I would expect that there will be interactions between variables eg. if the vegetation is grassland then the vegetation height variable will mediate the
interaction, if the vegetation is arable then crop type will be more
significant.

Would it be possible to use GLM or GAM models for this type of predictive
modelling?
The answer is probably.  I would recommend getting a copy of:
Mixed Effects Models and Extensions in Ecology with R (Statistics for Biology and Health) by Alain F. Zuur, Elena N. Ieno, Neil Walker, and Anatoly A. Saveliev Springer, 2009)

It covers things very nicely and gives specific R code.

Rob

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