From my point of view, if there is differences between gene tree and species tree topologies, such as we test the RF betweent the two trees. then it means that the evolution of gene is inconsistent with speices. So the gene are exogenous by horizontal gene transfer.
But i am not sure the conclusion is correct. Can anyone offer any other advice?
then, How can I prove whether a gene or a gene cluster is likely to be horizontally transferred? All I can think of is by GC content, codon bias, selection pressure, or the significance of gene trees and species trees.
Well, all you mention there an indeed be of use but will need to be correctly interpreted. As you might have read in our answers here, we don't say it can't (or won't ) be horizontal transfer, all we said was to not jump to that conclusion.
I suggest you read up on papers that deal with this issue, I'm pretty sure there are several of those around. They will likely also indicate somewhere how they determine HGT from other phenomena.
Thanks for your reply and valuable suggestion.