Male In, Re-bait: The Difficulties of Density

Thalamita crenata, the blue pincher crab, is abundant throughout the pond, but seems to show significant size differences at different sites. How real are these differences, really?

One of the greatest challenges that faces ecologists is that of estimating “real” processes from what we sample. It is our job to characterize observable phenomena, but when we do surveys, or set traps, or tag and recapture things, the data we get are just a tiny snapshot of ecological patterns and processes that occur on multiple scales may have unobservable patterns. I was inspired to write this post after a summer of crab trapping. In short, I wanted to estimate the density of mangrove-associated crabs at various sites throughout the fishpond, in order to determine whether removing mangrove causes crabs (of both the desirable edible species and the other– ahem– slightly less desirable, inedible species) to change their hangout locations.

The way most studies sample crabs or fish are by setting nets or traps, and checking them after a set amount of time. In the fisheries literature, we call this “Catch per unit effort” or CPUE: the “effort” is what I expend throwing the trap into the water, leaving it out for 30 minutes (or overnight, for the night-active species), and checking it, and the “catch” is how many crabs show up in that trap. More crabs caught at one site per net per hour suggests that the density of the crabs is higher there. Oftentimes CPUE is the only data we have for fishery species, and usually we have a LOT of it. As you can imagine, if a fishery is below a certain CPUE it becomes unprofitable to fish that species (the C is not worth the E). Therefore, this data is economically important and often widely available.

We sometimes use CPUE as a proxy for density. However, if you are using any species that aggregate, or you are searching and catching at aggregating locations, CPUE can be artificially high: consider something like sardines, which form enormous schools which can be caught with purse seines. Good density estimates depend on accurate measures of the number of individuals and the area you’re sampling (D = N/A). Therefore, when your populations are patchy, you only get a solid density estimate for the area you sample. If we only used CPUE from sardine fishing boats, we would think the whole ocean was packed with them. Here we have a good estimate for D, but it’s not realistic to extrapolate that to the whole range of the animal. Alternately, in trapping or mark-recapture studies, you can end up with a bad estimate for A, because you don’t necessarily know the area you’re sampling.

A classic method in population biology for estimating population density is the mark-recapture study, in which you capture as many individuals as you can, tag them, release them back into their environment, and then go back and again capture as many as you can. If I could tag crabs*, I would use this technique. The mark-recapture method is a widely accepted way of estimating density, and very easy: you plug into an equation the number of animals you captured on your first and second visits, the number of tagged animals recaptured, and you get an estimate for population size. However, the same problems can occur as with CPUE when you’re tagging and recapturing. You know how many there are in your trapping area, but what is the effective area you’ve covered? Surely if there are baited traps, animals will wander in from as far as they can smell. We had a visiting speaker here at UH this fall (Dr. James Russell) who used a relatively new and exciting modeling technique to overcome these issues: Spatially Explicit Capture-Recapture models (Borchers and Efford 2008). This method uses a grid of traps to estimate the density of individuals by approximating where their home ranges are (it’s like triangulating someone’s location from the grocery stores they shop at more often). Home range center can be modeled as a function of the probability of catching an animal in a trap within this grid:

ML SECR works by combining a model of the probability of recapturing one individual (on the right) with a trapping grid (on the left). An animal is very likely to be recaptured near its range center (its burrow, in the case of many crabs), and less likely to be recaptured the further the traps are away from its home range center. The result is an estimate of home range density (the blue dots on the left), which is much more accurate than individual density (image c/o J Russell).

This model essentially provides a map of where burrows occur, and therefore can give a good estimate of species density as well as a snapshot of how that density is distributed (are burrows concentrated in one area, or are they randomly dispersed? Dr. Russell used this grid to estimate the density of invasive rats on two islands near Madagascar, and confirmed the existence of “island syndrome” (larger body size, higher density, but lower rates of reproduction and population cycling) in the rat populations. But you could use it for any animal that has a home range: T. crenata, one of the most abundant crabs in the fishpond, is territorial and often roams from its burrow by about 5 meters. Samoan crab (Scylla serrata) roams widely to forage, but returns to its burrow. If we could tag them, we could end up with a great estimate for the number of active Samoan crab burrows in a certain location, which would be a more reliable measure of density than regular mark-recapture or CPUE.

There are a few caveats with SECR techniques: one is that it assumes that an animal is more likely to visit a trap that is closer to its burrow. This may not be true for some animals that use factors other than nearness to burrow to decide where to forage. For example, some mammals forage by remembering where food patches are. If, by chance, an organism finds food far from its burrow but remembers the path between that food source and its burrow, we might miscalculate the location of its home range center. Rats remember how to go through mazes and get better with practice– so chances are they might remember where a trap is, and return to it even if it’s far from home.

Though labor-intensive and still imperfect, this technique offers an accurate estimate of population density for any animal that has a home location and is an excellent example of the ways we can modify current methods to accomodate spatial variability.

*how do you label something that sheds its exoskeleton every few months? If you have ideas, reply below!

Crab nets awaiting deployment. Though trapping and mark-recapture are useful methods for estimating population size, a spatially explicit technique will be more accurate.

Update: I neglected to mention that you can tag some crustaceans using fluorescent dyes injected under the carapace. This works best with critters that have a somewhat see-through exoskeleton. One of my crustacean-savvy readers has informed me that you can punch holes in the tails of lobsters to tag them– the hole remains open for a couple of molts, so it would work for a shorter term mark-recapture experiment.


Borchers DL, & Efford MG (2008). Spatially explicit maximum likelihood methods for capture-recapture studies. Biometrics, 64 (2), 377-85 PMID: 17970815

Russell JC, Ringler D, Trombini A, & Le Corre M (2011). The island syndrome and population dynamics of introduced rats. Oecologia, 167 (3), 667-76 PMID: 21643994

Russell, James C., Abdelkrim, Jawad, & Fewster, Rachel M. (2009). Early colonisation population structure of a Norway rat
island invasion Biological Invasions, 11, 1557-1567 : 10.1007/s10530-008-9406-z

6 Responses to “Male In, Re-bait: The Difficulties of Density”
  1. Sam says:

    “They” say there are no dumb ideas when brain storming… with that caveat in mind, could the crabs’ tissue somehow be injected with a florescent dye similar to what is used to mark tumors?

    • Margaret says:

      Aahhh, Sam you beat me to it! Yes, injecting dye is a technique that some people use, though it’s best when the exoskeleton is thin or clear. There are a few others you can use too– see above for my edits on different tagging techniques.

  2. Kyle says:

    I think there’s a method for tagging crabs somewhere in “Beautiful Swimmers,” which you’d probably like anyway.

  3. Sam says:

    “…we used the internal, coded microwire tags to permanently mark batches of juveniles and adults > 35 mm carapace width, and used the multiple-release Jolly-Seber mark-recapture model (Jolly 1965, Seber 1965)…”

  4. fishthinkers says:

    Nice post, the simple explanation of CPUE etc is done nicely. One thought of tagging crabs; Putting an acoustic tag on an aquatic crab straight after they moult would give you at least a few months of tracking data and if you set up a fine scale array you could position them ago within a metre. That would give you a definite home range size over months. I know there have been studies on Lobsters using acoustic tags. It would get expensive losing the tags every few months though haha. What do you think?

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  • Mahalo Nui Loa

    I recently graduated from the Donahue Lab at the University of Hawai'i at Manoa and am currently a graduate student at the University of Washington. This research is funded by a Graduate Research Fellowship from the National Science Foundation, as well a scholarship from the Seattle chapter of the Achievement Rewards for College Scientists (ARCS) Foundation.
  • “Where do ecological ideas come from? …Most do not spring deductively from the minds of ecologists, like Athena from the head of Zeus. Instead, they emerge when ecologists absorb the essential spirit of individual places– their genius loci.”

    ~Mary V. Price & Ian Billick, "The Ecology of Place"
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