TEs vertical or horizontal transfers? After predicting and annotating all the transposable elements. For four related species.

Now I would like to find out these predicted candidates found in my costume library, either vertical or horizontal transfers?

are there any methodologies to suggest?
You make a phylogenetic tree of the "host species" and compare it to the phylogeny of the TE's. Homology is not a good idea for evolutionary trees.

There are two snags:


Concerted evolution, the TE's will risk recombining with each other within a host genome and that can mess up the phylogeneic signal (the theory as why is quite complicated)
If host species phylogeny are higher eukaryotes thats a lot of genetic material, so you'd need a short-cut. You can either use someones species tree, or focus on TE's within a subsection of the host genome and produce a tree of this subsection.


With point number 2 "a subsection of the genome" you can then assess synteny, i.e. has the TE jumped between position between species. If the TE hasn't moved then its an orthogonal proof of putative vertical transmission. 

What you are looking for is incongruence between host phylogeny and TE phylogeny as evidence of horizontal transmission and congruence to call vertical transmission. However, incongruence could occur due to the complexity of concerted evolution, so synteny would assist again as an orthogonal proof. Congruence is assessed as a "mirror tree", there is quite a lot of theory on this looking at host-parasite coevolution

For making trees RAxML or PhyML are flavours of the month particularly for TEs. 



A state of the art-of-the-art review is here, but it goes into significant detail into precise proofs, which in my opinion arn't needed