The fact that there is confusion about this (and this is not the first time) is indicative that it is not always clear to the end-user.

--jeff

jlaake wrote:Sure, the interval should make sense for the critter. I'm not particular whether you call it a probability or rate but it is a rate and the probability only makes sense if the unit time interval is known. The fact that there is confusion about this (and this is not the first time) is indicative that it is not always clear to the end-user.

--jeff

Estimated from discrete-time mark–recapture models, phi (say) represents the probability that an individual will be alive and in the sample at (t+1) given that it was alive and in the sample at time (t). In contrast, conceptualization of a survival rate (in my view) emphasizes change in hazard (odds risk) continuous time. We can estimate the latter if we make assumptions about the hazard function between (t) and (t+1). Given that estimation is (for much of what we're talking about) based on realizations of transition(s) over discrete time-intervals, I think 'probability' is to be preferred. This was also the conclusion of the 'EURING Convention - 2007' (see Thompson et al. Standardizing Terminology and Notation for the Analysis of Demographic Processes in Marked Populations).

Which is why I went through the MARK book and changed 'rate' to 'probability' whenever it occurred.

Sure you can call it a survival probability but it is not well-defined until the the unit of time is defined. Whether you call it a rate or not is immaterial -- it is a rate because it is a measure per unit time. The fact that you can change the interval from 1 to 12 to 365 for annual intervals between occasions and get very different results makes it clear to me. Even if you define it as the probability of survival from t to t+1 it doesn't specify the units of t. If t is measured in days then it is a daily survival probability and if it is in years then it is an annual survival probability.

--jeff