Can genomic data alone tell us whether speciation happened with gene flow?

The allopatric model, which requires a period of geographical isolation for speciation to complete, has been the standard model in the modern era. Recently, "speciation with gene flow" has been widely discussed in relation to the model of "strict allopatry" and the level of DNA divergence across genomic regions. We wish to caution that genomic data by themselves may only permit the rejection of the simplest form of allopatry. Even a slightly more complex and realistic model that starts with subdivided populations would be impossible to reject by the genomic data alone. To resolve this central issue of speciation, other forms of observations such as the sequencing of reproductive isolation genes or the identification of geographical barrier(s) will be necessary.