Robust design for marked populations?

[Todd]

I am having an impossible time adapting program MARK for analyzing capture history data collected in robust design format for a population of released animals.

The animals were all marked and released into an enclosed area to estimate survival. Some of the animals perished before making it even to the first capture interval. Thus, I cannot figure out how to incorporate this information into the analysis. Also, I cannot figure out how to condition the analysis on a known starting population without affecting the subsequent capture probabilities and therefore the survival analysis.


I have a detailed explanation of the problem below but that is it in a nutshell.

Thanks,
Brian Todd

Research Design:
30 animals are marked and released into an enclosed pen. They will be recaptured at later dates. The goal is to determine survival between intervals and capture/recapture probabilities. I have reason to believe that survival and capture/recapture probabilities vary over time and wish to do a robust design analysis.

The intervals are as follows:
Start – Initial release of marked population
Week 1 – two consecutive days of censusing
Week 4 – three consecutive days of censusing
Week 8 – two consecutive days of censusing

Graphically:
Initial release –> 1 week later – xx –> 3 weeks later – xxx –> 4 weeks later – xx
Where x equals a recapture day.

The problem:
Starting with a known population of animals makes robust design analysis difficult in Program MARK. 30 animals were released into the study pen and several of them are never recaptured. The question is how to condition the data so that there is a known starting population size at the initial release time. Due to the limits of the robust design, you cannot simply place a ‘1’ at the beginning of each capture history because robust design demands 2 secondary sampling periods within a primary period. It gets interesting here. Because, whether you “condition” the capture history with a ‘11’ or a ‘10’ has serious consequences for all estimates for the rest of the data. With a ‘11’, subsequent survival estimates are underestimated because the program thinks that capture rates should all be very high. With a ‘10’ the estimate may be either too high or too low but it is difficult to know for sure.

The end question is how on earth do you condition capture histories and which options need to be adjusted in Program MARK so as to ensure that the program doesn’t think that the first primary period (actually the release) is indicative of capture rates for the rest of the analysis?

[luciake]

Has any progress been made in how to adapt Robust design for marked populations in the last 5 years? I am in a similar situation and would greatly appreciate any help that could be offered.

[Bill Kendall]

Todd,
You were heading in the right direction, and I'm not sure where you ran into problems. You are correct that the robust design models require at least two occasions per primary period. You have four primary periods, the first of which has only one real sampling period. Since I am not sure exactly how you set yours up, I'll recommend something and you can tell me if you did exactly that without success.

You insert a dummy secondary sampling occasion right after the initial release, and insert zeroes in that entire column (therefore you would have nine total columns in your capture history). So you have two sampling occasions for primary period 1. Fix p=0 for secondary sample 2 (the dummy sampling period), and p=1 for the very first sampling period (the releases). This satisfies MARK's data structure requirements without affecting the estimation of survival (or transitions if applicable). The estimate of population size you get from MARK for primary period 1 should match the number of releases. The abundance estimates for the other primary periods of course refer to the abundance of marked animals that are left alive. Fixing the value of p in the first primary period should not affect the other parameter estimates.

Let me know if this does not work.

[luciake]

I tried fixing p to 1 and 0 for the release and dummy sessions respectively. The estimate of N for the second primary session is equal to the number captured that session, not the number of individuals still alive. The problem goes away beginning in session 3. Any thoughts? Is it okay to use the model or is that the sign that something else is also wrong?

[Jayna]

I have run into a similar situation with my data set. I stocked populations of individually-marked amphibians into large enclosures and I am interested in estimating their survival over the course of a year. I used a robust design recapture method with 4-day closed capture periods and 5 capture occasions. I therefore know that there may be no more individuals in the population than the number released, but I cannot be sure whether individuals who were not recaptured are dead or were missed. My hope was that I could use the abundance estimates returned by Program MARK to estimate survival within each enclosure over the course of a year.

As was suggested here, I had used a "dummy" capture period at the time of release, in which I fixed the capture probabilities to 1 and 0 and input all of the individuals that were released. I believe that the problem I am having with using the robust design to estimate the abundance of this stocked population basically comes down to MARK assuming that there may be emigration or immigration from/to the study area. For example, in one case the abundance estimate returned was 15 for the first capture period, but by simply counting the number of individuals found alive in both the first and subsequent capture periods, I can see that at least 23 individuals were alive at that time. Given that my pre-marked, enclosed population is closed to all processes other than death, using this method therefore results in inaccurate survival estimates. Seasonality contributes to this problem, as my capture probabilities are lower in the winter months, and some individuals temporarily emigrate belowground, so my abundance estimates are lower during the winter months than in the following spring.

I could compile the captures for each capture occasion and use a different type of analysis to determine survival rates, but I feel like I would be sacrificing some of my ability to return an accurate estimate, as I would basically be throwing out what I know about the capture probabilities within each closed capture period.

If anyone has any additional thoughts about dealing with this type of situation, I would very much appreciate any input!

Thanks,
Jayna

Additional info:
I have two treatments and eight locational blocks. Recapture probabilities vary interspecifically; I can easily get accurate estimates for toads, who have very high capture probabilities (~0.7), but MARK is returning estimates that appear to be less indicative of actual survival for leopard frogs (p ~0.4) and efts (p ~0.05).
100 American toads/pen x 16 pens
50 southern leopard frogs/pen x 16 pens
17 spotted newt efts/pen x 12 pens