Foundation stock

Foundation bloodstock or foundation stock refers to animals that are the progenitors, or foundation, of a new breed (or crossbreed or hybrid), or of a given bloodline within such. Although usually applied to individual animals, a group of animals may be referred to collectively as foundation bloodstock when one distinct population (such as breed or a breed group) provides part of the underlying genetic base for a new distinct population. 
The term is particularly common in older breeds for which a written breed registry was not created until after the breed phenotype was well established. However, many modern breeds can be traced to specific, named foundation animals.
The terms for foundation parents differ by sex, most commonly foundation sire for the father, and foundation dam for the mother. Depending upon the species in question, more specialized terms may be used, such as "foundation mare" for female horses, "foundation queen" for female cats, or "foundation bitch" for female dogs.
The first generation progeny of foundation stock of a hybrid are referred to as F1 hybrid animals, the second generation as F2, and so forth, usually through F4.
Dogs.
In dog breeding, a "foundation sire" is a male progenitor of a bloodline, while the corresponding term for the female is "foundation dam" or "foundation bitch". 
The American Kennel Club operates a breed registry for over 60 nascent and experimental breeds, called the Foundation Stock Service Program (FSS), through which breeders can seek to establish full AKC recognition of their new breeds.
Horses.
In horse breeding, the terms foundation sire and foundation mare or dam refer to the earliest progenitors of a breed. There are usually few foundation sires, but several mares, though in many cases, foundation mares are not always identified in old pedigree records, though in Thoroughbred breeding, pedigrees are traced to the tail-female line. In most cases, breeds that require that all members trace to specific foundation stock have a closed stud book and do not allow crossbreeding to other animals. The Thoroughbred, Andalusian and Arabian are examples of breeds with a closed stud book.
Some breeds, such as the Morgan horse, have a single named foundation sire, while others, such as the Lipizzan, may have several. In some cases, particularly with older horse breeds, some or all foundation sires may be unknown. However, in breeds with a well-documented breed registry, all or nearly all foundation animals may be identified. For example, there are three major foundation sires of the Thoroughbred, and another 24 or 25 minor foundation sires, along with 74 foundation mares. An example of a foundation bloodstock pedigree line within a breed are the Crabbet lines from the Crabbet Arabian Stud farm in England. These animals were bred by the same program for 92 years, were exported worldwide, and had a substantial impact on the breed. Some Arabian breeders today specialize in horses descended only from this breeding program. Similarly, in the Standardbred, the Clay Trotting Horses constitute a distinct foundation line within that breed.
An example of a breed formed by foundation stock from other breeds, but not necessarily all from named individual animals, is the Hackney horse, with bloodlines contributed from Thoroughbred and Norfolk Trotter. In other cases, where a breed or landrace is older than any written records, the foundation bloodstock is sometimes described by myths or legends, such as the mythical horses of Mohammad, known as "Al Khamsa" ('The Five'), said to be the foundation mares of the Arabian horse breed. 
Some breeds with an established phenotype and named foundation stock may still permit outside bloodlines to contribute to the genetic base of the breed; these thus have at least partially open stud books. An example of a partially open stud book is that of the American Quarter Horse, which still allows limited registration of animals with one Quarter Horse parent and one Thoroughbred parent. Newer breeds, such as many of the warmblood breeds, may have mostly open stud books, where horses that are registered may be of a variety of bloodlines, but must first pass a rigorous studbook selection process. 
The word "foundation" is also sometimes applied, in a different context, to horses of a phenotype that resembles that of the original foundation stock, particularly when the modern look of the breed has diverged from the original stock. The word may also refer to animals tracing only to a select number of the oldest foundation bloodlines, particularly when newer breeding has been added that changed the original phenotype.