Hi there;

One way recommended is: using PCA to reduce the variable numbers instead of removing them. The two-three first principal component can be included in model as reduced variables.

http://cdn.intechopen.com/pdfs/30012/InTech-Pca_a_powerful_method_for_analyze_ecological_niches.pdf

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0097122

I hope this helps.

Hi, I agree with the previous answer by Forough Goudarzi. The selection of predictors in a statistical model is a sort of "personalization of the model". For example: why did you use the 19 bioclimatric variables instead of the pure climatic factors (Taverage, Tmax, Tmin, Prec, etc..)? It is a good selection (in my opinion) but you should need a statistical reason... More in general, to model species distributions, you should be able to select the driving factors which are the most important for the species (e.g. minimum temperature of the coldest month, maximim temperature in summer, summer precipitation, and so on) but it is a very hard an tough exercise. In addition many climatic factors are correlated each other (collinearity) and the result can be highly influenced by this. If you use 19 variables and (for example) 2-3 of those are highly correlated each other it means that their "statistical meaning" is the same and that you are giving more importance (statistical weight) to this single variable because it sounds like a repetition of a unique variable. That's why, to solve this problem some authors decided to use "parsimonious models" by using few variables (5-8 predictors). In my opinion the best way to take into account the whole variability is to use the PCA and to include in the model the first 3-6 variables according to explained variance and cumulative proportion of variance. Remember that if you plan to project the species in future scenarios you must maintain the same centring and scaling for the two PCA.

For various ways to eliminate predictors including WorldClim and other climate variables see attached; reasons to do so are provided as well: parsimony (Ockham's razor) and avoidance of over-fitting and thus limited transferability of the SDM. We also show that elimination may depend on temporal resolution (seasons) for animal distributions and the ecological significance of such substitutions.

P rinciple components are hard to interpret as Alessandro already noted; you may also refer to some of my older articles including PCA although obviously not in a  SDM context.

Article Where the bears roam in Majella National Park, Italy

Article Transferability of species distribution models: The case of ...

Another reason not to use correlated variables in Maxent (or any other SDM) is that the model may by chance find a stronger correlation with a false variable and downweight the true variable. If all you care about is projecting the current environmental envelope, then this may be OK--you'll just get the right answer for the wrong reason.  However, if you're projecting to a different time/place, and the false variable changes in a manner different from how the true one changes, then you'll get the wrong answer.

A second issue might arise if highly correlated variables dilute one another--i.e., the SDM takes some from A and some from B, thereby making them both appear less important in the model.  Again, depending on your need, this may not be an issue.

Please note that this publication (below--and not my pub) says correlation is less a problem with Maxent than other algorithms--though they don't say how much is too much!

http://onlinelibrary.wiley.com/doi/10.1111/j.1472-4642.2010.00725.x/abstract

You can use a PCA or a Pearson test to exclude correlated variables

Hello,

Generally I previously evaluate which variables are correlated. Then, in each pair of correlated variables, I remove the one that has the least significant relation with the response variable (obtained through an individual test of the variable versus the species occurrence) or the least biological meaning.

Correlated variables should not be considered in order to be able to grasp each variable's contribution to the final model.

Cheers,

FMestre

Frederico Mestre.

It´s very interesting the way that you control correlation. What kind of test did you made to study the significant relation between the correlated variables and the species ocurrence?

Bests.

Javier Morente.

Frederico and Javier,

I have prepared a pdf slide show which explain how I extract correlated layers.

Regard,

Mahmoud

Hi again, just to add a simple thing, please keep in mind that the effect of collinearity is just on the importance of the variables (predictors) and not on the performance on the model. For instance, in case of linear regression, when you use two collinar predictors is the coefficient of each predictor they is influenced, not the r-squared or the MSE

Maurizio,

I think it's highly related to nature of our data. For example when we use about 20 layers of climatic and environmental records affected by changes in temperature, humidity and altitude, some of them show a strong correlation which we need to omit of some of them: 

mean precipitation over wettest quarter

mean precipitation over coldest quarter

mean precipitation over wettest month

mean precipitation over coldest month

....

they may causes some overestimate effects for some layers.

Not only correlation/multicollinearity and the ecological interpretability are important when you select from the available bioclimatic variables, but the way how the month/quarter the bioclimatic variable is based on will shift in time (and in space). Please refer to this paper:

Article The way bioclimatic variables are calculated has impact on p...

It is a good question. I am also facing the same problem. The answers provided here are good and helpful but it is always difficult to learn about new software. A concise and clear-cut procedure to test the collinearity between the bioclimatic variables would be highly appreciable.