If the fitness of children is not transfered from the root-parent, it is possible to think about upper and lower bounds on the loss of lineages. To consider the upper and lower bounds of genetic lineage loss, remember that the members of partition are sorted according to their unique fitness values. The lower bound (or the least) number of lineages preserved in the next generation will occur when the children of individuals from have a fitness ordering consistent with their root-parent ordering. Interestingly, this also holds true when the fitness ordering is the complete opposite of the root-parent ordering. In the former case, offspring produced by an application of the operator to their root-parent undergo small fitness value change from the parent. The upper bound (or the most) number of genetic lineages preserved in the next generation from will be when the children are ordered randomly compared to the root-parent ordering in the previous generation.
Admittedly, this caricature of tournament selection is elitist toward the better individuals, which are found in partition . This behaviour is emphasised to illustrate the loss of lineages, and that in a set of runs, those runs with more genetic lineages are probably performing a more parallel type of search.