What I was tought in my animal classes was "Father to daughter, Mother to son, But brother and sister should never be done". However, sometimes a brother sister doesn't do any harm from what I ha :shockedve seen.
Actually, that is all in breeding and really should not be done too often. Line breeding is the way to perfect the things that you want in your line. (thus called line breeding) 1/2 brother to 1/2 sister is also OK to a point, and only if they do not share the same faults. But, if you should have a 1/2 brother who has a good hip, nice body pretty head, but perhaps needs more neck and the 1/2 sister, she may have a long slim neck pretty head, nice body, but needs a better hip, that would be the way to go. In other words, if both have some of the same faults, do not breed them. Typically full brother and sister will focus more on all of the bad points that they and perhaps their parents may have.
When line breeding one can perhaps, focus on the pretty head and long slim neck. For instance, I have a stallion who is out of a Santana daughter (all of my Santana daughters were hand picked for long slim necks and pretty heads), she needed a better hip and was bred to a stallion who had one, but that stallion did not have that pretty a head and had a shorter thicker neck, also I needed more up headedness. The resutling foal, my stallion, has a topline and hip to die for!! And, he has the pretty head of his dam, is up headed, but more his sires shorter thicker neck. So, I bred him to another Santana daughter that I have, focusing on the pretty head and long slim neck. The resulting foal, has a beautiful head, long slim neck and the evel topline and huge hip that her sire has. Succes!! I have bred him back to that mare as well as to another Santana daughter that I have, plus a Windchaser daughter (who is a Santana son), again, more line breeding and focusing on the pretty heads and long slim necks.
Now sometimes it will work and sometimes I will still get the short thicker neck, but I am going in the direction of pretty heads and long slim necks, with a nice square body, lots of leg under them, flat top line, high tail set and huge hip. (They need to look like perfect little full size horses) This filly that I got from the first breeding, she will eventually be bred to Windchaser to cement the pretty heads and long slim neck.
I learned all of this line breeding from over 40 years of breeding dogs. Over 30 with Tibetan Terriers. I have had some of the top dogs in the country in the past and many of the Tibetans winning out there today have my dogs in their pedigrees.
In breeding is really not the way to go, as there are too many faults that will be enphasized. But good line breeding should get you where you want to go (
BUT, ONE MUST KNOW WHAT ONE IS LOOKING AT AS FAR AS CONFORMATION AND WHERE ONE WANTS TO GO BEFORE TRYING LINE BREEDING Just breeding pedigree to pedigree will get you no where.
The only down side is that it takes so many years to do it in horses, where dogs have litters and are ready to breed 2 years after they are born.