By Sekhmet
Genetics is all about probability, at its core. Here in PI we have 3 loci, or "locations" for genes. Hair, legs, and body. Each pony can get a maximum of two genes in each slot. One from the mother, and one from the father. This means it is impossible for a pony to have all three hair or leg s-genes. They only inherit one gene for each location from the mother, and one gene from each location from the father. There are only two "slots" available for each location, as, again, you get one from the mother, and one from the father. This means it is absolutely impossible for a pony to "carry" all three leg or hair genes. (sorry for the repetition, but it seems to be a point of confusion).
When it comes to if a pony carries a gene or not, here's where the probability comes in. Each pony has two genes for each slot, one from the mother and one from the father. When it has a foal, only one of those genes gets passed on, so there's a 50% chance that one gene will get passed, and a 50% chance that the other will get passed. When you're talking about, say, a visible faded, then you know for a fact that that pony has passed on a faded gene, because you need 2 faded genes to have a visibly faded pony.
For a carrier, it gets more involved. They have one special gene, and one gene that is more dominant than the special gene ("Normal", or a more dominant s-gene, like how socks is dominant over faded, etc). When that pony breeds it will either pass on the s-gene, or the other more dominant gene.
For simplicity's sake, let's make an example where a pony had a faded father, and a non s-gene'd mother. Since the father was a fade, and the mother had no s-genes at all, the baby is a fade carrier.
When the fade carrier is bred, it will either pass on the fade gene (gotten from the father), or the normal gene (gotten from the mother.). There is a 50% chance the fade will be passed, and a 50% chance that the normal will be passed. Let's hypothetically breed this pony to a few different ponies.
Fade carrier X visible fade
There is a 50% chance (1/2) that our fade carrier will pass on fade. There is also a 50% (1/2) that it will pass on a "normal" gene.
There is a 100% chance (1/1) that the visible fade will pass on fade.
So, doing the probabilities:
Chance that the baby will be fade:
1/2 (Chance that the carrier will pass on fade) * 1/1 (chance that visible fade will pass on fade) = 1/2 or 50% chance that the foal will be visibly faded.
Chance that the baby will be a fade carrier:
1/2 (Chance that the carrier will pass on "normal") * 1/1 (chance that visible fade will pass on fade) = 1/2 or 50% that the foal will be a fade carrier.
Fade carrier X Fade carrier
There is a 50% chance (1/2) that our fade carrier will pass on fade. There is also a 50% (1/2) that it will pass on a "normal" gene. The same goes for the other fade carrier. I will label them 1 and 2 to try and keep them straight.
Chance the baby will be visibly faded:
50% (1/2) chance that Fade carrier 1 will pass on fade. * 50% (1/2) chance that Fade carrier 2 will pass on fade = 1/4 or 25% that the foal will be visibly faded.
Chance that the baby will be a fade carrier
50% (1/2) chance that Fade carrier 1 will pass on fade * 50% (1/2) chance that Fade carrier 2 will pass on "normal" = 1/4 or 25% chance that the foal will be a fade carrier
ALSO
50% (1/2 chance that Fade carrier 1 will pass on "normal" * 50% (1/2) chance that Fade carrier 2 will pass on fade = 1/4 or 25% chance that the foal will be a fade carrier.
THEREFORE:
1/4 + 1/4 = 1/2 or 50% chance that the foal will be a fade carrier.
Chance that the foal will carry nothing at all:
50% (1/2) chance that Fade carrier 1 will pass on "nothing" * 50% (1/2) chance that Fade carrier 2 will pass on "nothing" = 1/4 or 25% chance that the foal will carry absolutely no s-genes at all.
This is also why it is very possible, that a pony does not carry all the s-genes in its pedigree. You can also see that they can't carry all of them, if there are say… stockings and fade in the same pedigree, but the pony itself isn't s-gened at all. If it carried all the s-genes in the pedigree, then it would have both stockings, and faded. And since you can have only two genes in each location, and stockings are more dominant than faded, the pony would show stockings. Since it does not, then it cannot carry both.
Now, we've covered a basic s-gene being carried along with a "normal" gene. As PI has multiple genes for each location, there is an order to them, and how dominant they are. This order is:
For hair
Tips is the most recessive. You have to have two tips genes to make a tips pony
Rainbow is the next most recessive. You have to have either two rainbow genes, or a tips and rainbow gene to make a rainbow. This is because rainbow is dominant over tips. (This is called a "visible rainbow, carries tips")
Stripe is next. To have a stripe, you have to have two stripe genes. A stripe and a rainbow, or a stripe and a tips. (these are called "visible stripe, carries rainbow" or "visible stripe, carries tips.")
Normal is dominant over all others. If there is a single "normal" gene, then the pony will not be visible for any s-genes.
For body
Zig zag is the most recessive gene. To have zig zag, you have to have two zig zag genes.
Paint is the next most recessive. To have paint, you have to have two paint genes, or a paint and a zig zag gene. (this is called "visible paint, carries zig zag")
For legs
Faded is the most recessive gene. You have to have two fade genes for a pony to be faded.
Stockings is the next most recessive. You have to have either two stocking genes, or a stocking gene and a faded gene. (This would be called a "visible stocking, carries fade")
Socks is next. You have to have two socks genes. Or you can have a sock and a stocking, or a sock and a faded. (These would be "visible socks, carries stockings" or "visible socks, carries faded.")
Yes, genes can be passed through a pedigree, but the probability becomes less and less with each generation, as the chance that the gene gets passed on is only 50% per generation. So if you multiply it out, the chance gets cut in half every generation. This does not mean that a pony with rainbow on the 2nd page of the pedigree does not carry rainbow, but that it is highly unlikely that it does.
Example:
Say you have a pony whose great grandmother was zig zag. This means she definitely passed on the zig zag to her daughter (your pony's grandmother.) Your pony's grandmother is definitely a zig zag carrier. Now, she only has a 50% chance of passing that zig zag on. She has a 50% chance of passing on the "normal" gene. So there's only a 50% chance that her daughter (your pony's mother) is a zig zag carrier. Now.. your pony's mother has a 50% chance of passing on the zig zag, if she even has it. She also has a 50% chance of passing on the "normal" gene.
Multiplying out the probabilities:
50% (1/2) chance that the grandmother passed the zig zag gene on to the mother * 50% (1/2) chance that the mother passed on the gene to your pony = 1/4 or 25% chance that your pony is a zig zag carrier.
You can see how each generation the probability gets halved. If your pony had a foal, then there would be a 50% chance that she would pass on the zig zag gene if she even had it, and so the percentage would get cut in half, again, to 12.5%
It's all about probability and understanding that a pony can only have two genes in each slot, and they only pass on one of those genes to their foal.
