@FireTigeris
All European-descended domestic geese (same species) have a diploid number of 80, while there is variation in diploid number in different swan species...Shouldn't karyotyping give us a good idea, then, given that the two species do not have the same diploid number?
Also, there is evidence of hybridization between species of different genera, which I believe is the arbitrary level that geese and swans differ. They wouldn't be the first birds to give that a go.
(also regarding phylogenetics and species definition, i have some people you could probably get into a fiery debate with on that! : p )