To discuss the utilisation of heterosis in plant breeding it is necessary to consider its genetic basis . In cross fertilized plants in which the phenomenon of heterosis is very important, such as maize, it appears that a great part can be explained by the mutation load . However in both autogamous or allogamous plants it is difficult to exclude a role of `marginal' overdominance which could justify hybrid variety production .
To know in a relatively short time whether it will be better to develop lines or hybrids it is necessary to know the parameters (mean and variance) of the distribution of all varieties of a given type which can be derived from the breeding population . A numerical application allows the determination of the situations where the best single crosses will be better than the best lines . With some approximate values of the necessary parameters, the case of grain yield in maize and in wheat is briefly discussed .
To develop lines or hybrids, a general strategy is given . Its main axis is population improvement which has to be adapted to the type of varieties to develop . It is shown that according to the situation the type of varieties to develop can change with time : single crosses can be more justified at the beginning and lines can be justified later if all heterosis were fixable . To develop hybrids the best scheme is reciprocal recurrent selection with half-sib or full-sib progenies followed by pedigree reciprocal selection initiated by full-sib progeny tests . With this strategy there is no problem of the prediction of hybrid performances . However it seems possible to develop some predictors of heterosis or of specific combining ability between two lines using some criteria of genetic distances . Preliminary results with distances computed from the behaviour of lines in a two-tester top cross design appears very stimulating .