For an example lets cross two pure breeds,
a Rat Terrier to a Manchester Terrier.
The first mating would be:
100% Rat Terrier crossed to 100% Manchester Terrier.
This produces a litter of pups that are 50% Rat Terrier and 50% Manchester called the F1 cross.
These pups are now carrying all the traits of a Manchester and a Rat Terrier. All these puppies would have hybrid vigor. But now they are crossbreeds and no longer pure bred dogs. In order to consider them pure bred, the cross back must continue for 6-7 generations before either could be considered a pure bred Manchester Terrier or a pure bred Rat Terrier.
Next the F1 cross is bred to a 100% Rat Terrier which produces 25% Manchester and 75% Rat Terrier puppies. This litter of pups are called the F2 cross. They still carry a significant percentage of Manchester blood at this point.
You then breed the F2 cross once again to a 100% Rat Terrier, the litter of pups now carry 12.5% Manchester Terrier and 87.5% Rat Terrier blood and are called the F3 cross.
These F3 puppies are again crossed to a 100% Rat Terrier and what is produced is the F4 cross with the puppies now carrying 6.25% Manchester blood and 93.75% Rat Terrier blood.
A percentage of 6.25 left might be said as insignificant cross blood but not so when it comes to recessive genes or hairless genes. It can be understood like this, lets take the chocolate gene for example. Suppose the first Rat Terrier cross was a chocolate dog bred to the Manchester Terrier. The resultant offspring would be 50% Rat Terrier and 50% Manchester and all the puppies would carry the chocolate gene but no pups would visibly show the trait. These are the F1 pups. These F1 pups are crossed to a Rat Terrier. The percentage of Manchester goes down and 50% of the pups carry the chocolate gene but still nobody knows which ones. In the next F3 cross the chocolate gene still will be carried down to 50% of the pups but again no one will be able to identify it. By the F4 cross the gene would continue be carried on but now completely unknown to anyone. Four litters have now been produced and no one is aware that they carry the chocolate gene. This calculation is correct provided none of the dogs that the (F) generations were crossed to carried the chocolate gene recessively. We are doing this calculation specifically this way in order to make a very important point.
Now suppose that the chocolate gene was a hairless gene. The hairless gene would get lost just as fast breeding back strictly to coated dogs and it would not be seen but indeed it would be in the gene pool. It would be glorious to say that all the first generations produced with a hairless would strictly be used for an outcross program or that all the pups would be spayed or neutered so as not to deposit them in a breeding gene pool. We all know that this won't happen. They will leak into the population.
The spreading of recessive genes begins with the stud dog who breeds to hundreds of females. It may be fine and well that he is a champion but should he possess a detrimental recessive gene it is now passed to many many offspring that will come together down the line and be bred together. By then it is already a serious problem and will be virtually impossible to erase out of the breed population.
Hybrid? What is the point of cross breeding a Rat Terrier with a Manchester or Toy Fox or any other breed? What is the purpose if the Rat Terrier is a pure breed? Not only are there enough Rat Terriers out there, plenty of them are in different sizes to breed up or down with and keep with their own type. The breed will not get stronger by crossing a Toy Fox with a Rat Terrier to size down. Oh contraire…… the specific hereditary problems and all of the particular breed's recessives come along with the package too. Toy Foxes and Manchester's have known problems within their breed. They will be carried over regardless of the care that some take because others won't.
Lastly it takes 6-7 generations of strict linebreeding to produce dogs that are pure of blood. Not many get that far because breeders are unwilling to do the necessary culling in the process. Culling means disposing of, not placing. In the meantime of all these 4 generation crosses you have not only produced many offspring that are hybrids but more than likely added detrimental traits into the breed.
Once you create a hybrid you now have a new breed. The only purpose hybridization serves is to lock in a particular trait. But you must linebreed, not cross back to a 100% pure breed for at least 5-6 generations to completely remove all other traits.
The effects of hybridization can clearly be seen in the Toy size of the Rat Terrier. Proper care was not taken to cross back to a pure bred or linebreed back in order to maintain the Rat Terrier head vs the Chihuahua head. Along with this change comes the lose of other natural desirable traits such as hunting ability and temperament. These dogs are now spread through the general Rat Terrier population.
The Rat Terrier has developed into a breed far superior to its predecessors. To reintroduce the predecessor's only serves to make the Rat Terrier more like that particular breed and takes out what has long been sought after and developed as the loving and wonderful traits of the Rat Terrier.