The first expansion measure is to decrease the selection intensity in sires and dams: more sires and dams are selected as parents for the next generation. It facilitates the inclusion of sires and dams from the whole population and guarantees the presence of the total variation in pedigrees. A high selection intensity works in the opposite direction: it may easily lead to a limited number of selected parents not representing the total variation in pedigrees. Especially a limited number of selected sires, as is often the case in less controlled breeding programs (horses and dogs), increases the future relatedness in the population and leads to future matings between offspring of such sires resulting in inbreeding. Thus the use of more sires and dams has a favourable effect on the average additive genetic relationship, but it should be realized that it gives less genetic improvement.
The second expansion measure is to import in a native population animals from the same breed living in other countries. In foreign populations of the same breed you may find animals with a pedigree containing ancestors not or less present in the pedigrees of the native animals. Thanks to the development of reproduction techniques it is possible to import semen or embryos of foreign animals and to produce offspring in the native population. Thanks to these foreign pedigrees the average additive genetic relationship in the native population decreases. This method can sometimes be used in dogs and horses, but when deep pedigrees are available, often the same early ancestors pop up. Often the breed is composed out of a limited number of ancestors and their offspring is spread over countries.
The third expansion is to cross a limited number of selected parents with selected parents from another foreign breed. In most situations it is most convenient to buy semen from a limited number of selected sires of the foreign breed and to inseminate a selected number of dams of your breed with this semen. The choice of the foreign breed is crucial: when the difference in conformation and size, in adaptive traits and in breeding goal traits is large, it will take many generations to obtain acceptable offspring and it will be difficult to get support from individual breeders for crossbreeding. In a lot of species and breeds “breed purity” is a real issue to account for and the breeding standard should not be threatened.
Why are all these three measures increasing the effective population size? All three result in more variation in ancestors in the pedigree of the selected animals and therefore to less constrained inbreeding in their progeny. Introgression of animals from another breed is very effective in this respect. Then, sires and dams are mated with no common ancestors in their pedigrees resulting in a sharp decrease in the average additive relationship and in an inbreeding coefficient of zero in the F1 animals.