Generalism - specialism index in microbial ecology
I've published a paper comparing different measures of specificity, if that is of any help. But if you plan to have, e.g., measures of performance on carbon sources, pH, and temperature, then you'll have three measures of specificity (i.e. one for each).

Also, worth to have a look at Graham Bell's inconsistency and responsiveness, as used by Venail et al. to classify specialists and generalists.