Enzyme Kinetics, Substitutable Resources and Competition: From Biochemistry to Frequency-Dependent Selection in lac

Trade-offs in catalytic efficiency at the lac permease of Escherichia coli produce alleles with different substrate specializations that are selectively favored on different galactosides. We show that differential resource utilization during competition for mixtures of galactosides produces frequency-dependent selection at lac. However, the polymorphism is protected only in a narrow range of galactoside ratios despite intense selection on the pure galactosides. Hence, stabilizing frequency-dependent selection protecting natural allozyme polymorphisms through differential resource utilization will be sporadic and ephemeral in randomly changing environments. A comparison of predictions, based on first principles, with experimental outcomes reveals an additional, unanticipated source of weak selection.