Issues of continuous partial sampling

[ASpencer]

Hello forum friends,

I’m working my way through the ‘Gentle introduction to Mark’ at the moment which is extremely useful, however I’m not a modeller and so the learning curve is steep. I have what I think is an unusual data set with regard to sampling protocol, and I'd like to assess whether MARK can work with my data or whether a more bespoke method may be necessary.

Here’s an outline of my data and what I’m trying to do:

• My objective is to calculate the edible crab population / density in several fishing hotspots off the NE coast England, UK.
• The crabs are migratory (season and sex dependent) so it’s an open population.
• 64 traps were set (4 strings of 16 traps) in each hotspot.
• Sampling was short term, with up to 8 sampling occasions over a 3 to 4 week period, with varying sampling intervals (due to weather).
• Overall catch for my main site was 4300 individuals, with an overall return rate of 3.6%.
• I have 2 groups (male and female) and individual covariates (size) recorded for all individuals.
• I have multiple release cohorts; all animals caught on each sampling occasion were marked and released.
• Trapping was continuous, i.e. traps were in the water over the entire 4 week period, apart from during sampling, after which traps were re-baited and re-set immediately.
• Trap ‘catchability’ is time-dependant, i.e. ‘catchability’ declines with soak time as bait loses its attractiveness and traps fill-up with animals.
• Sampling was partial, i.e. between 25 and 50% of traps were hauled on any 1 sampling occasion (again due to weather and time limitations).

I think the partial sampling may cause the greatest problem because;

a) there are 3 possible fates for non-seen marked individuals; 1) permanently migrated from the capture area, 2) still in the capture but not caught in ANY trap, or 3) still in the capture but caught in a NON-HAULED trap, although they would be recovered eventually on a subsequent occasion.
b) Partial sampling means ‘catchabilty’ rates are not ubiquitous across the 64 trap array because individual strings of traps were being re-baited and re-set at different times.

Any thoughts or advice on model selection / special features that can accommodate partial sampling would be very much appreciated.
Regards
Andrew Spencer

[Eric Janney]

Andrew,

Given that you want to estimate abundance/density, I see a number of major problems with your sampling design/dataset.

"The crabs are migratory (season and sex dependent) so it’s an open population."

Most CR models that estimate N are based on a "closed" population assumption. The Jolly-Seber model relaxes this assumption for demographic closure (i.e., births and deaths), but a population by definition must still be defined by some geographic boundary. The POPAN models allow the estimation of what is defined as the "super population" or the total number of individuals that were present in the study area at some point during the study period. But, the study area still has to be geographically well defined.

"Overall catch for my main site was 4300 individuals, with an overall return rate of 3.6%."

Any abundance/density estimate you are able to produce based on 3.6% returns will have terrible precision (i.e., enormous confidence intervals) thus severely limiting its usefulness.

You also most likely have a great deal of heterogeneity in catchability because crabs that resided/migrated close to where the traps were set had a much higher probability of being caught/recaptured than crabs that resided/migrated farther away from the trap. This will badly bias your abundance estimate.

[ASpencer]

Thanks for your comments Eric,

The low return rate will no doubt provide very wide confidence intervals and may prove unusable. The sampling was undertaken during the worse winter since records began, but there isn't much that can be done about that now unfortunately. Hindsight is a wonderful thing, however it’s all useful learning for future work of this kind, in terms of the timing of surveys and concentrating effort on recapture as opposed to marking.

In terms of defining the geographic capture area, this is extremely problematic in marine environments. In the case of baited traps and other static gear, sampling properties are not easily summarized. The area from which the catch is drawn is hard to measure and changeable and as you point out capture probability is unlikely to be homogenous within this area. However some work has been done on estimating the capture area in terms of area of ‘bait influence’, ‘trapping area’ and a notional ‘effective area fished’. All of which have assumptions and caveats attached, but at least provide a starting point for estimating area.

As I said in my original post, the issue I am most interested in is whether MARK has the functionality to deal with the issue of variable declining trapping effort across the array of traps, that resulted from the partial sampling protocol.
Any comments on this issue would be very welcome.