So if someone is only breeding for color in every other litter it would result in a litter with a good mix of agouti and color correct? Is it safe to assume that for a litter to be all color degu both parents must be that color?
Well that depends on whether the colour is recessive or dominant to agouti. For example with blue then yes, both parents have to be at least carriers for blue. It's hughly unlikely (although theoretically possible) that carriers would produce an all blue litter since Mendelian inheritance would put the number of blue pups in a litter at around 25%. A further 25% would have two copies of the agouti gene while the remaining 50% would be carriers like their parents in a perfect split. You could also breed a blue to a carrier which would give you an approximate 50/50 split of agouti and blue but all agouti would also be carriers.
Now if the trait is dominant the values are reversed. We wonder with patched if they share some form of co-dominance with the colours or perhaps it is a collective mutation over a number of genes which is why you see some that have loads of patching and some which only have a small spot.
If they consistently breed litters that are all the same colour then they are most likely breeding the same colours to each other. If the litter is a one off and all their other litters seem to follow inheritance patterns then it might have been a freak occurrence although I'd still be asking questions about the parents to see what they say.
Degus 221b Baker Street - Sherlock & Watson (Gotcha 26/02/2017)
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Yes, if both parents only CARRY the color gene, then, if it is a single, simple, gene inheritance, only one out of every four babies should show the color, based on the calculated odds. However, the odds are just that--a calculated prediction. If you do a bunch of coin tosses, you should get equal numbers of heads and tails, half heads, half tails. But, it IS possible to get more of one side than the other for a bunch of tosses. If you do six tosses, no guarantee of getting 3 heads, 3 tails. You could get 6 tails. If you do six thousand tosses, however, you will get pretty close to 3 thousand heads, 3 thousand tails, those irregularities you can see will even themselves out over a larger number. Same way with genetics. I'm sure we all know of families with all girls, or all boys, or one boy and five girls, when the odds say there should be an even number of each.
To try it out for yourself, you would toss two coins, as the baby gets one gene from each parent. If agouti is dominant (covers up any other genes present) and agouti is heads, then tossing the two coins, heads-heads is agouti. Heads-tails and tails-heads will show agouti, but is carrying the other color. Tails-tails is the only case where the color shows up. So you have three possibilities where you get agouti, and only one where you get color. This is a simple genetic case, where one gene determines the color of the animal, and one color, here agouti, is dominant to the other color, which is recessive (only shows up when no other color genes are present).
Now, many traits are not so simple. It takes two or three or more genes in combination to make the different traits show up. So, for two genes working together, you are tossing four coins, two from dad, two from mom. If it is simple inheritance, and heads is dominant, let's say that's agouti, any combination with a Heads means the animal shows agouti, whether you toss HHHH, HHtt, Httt, if H is present, you get agouti, and ONLY tttt shows the color. In this case, only 1 out of every 16 possible combos gives you the color.
But....if the genes share showing up, or certain mixes give other colors, then the numbers get much more interesting. You can have cases where only HHHH shows the first color, HHHt shows up as another or a variation, HtHt is another, HHtt is another.....get the idea?
Patched is probably something like the above case, where it is more than one gene interacting, so the more you breed patched together, the genes add up and increase the amount of white present. Seems to work that way in finches, tho some of the loudest voices in the finch breeding community here have very little understanding of genetics and just insist it's "split for" (carrying, correctly termed heterozygous) pied (bird people call it pied, degu people call it patched) or all pied, even tho it can vary from a single spot of white to a mostly white bird, and the more you breed together pied birds, the whiter the offspring come out. Clearly, it is a bunch of genes that add up the amount of whiteness they create. Would bet degus are the same.
Another thing to remember is that different colors and variations like pied may not all be coming from the same gene. One gene may give agouti, with other variations of it changing the color, a completely separate gene location may be giving the patched appearance, a separate gene that is saying "show color/don't show color". Different colors could also come from different gene locations, one says "agouti/other color" and a separate one says "lighten the color/darken the color" which alters the agouti or other color making it look like a new color, it could very well be that way with black, for example. Someone would have to study the inheritance patterns, and study the hairs themselves, are they just a new color, black, or are they still agouti with the multiple colors per hair, only they all got so dark they just look black? (Think of a black leopard, if you look closely, it still has black spots in its black coat.)
Now, to answer your question simply, IF the color they are breeding is recessive to agouti, meaning agouti shows up if genes for it are present, and the litters are always entirely the new color, then yes, they are breeding color to color.
If they bred color to agouti to create agouti-carriers of the color, then bred the agouti-carriers, they would get some color, and some agouti, usually more agouti than color, but sometimes you beat the odds and get more color.
If the color is dominant, so it always shows up, and they bred color to agouti, they would get all color, but carrying agouti, so next generation agouti could show up again.
However, IF color is recessive, and they breed color to agouti, getting agouti-carriers, then they breed those agouti-carriers to each other, from the same parents, then are not outbreeding, they are inbreeding because related animals are being bred together, and while they may have introduced some genetic variation with the one cross to agouti, they're still inbreeding and it's not good.
The size of an individual litter isn't big enough to show up the 25% - 50% - 25% average. So it's not possible to say categorically what the status of the parents is. Unless they breed the same pair many times, you wouldn't even know if a particularly parent carry's both copies of a particular gene or only one - especially as we don't know for sure which colours and patterns are dominant or recessive. And you aren't likely to know the gene status of the parents of the parents. And we don't know how many genes are involved.
Also bear in mind in your example you can get a different coloured degu from two parents that are agouti if the parents are carriers for the colour (i.e. have one copy of the gene which is agouti and one in the colour).