IQTree is a fashionable method for speeding up bootstrapping and used on ultra large datasets. What IQTree might be doing is rigidly fixing a model and parameterisation is not estimate via the ML. This might be how it achieves its performance.
In context, IQTree can use an establised mixed model, which is one approach to protein phylogeny. As a personal note, I don't favour it and come back to the reason later. It MIGHT also generate its own mixed model. There are not 700 established (published) amino acid matrices plus established mixed models, combined there are no more than 50.
There are around 30 protein mutation matrices, Dayhoff models (I honestly don't who Dayhoff is), one for insects which might be for mtDNA ... mtArt, one for mtDNA, mtREV I think and so on. Please check carefully the number of models it is evaluating.
Its easy to see how 4 or 5 combinations (or possibly permutations) of 30 become 700 models if it is generating its own mixed model.
Alternatively, what it does (mixed model or not) BIC and AIC do is given a tree estimate (prior) what's model is the best probabilistic fit. In your case Q.insect is cropping up, whether this is mixed model or not ... dunno.
What I don't know is how it calculates the mixed model, is it creating a new singular matrix by averaging (which is probably closer to the algorithm), or is it sequentially passing the data through first one model, then another etc ... Personally, I avoid mixed models for precisely this reason, I dunno what the actual matrix is, but accept it can provide strongest AIC/BIC.
It suggests either:
- BIC/AIC results in an outcome that isn't biologically realistic .... OR
- there has been some weird parallel/convergent evolution - this happens in parasites for certain
If you are using a single matrix not mixed model and Q.insect is cropping up - I would be concerned. If it is part of a mixed model, I wouldn't worry.
Is it checking 30 models (plus published mixed models) or 700 matrices??
If the final point was correct (biologically real result), you check it via blast - simply exclude bacteria and see if you get a plant of insect sequence as the top hit.
Ultimately, the uncertainty is the reason I avoid mixed models.
To answer the question, I'm not aware of a bacterial amino acid matrix. HOWEVER, you can select a mixed model. It might just be screening around 50 models via AIC/BIC and within that Q.insect is the most probable.
The alternative is to look for support using a general amino acid matrix (for example JTT, LG or JTTDCMut).
Personally, I would be very cautious about proceeding with a matrix generated by insect genomes outside a mixed model for bacteria and in the absence of any biological support. FOR EXAMPLE, if these were insect symbionts - that makes sense.
Which ever approach is used a Bayesian approach is often required.