Well, the idea is that you detect the major axes of variation across the area of analysis. The first step is to identify that area of analysis ... it should be equivalent to "M" in the BAM diagram (see Soberón, J., and A. T. Peterson. 2005. Interpretation of models of fundamental ecological niches and species' distributional areas. Biodiversity Informatics 2:1-10.), and these assumptions about M need to be stated explicitly as the basis for the calibration area for your models (see Barve, N., V. Barve, A. Jimenez-Valverde, A. Lira-Noriega, S. P. Maher, A. T. Peterson, J. Soberón, and F. Villalobos. 2011. The crucial role of the accessible area in ecological niche modeling and species distribution modeling. Ecological Modelling 222:1810-1819.).

You would then do your PCA over the entire M region (calibration region). That will give you a new, simpler environmental space defined in fewer, and fully orthogonal axes.

Well, the idea is that you detect the major axes of variation across the area of analysis. The first step is to identify that area of analysis ... it should be equivalent to "M" in the BAM diagram (see Soberón, J., and A. T. Peterson. 2005. Interpretation of models of fundamental ecological niches and species' distributional areas. Biodiversity Informatics 2:1-10.), and these assumptions about M need to be stated explicitly as the basis for the calibration area for your models (see Barve, N., V. Barve, A. Jimenez-Valverde, A. Lira-Noriega, S. P. Maher, A. T. Peterson, J. Soberón, and F. Villalobos. 2011. The crucial role of the accessible area in ecological niche modeling and species distribution modeling. Ecological Modelling 222:1810-1819.).

You would then do your PCA over the entire M region (calibration region). That will give you a new, simpler environmental space defined in fewer, and fully orthogonal axes.

I agree with Andrew, you should use the whole area, if possible, or at least a subsample of points from it (10,000 might be too many).

the idea is to represent your environmental characteristics without redundancies.

remember that you might have some variables that do not correlate with the others in a significant way and I would exclude them from the PCA per se, but I would include them back later on for assessment in your SDM.

Once you have your equations though, you need to apply them to your own points and obtain the PC scores instead of the original variables, and use them in your SDM (I guess you are aware of that). Some people like to calculate those scores in a way that forces them to be orthogonal. I do not mind that.

Also PCA helps you to understand the correlation in your data and in many cases, discloses some interesting patterns that may also help you later in interpreting the SDM results.

hope this helps somehow

Ale

Thank you Andrew and Alessandro for your helpful answers. I am trying to now run a PCA across my entire study area, but R is having trouble doing pairs plots for my correlations, possibly because of the large number of points I am now using. I will keep on trying!

Hello Anna

About your specific questions:

1. Based on the fact that the species to be modeled can differ greatly in the number of localities of presence, I use the accessible area defined for each species (sensu Barve et al. 2011). This area is the "Extent" defined by the modeler, as the potentially sampled area in the history of the modeled species. On that extent I take 5000 points at random (or other number of points according to the size of the Extent) and on the climatic data of those points I do the correlation test. I think the important thing is that each variable is well represented with all the possible values along the selected extent.

2. I believe that the defined extent for modeled species is again important. For example, 10,000 points for all of South America may be adequate. On the other hand, for example, for a species only present in a small part of Andean forests, the extent will be much smaller and 10,000 would be an enormous number to evaluate the correlations of the variables.

See ->

Barve, N., Barve, V., Jiménez-Valverde, A., Lira-Noriega, A., Maher, S.P., Peterson, A.T., et al. (2011) The crucial role of the accessible area in ecological niche modeling and species distribution modeling. Ecological Modelling, 222, 1810–1819.

Owens, H.L., Campbell, L.P., Dornak, L.L., Saupe, E.E., Barve, N., Soberón, J., et al. (2013) Constraints on interpretation of ecological niche models by limited environmental ranges on calibration areas. Ecological Modelling, 263, 10–18.

I hope I have helped in the doubts raised.

Regards,

Ignacio

Hi Anna,

You could try R tools which can handle large data sets. Rattle would be one example of such a tool in R. If you still have trouble in plotting the pairs send me a message. I could look into the issue and try to help you.

Hi Anna :)

I have an R script ready to make a PCA for all the background area, if you want I can send you by email.

Hugs,

Marília