What methods are used to determine ploidy aside from educated guesses based on parentage and or fertility? Are they methods that can be applied at the hobbyist level?
You can purchase a used microscope and look at pollen size, see:
The idea of using pollen diameter to estimate ploidy of the parent plant and more importantly the ploidy of the pollen grain is a great option. Henry has done great work studying and recommending affordable digital imaging equipment to hook up to microscopes for us. One can purchase affordable, relatively simple microscopes too.
The best ploidy documentation is to actually visually see and count chromosomes within cells. To do so we need to have cells at the right stage of development preparing for cell division when the chromosome are condensing and can individually be seen. This isn’t very hard, but does take skill collecting root tips or shoot tips in active growth and preparing them with relatively simple chemicals (acid, alcohol, and a chromosome darkening stain like acetocarmine).
There is another method to estimate chromosome number and that is by a technique called flow cytometry. There is a dye that causes DNA to fluoresce. The general amount of DNA per cell generally corresponds to a specific ploidy level. This isn’t always 100% accurate since there can be a lot of variation for DNA content based on species and other factors. For instance, it is common for interspecific crosses in an effort to stabilize to have more transposon activity and accumulate more DNA within chromosomes. This has been documented in other species and probably is possible in roses.
Anyways, looking at pollen diameter is a great tool for the breeder. It gives us an estimate of the percent that is empty and obviously aborted as well. We can also do pollen germination assays in sugar/boric acid solution to look at rate of grains that actually germinate and estimate fertility that way too which is even more accurate.
P.S. Unfortunately it looks like in Modern Roses 12 rose cultivars that have been documented for ploidy and that ploidy has been listed in Modern Roses 11 has been ommitted. It would have been nice if ploidy had been retained for everything where it has been documented and the new information included on ploidy for easy access.