# How does one deal with correlated predictor variables in SDM studies?

I utilize climate and terrain data with GLM for species distribution models (SDM). I know that the predictor variables have to be independent. But when I check correlations within a correlation matrix and a pairs plot (in R using pairs() and cor()) nearly all of my variables seem to be correlated. After Dormann et a. 2013 the collinearity issue cannot be solved and one logical step is to exclude one of the variables and keep the ecological relevant predictor. This is tricky in my case, because if I sort out variables with a correlation coefficient >0.7 only two remain.

Most of the climate variables are strongly correlated by nature (e.g. altitude and temperature). How does one deal with this issue in SDM studies? Is collinearity such a problem? I am asking this because my distribution maps look quite well. Also AIC scores are around 0.9.

• Yes. In math, if $a_1x_1 + a_2x_2 + ... + a_kx_k=0$ for some $a_i \ne 0$ is called complete colinearity. Or from the values of k-1 of $x_i$, you can DETERMINE the value of $x_i$ that is not included in that k-1. – user158565 May 4 '17 at 19:50