Bicolor refers to an Australian Shepherd that only has two colors. Red or Black with white, and no tan points. Tan points are what is called Agouti expression. Tan points are recessive to the dominant black gene. Dominant black on the K Locus is what causes bicolor. In this case, 'Dominant Black' is just referring to the absence of tan points. The dog's actual color is dependent on the B and E Locus. Reference the photo below to see all the accepted colors of the breed standard.
​KB/KB-The dog has two copies of dominant black, no tan point is expressed and all offspring will not have tan points
KB/Ky- The dog does not express tan point and appears bicolor. It carries one copy of dominant black, and one copy of Agouti. 50% of offspring will not have tan points and 50% will have tan points
Ky/Ky- The dog carries two copies of Agouti and will have tan points. Offspring will have tan points as long as both parents are Ky/Ky. This is a recessive gene and therefore is only achievable by putting dogs together that have two copies of it.

Yellow occurs in the Australian Shepherd breed naturally. This color originates from the formation of the breed, some of the breeds used to create the Aussie came in this color, such as the Border Collie. This color is more commonly seen in Golden Retrievers or Labrador Retrievers. Yellow is associated with the E Locus, and it takes two carriers to produce, much like the brown color on the B locus, often referred to as "red" in the breed. A big difference, however, between yellow and brown, is that yellow is a masking color. Masking refers to the color the dog appears visually, while the true color of the dog hides "underneath". In our case with Aussies, this means the dog could be a black tri genetically and appear yellow physically. Yellow also masks Merle, so you will not see a yellow merle dog. Depending on the dog's true color "underneath" the yellow, the dog can have a black nose if it is black based, or a brown nose if it is brown(red) based. 
Yellow is not an accepted color in the breed standard. It was not a color that made the final cut when that decision was made for the breed. It is considered a disqualifying faulty color in the show ring, and should not be used to breed. There are many colors/patterns that didn't make the cut, this is just one of them. To reiterate, this color does occasionally occur in the breed-often accidentally since this is a color that breeders, including ourselves, do not breed for. 
We do want to heavily caution against seeking out a yellow Aussie intentionally. Any breeder who breeds for them on purpose, is often disregarding the breed standard and the very important health screenings required to breed as well. Reputable breeders do what they can to avoid this from happening, as it's not desirable to produce them.
All of this being said, these dogs are very much still purebred Australian Shepherds and have much to offer you as a companion and pet if your ethical and responsible breeder happens to have it occur in one of their litters. They may not be desirable in the show ring, but you can love one just the same in your home.

Before we get into all the details about fun inherited traits, we need to understand how things are inherited. Let's talk about what each term is and what it means first.
DNA- This is the double helix you learned about in your science classes in school. If you aren't familiar, a double helix is much like a ladder that has been twisted over and over. Each "rung" on this ladder is made of a pair of molecules. We call this a base pair. These molecules are made up of alternating sugar and phosphate groups. Each molecule is one of four different bases: Adenine(A), Cytosine(C), Guanine(G), and Thymine(T). Adenine always bonds with Thymine and Cytosine always bonds with Guanine, hence why they are referred to as the base pairs. These pairs are sequenced in an order on the DNA strand, making a Gene per each segment.

Chromosome- This ladder of DNA is spun like a string on a spool. The "spool" is a protein called Histone. A full histone spool holds about 150 base pairs of DNA strand on it, and each segment of "full spool" is called a nucleosome. The nucleosomes bind together to create Chromatin fiber. The Chromatin fiber weaves together and this is what makes up a chromosome. In dogs, there are 39 different pairs of Chromosomes. So 39 from the mother, and 39 from the father. 
These particular details only matter when we are talking about what makes up the chromosomes. Now we'll be talking more about genes ON the chromosomes!

Allele- We read the Locus to find the Allele variation. For example, when talking Aussies, we look at the B Locus to see what color the dog is. They can either be black or brown(though brown is often referred to as red). Alleles can also work in combination of each other to create different appearances on the dog. Let's say the dog is brown on the B Locus, and merle on the M Locus. So this is how we get Brown(red) Merle dogs. Everything we can read about the Alleles of the dog is what traits appear. 

Okay, now that we've covered what these terms mean, now we can talk about inheritance! Inheritance is seemingly random, but it's actually a very calculated formula of likelihood. Remember how each dog has two sets of genes, one from each parent? Well each parent has their own set of genes, but the mother will only pass down one, and the father will only pass down one. So of the four genes between the two of them, there is a likelihood of inheritance. 
Let's just look at the B Locus for a second. Black is dominant and brown is recessive. We write black as a capital B, and brown as a lower case b. Since every dog has two copies of the gene, they can have two of the same OR two different alleles. So when a dog has a dominant allele, that is what will always be expressed visually. They can carry a recessive allele though and pass it on to their offspring. A dog with two recessive alleles will express the recessive trait.  A black dog with two copies of black is written as BB, while a Black dog that carries brown is written as Bb. A brown dog is written as bb, which is the recessive color. The easiest way to look at the likelihood of inheritance is by putting it in a Punnett square. The photo example below is a fantastic representation of this by UC Davis Genetic Laboratory. See how the two dogs used are both Black dogs, who carry brown.
By crossing these two together the following is possible:
A 25% chance of offspring coming out with two copies of the black gene, BB.
A 50% chance of offspring coming out with one copy of black, and one copy of brown, Bb.
A 25% chance of offspring coming out with two copies of the brown gene, bb.

We use this method to look at what our chances are in the offspring when we breed dogs. Every trait is calculated in this manner. In the Australian Shepherd breed, there are accepted colors/traits and unaccepted colors/traits in the breed standard. Aussies can come in many colors and patterns, but the only dogs that should ever be used for breeding is black and brown in solid or merle.
So now that you understand the nature of inheritance, we can look more at what colors and traits can be inherited in the Australian Shepherd breed!

Genetics are anything and everything that make up your Australian Shepherd. They make up everything that is living, in fact! You, your dog, and even plants have genetic makeup. Selective breeding has been in practice for centuries. The ancient Romans used selective breeding to create better crops, better livestock, and they even selective bred dogs for better hunting, herding and protection. Charles Darwin studied and discussed how selective breeding was successful in producing change over time. It is how we domesticated dogs and other animals, and how we got the traits we desired in them.
Before we had the technology to observe the genetic makeup of things, breeding was done on a trail by error format. Two dogs would be chosen based on their traits, whether that be a physical trait or a personality trait, and the litter would be observed for those traits and if the trait that was desired was replicated, a dog or dogs would be chosen for the next generation of selective breeding. If the breeding wasn't successful in replicating the desired trait, those dogs would not breed the next generation. And so, this is how we began to understand the basics of genetics before we had the genetic labs or testing to rely on.
Flash forward to today, we have the end product of many generations of hard work that created our beloved Australian Shepherd breed. When a breed is purpose bred, a breed standard is created. This is like a rulebook of what the dog should appear like physically, as well as what their personality should be like. So every aspect of your dog that you have today, was carefully thought out and bred for.
I am hoping to shed some light on what those things are, from health, to personality and temperament, to structure, to coat colors and so much more. With each topic, I'll talk about what it is, what it means, the history and the function.