With all the sillyness I've heard on the MU*s about greens clutching, etc.
I asked Anne about it and was told that greens are sterile because they were
Engineered that way, which sparked the following hypothesis.

Golds are recessive. Lets call them g
Greens are dominant. Let's call them G (for now)

This leads to that triple helix gene thing..Ie. THREE strands of DNA.

Obviously, this is a gender related color gene, much like calico cats in nature.
You have females who carry either g or G genes.

You would have

Gold ggg  
Green GGG (Not possible, as the gold cannot give a G for this.)
Green GGg (Possible is brown-gold matings)
Green Ggg (Most common in Bronze-Gold matings)

Now this makes it look like a green could produce a gold if bred, but if G
carries a lethal gene, this prevents them from reproducing when combined with
others carrying that lethal gene. From what I gather, the Ggg can lay eggs
but they are always duds and infertile. The G inhibiting the ability of the
egg to fertilize.

Since greens outnumber all other colors combined, it stands to reason that
the males carry the genes on the X chromosome. All males (At least on Earth)
carry one X. If the color gene is tied to the gender, then perhaps it would be
mapped like this.

Bronze bgG (As the color gene is attached to the gender, b is a recessive.
Otherwise there would be less greens..)
Brown bGG  
Blue bGG  

This shows Bronze carrying the ability to sire all colors, depending on how the chromosomes remix. The egg either keeping two strands and only swapping one or keeping one and swapping two, either way it works out, as only one Y chromosome is possibly swapped, though in Ruth's case, he may be a weird case where he has four chromosomes, like a male calico cat is a XXY (normal male cat would be XY) due to one strand failing to split off like it was supposed to. Male calico cats are sterile though.
This would make Ruth a XXXY, as an extra Y gene would have made him larger and not small and light built as he was.

Ruth bGG XXXY Color effected from extra X gene, producing white in this case.

This allows Bronzes to sire all colors when combined with a golds genes, but browns cannot sire golds as they lack the recessive g gene. A blue could only sire blues and greens though, unless b is an incomplete res gene, so that it only works with other genes present.

Gold ggg XXX  
Bronze bgG XXY The b carried on the Y gene.
Brown bGG XXY The lack of g making it a brown, as browns can't sire gold.
Blue bGG XYX The X chomosome reacting with the Y due to another gene(s) (N/n).
Green GGg XXX  
Green Ggg XXX  

Let call the other gene N or n....

Bronze bgG YXX Nnn or any combo, as the N/n doesn't trigger in the presense
of a g (gold) gene.
Brown bGG YXX NNN or nnn (More rare then a mixxing of N and n.)
Blue bGG XYX Nnn (Mixing N's causing the reaction between the gender
chromosomes with no g present, producing blue.)
Blue bGG XYX NNn

Working this out has given me a headache, but as long as it works, it helps explain how greens can be genetically sterile. F'lar simply thought that firestone was the culprit, since noone had ever seen a fertile egg from a green and it was 2500 turns from the time they were engineered, noone knew by F'lar's time that greens had been genetically engineered, much less the reason why greens were sterile. Note that F'lar thought dragons were 'bred' up from firelizards over time, not created in a lab in a few months.