In the ideal population inbreeding is at a very low level, mutations with adverse effects do not pop up and the random loss of alleles with a low frequency does not happen. Therefore the ideal population is large and many males and females are used for breeding. This decreases the forced mating of related animals, carriers of rare alleles produce indeed progeny and carriers of mutation with adverse effects have not be used to produce progeny.
The ideal population is large: scientific literature pleads for the use of more than 100 animals as parents for the next generation. This facilitates natural selection to cull mutations with adverse effects, it avoids the random loss of rare alleles and it maintains a large genetic variation in the population.
In addition to the size of the population, the structure of the population contributes to the ideal population. The structure depends among others of the contribution of the parents to the number of offspring. When this contribution is proportional (evenly spread) then the average genetic relationship does not increase more than necessary. When a few sires dominate as parent of offspring then the relationship among animals increases sharply in the next generations and consequently inbreeding will increase sharply. See also the explanation of genetic contributions in the chapter “mating”.
The number sires and dams and the variation in the number of their offspring determine the genetic composition of the next generation of their offspring. The variation in the number of their offspring is of great importance. In well controlled breeding programs it is tried to keep this variance as small as possible: it is tried to get an equal number of progeny selected individual. But in a lot of species dams give birth to multiple offspring and then variation in litter size is always present. In less controlled breeding programs a lot of variation is often found in the number of offspring per sire. Popularity of sires is responsible for that: show champions are widely and often unlimitedly used as sires. The number of animals that contribute in different extend to the next generation is crucial in the management of a population when you aim at reducing the rate of inbreeding.