Hi Chris,
The latest version of StarBEAST2 (v15) available in BEAUti includes an AIM template.
AIM and the multispecies network coalescent (MSNC, implemented in the SpeciesNetwork package) are different models. The AIM model is based on a species tree, with continuous gene flow occurring between all pairs of species that exist at the same point in time - it is an approximation of the IM model where the species tree is jointly estimated with the migration rates, but the migration histories of the gene lineages are integrated out. The MSNC model is based on a species network, where reticulate nodes represent instantaneous transfer of genes from one species to another, including transfer from species from lineages which may have no living or no sampled descendants in the present.
Both of these models and methods are very new. My personal opinion is that we don't know at the moment which model is a better representation of gene flow. It could easily be the case that some biological systems better fit the AIM model, and others better fit the MSNC. We also don't have any kind of systematic study of the computation scaling of the models and methods, as has been done for species tree methods (e.g. Ogilvie et al. 2016). Hejase and Liu published a paper on the scaling of non-Bayesian methods of species network inference (
https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-016-1277-1 ) but AIM and SpeciesNetwork are both Bayesian methods.
- Huw