Can few sampling intervals and recaptures bias survival?

questions concerning analysis/theory using program MARK

Can few sampling intervals and recaptures bias survival?

Postby jbauder » Thu Sep 21, 2017 12:14 pm

Hello,

I have a mark-recapture data set for rattlesnakes with 89 adult individuals captured and marked over 2.5 years and I would like to estimate annual survival. Capture occasions occur at the den in the spring and fall so I have five sampling occasions: spring-fall-spring-fall-spring. Of these 89 individuals, 70 have no recaptures, 12 individuals have one recapture, 2 individuals have two recaptures, and 5 individuals have three recaptures. I know these small sample sizes and the short duration of the study make getting accurate annual survival estimates questionable but I was able to fit some simple CJS models (e.g., constant phi and time and/or sex dependent p). The best model had constant survival and sex-dependent recapture rates. My recapture rates are about 0.35 (± 0.10 SE) which is higher than what I’ve seen in other rattlesnake mark-recapture studies but not unreasonable. However, my annual survival estimates are about 0.38 (± 0.10 SE), which is much lower than I would expect for adult rattlesnakes. I would expect annual survival to be 0.70 or greater.

I have two questions. First, based on my sample sizes and short study duration is there any statistical reason to doubt the validity of these estimates? I know low recapture rates can bias survival estimates but are estimated recapture rates of 0.35 considered “low?” But biologically speaking we have no reason to suspect such low mortality. For example, in a concurrent radio telemetry study over this same time period, only one of 20 telemetered adults died. Second, could anyone provide suggestions for how I can use simulation to determine if I can reliably estimate annual survival given my sample sizes and study design? If I cannot provide the funding agencies with accurate survival estimates then the next best thing would be recommendations for a study design that can.

Thanks so much,
Javan
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Re: Can few sampling intervals and recaptures bias survival?

Postby ehileman » Thu Sep 21, 2017 1:55 pm

I have a mark-recapture data set for rattlesnakes with 89 adult individuals captured and marked over 2.5 years and I would like to estimate annual survival. Capture occasions occur at the den in the spring and fall so I have five sampling occasions: spring-fall-spring-fall-spring. Of these 89 individuals, 70 have no recaptures, 12 individuals have one recapture, 2 individuals have two recaptures, and 5 individuals have three recaptures. I know these small sample sizes and the short duration of the study make getting accurate annual survival estimates questionable but I was able to fit some simple CJS models (e.g., constant phi and time and/or sex dependent p). The best model had constant survival and sex-dependent recapture rates. My recapture rates are about 0.35 (± 0.10 SE) which is higher than what I’ve seen in other rattlesnake mark-recapture studies but not unreasonable. However, my annual survival estimates are about 0.38 (± 0.10 SE), which is much lower than I would expect for adult rattlesnakes. I would expect annual survival to be 0.70 or greater.

Hi Javan, Given that apparent survival estimates are generally asymmetrical, I'd be curious to know what you upper confidence limit is. Does it bracket a plausible estimate? Also, did double check to make sure that the uneven intervals are properly accounted for?
I have two questions. First, based on my sample sizes and short study duration is there any statistical reason to doubt the validity of these estimates? I know low recapture rates can bias survival estimates but are estimated recapture rates of 0.35 considered “low?” But biologically speaking we have no reason to suspect such low mortality. For example, in a concurrent radio telemetry study over this same time period, only one of 20 telemetered adults died. Second, could anyone provide suggestions for how I can use simulation to determine if I can reliably estimate annual survival given my sample sizes and study design? If I cannot provide the funding agencies with accurate survival estimates then the next best thing would be recommendations for a study design that can.

Remember, an estimate is only biased if the confidence intervals do not bracket the true value, bias is related to the error, not the point estimate. The precision of your apparent survival estimate is, not surprisingly, low (coefficient of variation, CV~29%), well over recommended guidelines of ≤20% CV (Pollock et al. 1990). If your upper confidence limit is reasonable, your low point estimate may simply be related to low power. Alternative, it could be a transience issue (i.e., some animals may be passing through your sampling area and are therefore captured only once, which will look like mortality if it's not modeled accordingly). I doubt you have enough data to do this, but you could consider modeling transience (see Williams et al. 2002 for details). At the very least it might give you an idea of whether this is a data sparseness or geographic closure issue. You could also simulate this relatively easily in MARK. Feel free to contact me offlist if you'd like to chat about using simulations. Hope this helps!

Cheers,

Eric
    Pollock, K. H., J. D. Nichols, C. Brownie, and J. E. Hines. 1990. Statistical-inference for capture-recapture experiments. Wildlife Monographs:1-97.

    Williams, B. K., J. D. Nichols, and M. J. Conroy. 2002. Analysis and management of animal populations: modeling, estimation, and decision making. Academic Press, USA.
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Re: Can few sampling intervals and recaptures bias survival?

Postby jbauder » Thu Sep 21, 2017 2:27 pm

Hi Eric,

Thanks for your response! Here are the estimates, SEs, and 95% CI for phi and p, which all bracket plausible estimates, except that an annual phi of 0.36 seems very low.

Phi 0.3594196 0.1000205 0.1931993 0.5679731
p gFemale 0.1792891 0.0809270 0.0691939 0.3909776
p gMale 0.3892142 0.0942477 0.2265901 0.5808915

You raise a good point about bias and power and perhaps this is just an issue of low statistical power. I do not think we would have transience since the data are from only one population so there really is no where for individuals to pass through to. Given the high den fidelity in our snakes (and communally denning rattlesnakes in general) I would assume that no individuals are permanently leaving the population. Sounds like some simulations are definitely in order!

Thanks,
Javan
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