Heredity is the result of the random combination of countless genes. In the canine genome there are 39 pairs of chromosomes (for a total of 78 chromosomes) and about 80,000 genes. Chromosomes are strands of DNA that contain a sequence of genes. When chromosomes pair up, their corresponding genes also pair up. The gene pair then determines the expression of a particular trait.
The sire and dam contribute equally to the genetic makeup of their off- spring. Unlike other cells in the body, as the egg and sperm cells are formed, 39 chromosomes are retained and 39 are discarded. So each germ cell contains 39 single chromosomes. It is a matter of chance which chromosomes will be retained and which discarded. When the egg and sperm combine during fertilization, the 39 chromosomes in the egg and 39 in the sperm join up to form 39 pairs in the fertilized embryo.
Because the egg and the sperm each contribute one of two chromosomes to every pair, the possible number of combinations for a given chromosome pair is four. Similarly, the number of gene pair possibilities at any specific site is limited to four. However, if you consider the genetic potential of the breed as a whole, the number of different pair combinations that theoretically could occur at a specific site is twice the number of reproducing individuals in the breed. So the greater the number of reproducing individuals in the breed, the greater the genetic diversity of that breed.
A breed with a large population of unrelated dogs is genetically diverse. This is good, because reproductive efficiency and survival are high in genetically diverse populations. It also means breed clubs with only a few foundation animals, which have not been able to bring in new blood, or breeds in which a few closely related individuals are frequently bred, face problems.