POPAN and effort constraints?

[timkdavies]

Hi,

I have a 6 year mark-recapture data set made up of opportunistic sighting reports (i.e. photographs), and split into 24 quarterly capture sessions. The number of photo submissions has varied quite dramatically over time, from 10 or so sightings per capture session early in the study, to hundreds in latter years, although this is almost certainly due to more people submitting photos rather than an corresponding increase in abundance.

CJS models work fine with this dataset, but I'm not sure how unconditional models such as POPAN will work. Are they capable of handling such dramatic variation in effort, and if so, how do I instruct MARK what this variation is? If I need to add effort as a constrain in the Design Matrix, do I need to apply this constraint to both capture probability and pent?

I've been through "The Guide" with a fine tooth comb, and have not found an answer for this (at least not with application to POPAN models). Any clues would be great!

Cheers,
Tim

[cschwarz@stat.sfu.ca]

Open population models actually include CJS models as a sub-component to deal with the the resightings, so can deal with variations in effort in the same way, i.e. the p_i will vary over time.

HOWEVER, the key assumption to estimating abundance is that unmarked animals have the same probability of being captured as marked animals at each capture occasion. In addition, estimates of abundance are VERY sensitive to heterogeneity in "capture rates". Given that you are using photographs as "captures", easily-identified animals have a higher chance of being "captured" than hard-to-identify animals. I would be very cautious of estimating abundance. Lastly, if you are actually estimating abundance, what is the scope of the population unit? Is it geographically isolated etc??

You would enter covariates for effort for the p_i in the same way as in CJS models. However, it seems UNLIKELY that you have covariates for the pents - these are the proportions of animals that enter between sampling occasions -- presumably this does NOT depend on sampling effort.
[Sampling effort changes the number you see, not the number present in the population.]


Carl Schwarz

[timkdavies]

Thank you Carl,

Just to clarify further - are abundance estimates sensitive to variation in capture rate because of the relationship between the pents and capture rate?

Obviously a higher pent estimate means more animals enter the population at that point, but will just one or two capture occasions with much higher capture probabilities - lets say because of increased effort - "take in" a disproportionate proportion of the superpopulation, i.e misrepresent a trend in the population? Or does constraining effort deal with this?

Tim

[cschwarz@stat.sfu.ca]

The pents have nothing to do with the sensitivity of estimates of abundance to heterogeneity in capture rates among individuals. To illustrate, suppose that some animals have 0 catachability (an extreme form of heterogeneity). Then they NEVER appear in any mark recapture sample regardless if there are a million or a billion of them, and estimates of abundance will always underestimate the true population.

The estimates of abundance (ignoring heterogeneity for now) do NOT depend on the capture probability, i.e. if the true abundance is 1000 the estimated abundances should be around 1000 if the capture rates are 5% or 20%. The precision of the estimate will depend on the capture rate with higher capture rates leading to estimates with smaller standard errors.