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Average allele frequency at segregating loci of F2 populations derived from pure line crosses is expected to be p = q = 0.5. From now on, however, we will use as source material genetic broad-based populations with arbitrary allele frequencies. This means that special case of p = q = 0.5 often does not apply. Therefore, p is not equal to q.

The inbred–hybrid concept was created in the public sector with the direct influence of Darwin, Festetics, Mendel, and Vilmorin. East related those biological principles to the more practical plant improvement studies to achieve his goals (Hayes, 1956). The progeny test was defined by Allard (1960) as ‘a test of the value of a genotype based on the performance of its offspring produced in some definite system of mating.’ It was used as early as 1850 by Vilmorin in France, and it proved to be a highly effective procedure for the improvement of sugar content of sugar beets (Beta vulgaris). This method of line selection with progeny testing was known as the ‘Vilmorin method’ or ‘Vilmorin isolation principle’ and was introduced in several plant breeding programs in the latter part of the 19th century. The progeny test in maize was first used in 1896 by Hopkins, starting the well-known program for half-sib recurrent selection of maize oil and protein content (e.g., the ear-to-row half-sib selection procedure).

The degree of relationship between relatives depends on genetic resemblance. They are very important to breeders since they are not only used to estimate the genetic variances of reference plant populations but also used in breeding methods used for selection. All breeding methods deal to some extent with resemblance between relatives.

The scientific basis of maize breeding and selection based on planned experiments started at the end of the 19th century. The first methods (mass selection and ear-to-row selection) were soon abandoned because of their supposed lack of efficiency in improving complex traits, such as grain yield. Some other methods and modifications of the previous ones have been used during the 20th century for improvement of populations, mainly after recurrent selection was recognized as a useful method to increase the frequency of favorable alleles in populations (Jenkins, 1940; Hull, 1945; Comstock et al., 1949; Lonnquist, 1949; Sprague and Brimhall, 1950; Jenkins et al., 1954). Also, improvement of populations was recognized as an imperative to increase the probability of obtaining superior and diverse inbred lines and hybrids.

Choice of germplasm as source of elite inbred lines is the most important decision the breeder takes. No tool or breeding methodology will be successful if a poor choice is made on source populations.