You have 20 variables bio1 -bio19 and elev with many of highly pairwise correlated. This means that there is redundant information and uncertainty in the data that makes it difficult to attribute and interpret the contribution of one or more variables. Knowing the pairwise linear correlation coefficients does not help to reduce redundant information and extract meaningful information for separate contributing factors.

I suggest using a principal component decomposition methodology that allows one to perform a multivariate correlation analysis and to identify redundant variables that carry little or no independent information while retaining only a few mutually uncorrelated principal variables (components) that contain practically all original information. This technique is a special case of a matrix approximation procedure called singular value decomposition. The higher the level of correlation between the columns of data of the original matrix, the fewer the number of new (principal) variables is required to describe the original data set.

You can perform principal component analysis using various statistical packages, such as R, Matlab, or Minitab. The latter requires no coding at all.

An overview of principal component analysis can be found in many books on multivariate analysis.

Dear Abprez,

I would like to suggest you check the significativity of your coefficients of correlation along with a VIF checking who would be less than 10.

Besides, ecological data does not always follow a linear trend so think about non-parametric tests of correlation.

Good luck.

• Remove some of the highly correlated independent variables.
• Linearly combine the independent variables, such as adding them together.
• Perform an analysis designed for highly correlated variables, such as principal components analysis or partial least squares regression.