Detection Probabilities with Huggins CC Model

[SDF]

I’m a new user of MARK. My task is to calculate detection probabilities for counts of amphibian egg masses (3 different spp) at 7 breeding ponds conducted using the dependent double-observer method. Is the Huggins closed capture model appropriate for this application?

[murray.efford]

I can't give you MARK advice, but maybe these comments will help. The dependent double observer (DDO) method is esentially a removal method, so although it doesn't seem to appear in MARK as such, maybe you can rig something that will do the job - Huggins closed captures might be the way. Using MARK has the advantage of letting you compare models with pond-specific or species-specific vs globally constant detectability etc. However, if you just want vanilla DDO as in Nichols et al 2000 it's simple to do the sums yourself (see R function below; just cut & paste at R prompt).

My larger worry would be that these methods are very susceptible to individual heterogeneity (egg masses vary in detectability), so the estimates can be fairly meaningless. If you have covariates that strongly predict detectability then Huggins closed captures may possibly save you.

Murray

DDO <- function (x) {
## Dependent double observer estimate of N (e.g. Nichols et al. (2000) Auk 117:393)
## MGE 29 Aug 2009
## x is vector or matrix with counts in order: obs 1, obs 1 primary;
## obs 2, obs 1 primary; obs 1, obs 2 primary; obs 2, obs 2 primary
x <- matrix(x, nr=2)
x11 <- x[1,1]; x12 <- x[1,2]; x21 <- x[2,1]; x22 <- x[2,2]
p1 <- (x11 * x22 - x12 * x21) / (x11 * x22 + x22 * x21)
p2 <- (x11 * x22 - x12 * x21) / (x11 * x22 + x11 * x12)
p <- 1 - x12 * x21 / x22 /x11 ## overall detection probability
betaobs <- apply(x,2,sum)
varp <- (1-p)^2 * p / sum(x) * (1/p1/betaobs[1] + 1/p2/betaobs[2] +
1/p2/(1-p1)/betaobs[1] + 1/p2/(1-p1)/betaobs[2])
c(phat = p, sephat = varp^0.5, Nhat = sum(x) / p, seNhat =
( sum(x)^2 * varp / p^4 + sum(x) * (1-p) / p^2)^0.5 )
}
## for example
> DDO(c(38,7,5,29))
phat sephat Nhat seNhat
0.968239564 0.002239343 81.591377694 1.646812095

[bacollier]

I’m a new user of MARK. My task is to calculate detection probabilities for counts of amphibian egg masses (3 different spp) at 7 breeding ponds conducted using the dependent double-observer method. Is the Huggins closed capture model appropriate for this application?

I am not the expert others on here are so I expect someone else will chime in once the weekend is over, but I think that to do this in a Huggins CC, you have to fix the recapture probability to 1, since you will not have any 'recaptures' under a dependent design, thus your capture histories will never have a 10, as the second observer can never miss a individual the first observer sees.

Bret

[jlaake]

Bret is quite correct. Your capture histories should be 11 or 01, and you need to fix c=1 (recapture on second occasion is certain) and you cannot have time (observer) dependent capture -- p1 must = p2 but you can have individual covariates for each detection.

--jeff