Evolutionary potential: a mathematical hypothesis of mouse hemoglobin beta chain evolution.

This paper examines the possibility that the linkage arrangements and regulatory properties of genes may be influenced by selection. A mathematical hypothesis is developed in order to show how selective properties of hemoglobin beta chains could have influenced the linkage and regulation of their structural genes. The hypothesis is applied to the case of mouse hemoglobin beta chains. In most mice, closely-linked pairs of loci (doublets) code for two structurally divergent beta chains in unequal amounts. Some mouse strains have singlet alleles, however, coding for another beta chain variant. With the mathematical hypothesis, one can show that selectively determined "evolutionary potentials" may have favored changes in proportions of major and minor chains produced by a doublet allele. In the extreme case, zero production of the minor chain may give a selective advantage, leading to a singlet; conversely, selection may favor linking another gene to the singlet locus to give a doublet. A specific prediction of the model is the stable maintenance under certain conditions of multiple alleles at regulatory loci. The concept of evolutionary potential thus suggests that selection could have influenced the evolution of genotypic fitnesses, in addition to causing changes in gene frequencies as in standard population genetics models