Compensatory Drift and the Evolutionary Dynamics of Dosage-Sensitive Duplicate Genes

Dosage-balance selection preserves functionally redundant duplicates (paralogs) at the optimum for their combined expression. Here we present a model of the dynamics of duplicate genes coevolving under dosage-balance selection. We call this the compensatory drift model. Results show that even when strong dosage-balance selection constrains total expression to the optimum, expression of each duplicate can diverge by drift from its original level. The rate of divergence slows as the strength of stabilizing selection, the size of the mutation effect, and/or the size of the population increases. We show that dosage-balance selection impedes neofunctionalization early after duplication but can later facilitate it. We fit this model to data from sodium channel duplicates in 10 families of teleost fish; these include two convergent lineages of electric fish in which one of the duplicates neofunctionalized. Using the model, we estimated the strength of dosage-balance selection for these genes. The results indicate that functionally redundant paralogs still may undergo radical functional changes after a prolonged period of compensatory drift.