Probably some more information is needed about the problem. Could you provide it?

What does fixed area counts mean? Are these counts of individuals out of several species within fixed areas? Or is it just one species? Or something else?

If species: are you interested in extrapolated individuals numbers (N), or species numbers (S)? N doesn't make too much sense unless you know which conditions produce which amount of individuals (which is rarely the case). Or you would simply multiply by area.

For extrapolating S according to a higher (or infinite) sampling effort, several methods exist (Jackknife 1 & 2, Chao 1 & 2, Michaelis-Menten, lognormal, etc.).

Thanks Armin. Yeah, you got it.  I am using a pipe sampler that has an area of 0.5 m^2 to sample amphibian larvae and invertebrates in a series of wetlands (that's the fixed area count part). I take 10 samples per wetland. The area (and volume) of both the sample and wetland are known/estimated at the time of sampling. I am interested in extrapolating the total N for each species for each wetland, based on knowing the area sampled and the area extrapolating to. Does that make more sense? I am not focused on S in particular, more like N for a few species.

I have explored a few methods. Proportional extrapolation, e.g. 10 individuals caught in 5 m^2 in a wetland that is 50 m^2 so 100 individuals in the wetland, or as the counts are almost always overdispersed, used a negative binomial probability distribution based on the mean and variance of each species at each wetland to estimate the  total N. 

It seems like a fairly simple thing to do, but as the wetlands change constantly in surface area and volume, it seems important to factor the dynamics into any assessment of an estimate of total N. It might have been better to try a capture-recapture method.

Thanks,

Paul

Hi Paul,

would be simple if your samplings would be representative for a certain wetland which is quite homogeneous. Then I would go for proportional extrapolation.

However, if the area is not that homogeneous and the species is patchily distributed (as probably the case), then 10 samplings might not be enough since you might miss any hotspot. Then you might run into underestimation of numbers. But it would be difficult to assess the relevant scales of heterogeneity and the minimum numbers of samplings to be representative for a certain wetland and species.

As to the dynamics, I would suggest the species don't leave the region but maybe are a bit more crowded in the remaining available area. So the density (N/area) might change. Might be interesting to go into metapopulation dynamics if you have several wetlands somehow separated but also connected (Hanski 1999: Metapopulation Ecology. Oxford University Press, Oxford. ISBN 978-0-19-854066-3)

Interesting topic. I have to think about it a bit more...

All the best

Armin

Thanks Armin, the wetlands are fairly heterogenous, with different vegetation communities in the littoral and deeper zones. We did sample "haphazardly" (as close to random as we could) so although the area sampled could be a low % of the overall wetland, we did our best to include all types of habitat. 

I agree, 10 was probably not enough, but all that logistics could provide without reducing the number of wetlands sampled and the sampling times. Something I will consider changing next year. 

Thanks for your recommendations.

Paul

I also considered a capture(mark)-recapture method but for determining termite numbers in a colony. In the end we opted for full mound excavations and for the counting process followed an aliquot method of Clark et al. referred to in Meyer et al. (2000).

Population density was derived for mounds by the simple formula d = n/s, where n = number of mounds sampled and s = area sampled (see Meyer et al., 1999).

The most abundant species was then chosen for estimating biomass and eventually food consumption, published in 2001 and 2003, respectively (not attached here).

Article Distribution and density of termite mounds in the northern K...

Article Intracolonial demography of the mound-building termite Macro...

Thanks for your comments and for the papers Victor. I see you had to deal with clumped distributions in the termite mounds and you used the mean to extrapolate out for each landscape type.

Do you think that as your transects were established randomly, and you sampled all the landscape types into which you made the extrapolations for total N, the mean did a good job on this?

I would say, yes, Paul. We were setting up large-scale baseline data and there was nothing else to compare our results to for that region. Some studies for habitats further north in Africa supported our findings, but some did not. However, most recently Davies et al. (2014) have found similar densities for the very same region (Kruger Park). Our transect method (bias-free) also picked up on some hotspots, specifically in the case of Cubitermes (also attached).

Data Cubitermes Map (colour-enhanced)

Article Spatial variability and abiotic determinants of termite moun...

That's great. Thanks again Victor.