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Muru is a great potato.  I grew it for years and hundreds of seedlings out of it.  Delicious, heavy yielding, and pretty disease resistant.

Unfortunately, I don't have any tubers at the moment.  I'll probably have them again next year.  I can send you in vitro plantlets.  My normal offering is 5 tubes for $30 shipped and it takes six weeks to get them transferred and up to size.  Hit me up by email if you want to do that.

All of the varieties that you mention are available from the USDA except OBxCR.  I doubt that Tom has any of the clones anymore, but he might have seed of some of them.  For OBxCR, you might contact the lead author to find out if they still have it in the lab at MSU. They might be willing to share.  I also have Muru in tissue culture.

The way that I read the OpenMTA, it places no burdens on derivatives and therefore is compatible with OSSI.  That's not an official position, as I am no longer on the board, just an opinion based on understanding how OSSI has decided these things in the past.  As long as a restriction applies only to the source materials and not their progeny, it does not affect OSSI pledging of the progeny.

The other thing that you might need to look out for is material transfer agreements (MTAs or bag tags).  These are very common on materials shared from genebanks and corporate seeds and are often not passed along when the original requester/purchaser shares the material.  Unlike patents or PVP/PBR, MTAs are contracts that can specify anything, including things like limited generations of propagation or no breeding.  Many genebanks pass "public domain" MTAs that specify that either the variety (common) or the variety and its derivatives (rare) must remain in the public domain.  The latter is not compatible with OSSI.

I wish that more genebanks would just start charging a fee for their materials.  That would instantly cut down on the number of non-serious requests and also give them an additional source of funding so that they could staff up as appropriate.

Overall, it has been my experience that most genebanks will work with you if you show them that you are really doing work with the accessions and not just playing.  That is one of the major reasons why I document the accessions that I have requested.  It doesn't have to be anything fancy.  I think something as simple as a thread on this board where you describe your use of genebank accessions and report your results would be sufficient to get access much of the time.  The main hurdle is usually getting your first order accepted so that you have something to report on, but there ought to be enough commercially available varieties of most crops to get some experience, show some results, and then be able to credibly describe how access to the genebank would benefit your work.  A good alternative is to find someone in the community who already has access and ask them to make a request for you.  That is something that we could easily facilitate on this board.  We could have a sub where people can post requests and hopefully match up with someone who has access.  We could also potentially find a volunteer each year willing to make a mass request for the forum and then distribute the materials, which would reduce workload for the genebank.

I think the best approach would be to find a way to work with what already exists.  In the USA, I really think that the NPGS is already the genebank that we need.  It is public.  It is generally friendly to independent breeders as long as the resources aren't too scarce.  If there are other genebanks that refuse to work with independent breeders, maybe the solution is to get people who do have access to request those materials and then donate them to the NPGS so that they can be distributed more widely.  OSSI might be able to help as a bridge, but running a genebank is a big job, requiring facilities and manpower.  It is probably best not to reinvent the wheel.  Also, any genebank will have to be based in a particular regulatory region and it will not be easy to send many seeds between regions.  That means starting multiple genebanks.

I wouldn't expect to get seed in 90 days.  To do that, you would probably need to save intact root balls, let them sprout early indoors, and transplant them out.  If you do that, you might make it before the end of the season.  Of course, if you sow enough seed, you may find some early flowering varieties.  Every once in a while, I see one that flowers a month early.  If you find a few of those and concentrate on them, that might get you where you want to go.

I don't think that you will have any trouble getting plants that produce a useful yield from seed if you are starting them indoors.

The tubers are a possible indication that the plant is a short day tuberizer.  It is common to get lots of small tubers late in the season in short day plants.  Also possible that it just makes small tubers, which is the default in wild potatoes, after all.

As for the color, you likely have a plant that is homozygous recessive for the developer (D) gene.  It has at least one P (purple) allele, but the recessive dddd configuration prevents distribution of anthocyanin to the tubers.  Many white potatoes are quadruplex for d while few colored potatoes are quadruplex for D, and white potatoes are common, so there is usually plenty of pollen floating around ready to turn off the color in your seedlings.

Beet color genetics are pretty straightforward.  It is a two gene system: R (red) and Y (yellow).

R-Y- gives red.
rr-Y- gives yellow.
--yy gives white.

Another way to look at it is that Y is the master color gene.  A dominant Y gives you the possibility for yellow or red, while homozygous y gives no color.  I don't know anything about the specifics of sugar beet or chard genetics, but assuming that they do not have additional genes involved, the sugar beets should all be --yy.  They might well have dominant red alleles that are not expressed, which opens up the possibility that reds will outnumber yellows in the F1.  My guess is that, since chard has been selected for intense stem color, the yellow chards are probably rrYY and the red chards are probably RRYY or RRYy. 

If those assumptions are correct, then your more intense reds are probably RRYy, while the pinks are RrYy, with lower dosage of the color alleles giving less intense color.  There are probably other, lesser, probably quantitative genes involved since there almost always are.  Your yellows would all be rrYy.  You probably don't have any --YY plants because they have all inherited a recessive y from the sugar beets.  In that case, the goal would be to cull everything that lacks intense color because you want to get rid of as many contributors of the recessive y as possible.  You might also want to separate the reds from the yellows, since your population will favor reds in the event that the sugar beets carried a red allele.

I am curious to learn about your taste testing results.  My guess would be that the leaves of the colored varieties will taste more like chard, because it is the betalain pigments that are producing much of the flavor.  If they are non-bitter like sugar beet greens, that points the finger elsewhere.  Are non-colored chards as bitter as the colored varieties?

In general, with a triploid, you are going to get a distribution of gametes ranging from x to 2x, concentrated around 1.5x, but not making up something as predictable as a normal distribution.  Depending on the species and what other sanity checks it performs against gamete configurations, you might find that only the euploid (x and 2x) gametes function in crosses with partners of equal ploidy, that some aneuploid (x+1 to 2x-1) gametes function, depending on which chromosomes they contain, or all of the aneuploid gametes work at least well enough for fertilization.  Whether or not the seedlings produced in aneuploid crosses will be viable is another matter, but they commonly survive in some species.

In species that have an EBN system (I don't know if sorghum does), most aneuploid gametes will be rejected because they don't have the required EBN chromosomes.  In species that lack this check, any extra chromosomes from aneuploids may still be dumped in the remarkable process of genome elimination.  So, either only euploid gametes make it to fertilization or only euploid zygotes come out of fertilization.  In other cases, aneuploids make it all the way through and manage to produce a viable progeny, although it seems that the extra chromosomes most often get lost in the next generation if the plant is fertile.  In short, nature finds a way.

My expectation would be that you would get haploids reliably from triploid x diploid crosses when the 2x gametes produced by the triploid are fully incompatible with the x gametes from the diploid for whatever reason and perhaps the aneuploid gametes are all resolved by genome elimination.

I really love this stuff.  It is neat to see how nature makes rules and then immediately sets about finding ways to break them.

In the paper that you referenced, they produced the hybrids by somatic fusion.  That is a laboratory process in which the cells of the two species are dissolved and then re-fused together.  It is indeed possible to make many wide "crosses" this way, but it doesn't indicate that the species are sexually compatible.  Backcrosses typically dead-end, if they are possible at all, as in this case.  Presumably, genetic engineering will make it possible to fuse genomes less haphazardly and produce fertile progeny in the future, if it hasn't already.

While colchichine is dangerous and difficult to obtain, oryzalin is widely available and is nearly as effective at doubling most species.

I think it might be a lot easier than anyone expects.  I have tasted quite a few potato berries and they are often non-bitter when fully ripe, which means that they must be pretty low in at least the most common glycs.  Short day diploids can produce plants with hundreds of fairly large (1 inch or better) berries.  A plant like that could certainly compete at the cherry tomato size.

The hardest part as an amateur would be getting to a sufficient level of certainty that the plants produce low enough glycs at all levels of maturity and under varying conditions.  That would be a lot easier and more reliable with laboratory TGA testing and that is neither easy to do at an amateur level nor commonly available commercially.

Burbank had an edible fruited potato at one point that he called a "pomato."  He thought that it was a hybrid with S. maglia, but he was probably wrong and it was just a domesticated potato with large berries.

There are also a few wild species with berries that have been eaten traditionally, S. demissum for example.  It seems that a lot of Solanum berries that are toxic when green become non-toxic when ripe.  The only problem is figuring out which is which without repeatedly poisoning yourself.

You may or may not be able to breed with a patented variety, depending on the type of patent and the license offered by the patent holder.  A standard utility patent on a variety forbids breeding with it.  A utility patent on a trait may forbid recreation of that trait even from other genetic sources, although that is not something that we generally consider.  You can breed from a PVP, unless what you breed from it is "essentially derived," which is generally considered to include sports.  And systems outside of US law vary in their details.  Also, varieties are increasingly bag-tagged or come with a separate contract that can specify almost any restriction that is valid under contract law.

So, we have to take some care in evaluating new varieties.  Overall though, the more common problem is that people submit varieties that don't involve a clear case of breeding.  For example, growing a variety for multiple generations for local adaptation without ever intentionally crossing it.  When there was an intentional cross and the phenotypic change is evident, it is a lot easier to make the case for breeding than when the phenotypic change is small and likely within the normal range of expression for a given variety.

Increasingly, people are breeding from OSSI pledged varieties, which makes all the progeny automatically OSSI pledged.  That may be the bazaar that you are looking for, Nicollas.

You can declare your varieties open source without pledging; they just won't be OSSI open source.  The OSSI requires official acceptance of varieties in order to ensure that they are defensible.  We take a breeding history, determine that real breeding has been done and that there were not patented or protected varieties in the background of the variety, and document it on the website.  It is a higher standard than simply public domain or open source.  Without review, we would have a big mess of undefensible varieties and, if OSSI varieties were widely regarded as indefensible, then there would be nothing to stop people from using them in patented/protected breeding work.

I am a member of the variety revew committee and would be happy to help anyone get their variety pledged, but it is best to email me at bill@cultivariable.com.