I published a few papers a couple years back with Douglas Tallamy on the abundance and alpha diversity (species at one point in space) of insect herbivores on native vs. nonnative plants (see Research for more details). One thing that always bothered me was that I hadn't yet quantified the variation in in these insect communities either among host plants or across space (beta diversity) so it was difficult to get an idea of whether alpha diversity differences are compounded or mitigated by beta diversity effect.
The take-homes for me were that alpha diversity differences are the primary driver of differences within the herbivore communities on these plants. However, immature insects on non-native plants that aren't closely related to any native plants host a community of insects with lower host specificity among tree species than do natives. In addition these communities are more redundant across space, suggesting that widespread introductions on non-natives may lead to homogenized communities. Thus, measuring alpha diversity alone on non-native plants likely underestimates the negative impact of phylogenetically distinct non-natives on immature herbivore communities (see figure below plus figures in the paper).
Secondly, when we separate feeding guilds we see increased generalization across sites within communities (such as non-native congeners of native plants) that don't reveal differences at the whole community level. For example adult mesophyll and phloem feeders show strong negative effects on species redundancy on both on nonnative plants that do and do not share native relatives, but no difference was found at the whole community level.
Read the whole paper:
Burghardt, K. T., Tallamy, D. W. 2015. Not all non-natives are equally unequal: Reductions in herbivore β-diversity depend on plant phylogenetic similarity to native community. Ecology Letters. PDF or accessed at http://onlinelibrary.wiley.com/doi/10.1111/ele.12492/abstract