The use of rarefaction could provide a solution. Its principle, simplified, it is about statistically reduce the large samples to be comparable to the smaller ones. As I am not deeply familiar with the finer points of thismethod, I recommend reading texts of wiser people on the subject. But, this could be one option.

a rough "hind" would be to model recapture rates as being time-dependent and use MR spatially explicit models to pick up the time*space interaction ? Or to subsample (bootstrap)in recapture histories / added traps and check for sensitivity in the resulting estimated N ? Maybe a stupid suggestion, check with robust biometricians !! ;-)

Could you standardize your data?  Basically put it into some sort of "per unit effort" form?  So, how many mammals caught per trap?  Then proceed from there?  Just a suggestion :)

How is the sampling process? I mean, are you going to use capture-recapture? Then if you have recorded trap positions (or you can get it, not necesary geographical coordinates, you can use your own system) you can apply secr than will allow you to directly estimate animal abundance. Once you have built your grid of traps (including the added in 2009) you may just consider them as unavailable in the previous sessions. Anyway, from what you have written, you have a third component, that means elevation from the ground, so you have to include it as a site-trap covariate that will go though species specific capture probability. If that is the case , I suggest you to dive a bit in http://www.otago.ac.nz/density/index.html and also in recent papers by M. Efford, B. Gardner, A. Royle and so on.  there is also a book on the topic http://store.elsevier.com/Spatial-Capture-Recapture/J_-Royle/isbn-9780124059399/  and you can apply most models directly within R packages (or R + OpenBugs/jagss)

If your data is refering just to number of individuals because they are not retrappable or are removed (killed) then is a bit harder unless the species shown dramatic variations (manifold) between years.

I would not reccomend to try to use animal catches per trap (or trap/nights) when the number of traps varies, as it can lead to spurios results ( one year, if you increase the number of traps, you may  get a lower index value with respect to the previous year, pointing to a reduction of the abundance, while the population have actually increased, as the index is strongly influenced by the number of traps), specially when it looks from your text that not all traps are randomly available to the species-individuals

It's hard to determine whether you have marked individuals, but assuming you have, then open population estimators could work given the multi-year study you have. Program MARK is freeware and has a range of open population estimators and cann be incorporated into R.

I would advise staying away from captures per unit effort as this is an index that ignores variation in detectabilty between years/trap sites etc. Mark recapture methods do account for detectabilty and are far more robust.

I think you can simply standardize your data by estimating catch per unit effort (i.e. dividing totals by number of traps). However, I do not have enough details whether you are doing mark recapture or just surveying the population for abundance. If you are just trying to get abundance, I would suggest standardizing your data.  

Rarefaction is a technique to assess species richness. Throught this technique you could know if the number of species found in your samplings varied over time due to the different sampling effort you applied. You would expect that greater sampling effort would yield a larger sample and more species, so you can't just compare the number of species by this technique. However, you are speaking about abundance of the populations.

In this case, a first approach could be to compare statistically your abundances after you change the sampling effort (2009). For this, you must compare the abundance that you obtained when you increased the sampling effort with the abundance obtained if you had not increased the number of traps (ANOVA).

If you don’t find statistical differences, you have a good chance that the different sampling effort in the study area would have not an effect on the population abundance estimates.However, if you find significant differences, Ii think you may try to standardize the data into some sort of unit effort

Regards

Thanks for all your answers.

The rarefaction suggestion is a very good one. I'll try it. Thank you Lauri Kaila and Jose Luis Carballo.

Eric Marboutin, the bootstrap is also possible. Thank you.

Matt Nicholson and Sujan Henkanaththegedara, the problem with indices like number of caught per trap-nights is that not necessarily the relationship between the number of captured individuals and sampling effort is linear; probably is non-linear. Some papers already discussed it and discourage the use of it.

Fernando, we do mark and release the marsupials. We have 3 trapping grids with 25 trapping stations; in the beginning of the study, live traps were placed on the floor and canopy. After 2009, we added in all trapping stations one more trap in the understory.

About SECR, I already though about it, nonetheless I never really got in contact with it so I didn’t know that I could use it to correct the increase in the sampling effort. Do you think it is possible to determine the three elevations in the analysis?

Matt W Hayward, I agree with you about the use of population indices. About MARK, I’m working with it to answer some other questions I have, but I think if I estimate population abundance with the Robust Design, for instance, it will also be affected by the sampling effort. 

Hi back, some more points... if you are planning to use robust designs as mentioned in the previous post (so covering other state parameters like emigration, integrate real survival etc) you actually can do it within secr framework. Have a look to http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12133/abstract (this model is not included in the secr book). So your estimates would not be affected by sampling effort (well, also depends on your asumptions and the species specific natural history)

Regarding using the third dimension, secr is actually a 2d dimension model, but you can include elevation, in your case just a as a factor covariate (understory, floor and canopy) depending how do you make your model formulation. I am pretty sure you can do it in the model developed in the paper I have linked here, in more older formulation I guess so, but I cannot give you a 100% sure answer whiout making a few checks. There is a google group for secr stuff related to the spatial capture recapture book, and I think most people developing the models is there (appart of the core developers, of course), so you can direct questions there if you choose to use that approach. https://groups.google.com/forum/#!forum/spatialcapturerecapture

Of course, you can use secr with varying effort, that is one of its many strengths, it does not need standarized, regular, and unmodified field trapping grids, and you can vary the traps locations (but not in a daily basis, for example) . 

The only general concerning I can say is linked to trap saturation, but they may be other species specific constraints that I do not know for your species. And of course, secr, specially if you move to the robust design approach, is quite painful for standard computers, depending on how many individuals, traps an days yo can even go for vataion and come back while the model has not ben fit.... it takes a long time...

I agree with Fernando. The SECR model (or maybe the Spatial Mark Sighting -SMR, if you have both marked and unmarked animals in your study, or a Open SECR model if you are studying several years) is the best option.  Another way is using a dynamic site occupancy model for several species (see link)

http://www.uvm.edu/rsenr/vtcfwru/spreadsheets/occupancy/Occupancy%20Exercises/Exercise16/MacKenzie_et_al_2009.pdf

http://www.r-bloggers.com/multi-species-dynamic-occupancy-model-with-r-and-jags/

Everything depends on the type of sampling design and reliability has been raised from the beginning.

If the first design is well planned, and you get an acceptable standard deviation, increased sample size will increase the reliability and not the size of the population.

Hi Paulino, thank you. Which would be an acceptable standard deviation? Can you suggest me a paper? Actually, I didn't have an increase in population size, but what I don't know is if the number of individuals would be lower if I kept the original sampling effort.

Virtually any SD might be acceptable (joke !) ... but power of further tests will decrease dramatically with increasing variance (see e.g. http://blog.minitab.com/blog/adventures-in-statistics/variability-and-statistical-power). I would say, decide first what minimum difference in N (between years, betwwen sites) you would like to statistically detect, then you may have an idea of what SD is acceptable ?

I see that people have already suggested use of CR/SCR, and that should take care of variable effort over time. Just don't pool data over time to estimate parameters related to detectability (p, c in CR; lam0/g(0) and sigma in SCR) as you would then be dividing observed counts by a constant. Also, you cannot estimate things like population rate of change (e.g. finite growth rates) and recruitment when study area changes (not sure it has in your case).

Also, was just looking at some previous responses and wanted to clarify that if you estimate abundance/density separately each year, that fully accounts for variable effort: the years you had larger traps will simply have higher capture probabilities both in the field and estimated by your model, therefore estimated abundance will be unbiased.

By the way, and keeping in mind D.J.'s comment on constancy in the design over time to estime growth rate, juste remind you also can estimate population growth rate using a modified version of Pradel(1996) model in case where the sudy area is changing. See:

http://warnercnr.colostate.edu/~gwhite/fw663/Hines%20and%20Nichols%202002%20JAppliedStatistics.pdf

Time for you now to make the computer warming up !!! ;-)

Hi Mariana,

I am not an expert in the field, but I think that differences in sample size can be accounted for by specifying an offset variable in a GLM with Poisson error distribution. A useful book may be "Mixed Effects Models and Extensions in Ecology with R" (Zuur et al. 2009).

Hi, just a quick response to the last two points (in reverse order):

- Specifying an offset in a Poisson error GLM accounts for variable exposure across data points. For example, if one were looking at rate of encountering road-killed small mammals along road segments as a function of some predictors, but the roads were all of different lengths, log(length) could be used as an offset to estimate encounter rate per unit length as a function of the predictors. I don't see how it can be used to account for variable effort or sample sizes. Just need to model detectability separately by year, that should take care of it.

- Dr. Marboutin, thanks for the paper, I had seen it cited but never actually read it. However, I see that Jim and Jim point out that estimates of population change WILL remain biased if the study area changes.

 "Leonid Voyta" : Relative abundance. Need all the catches for each year converted to 100 traps per day. After thet we can compare properly.

Keep it simple: you can do a sort of standardize curve...when you see that the relationship between number of captured mammals and number of traps (the effort) give a similar value you know which is the minimum number of traps that you need. Then starting with this minimum number of traps you weight your capture by your traps. You should not use the data coming from a number of traps much smaller than the minimum. On the unit of measure the suggestion of Andrew is good even if the number of traps cannot be much higher than the one you really used.