The Malthusian parameter in microbial ecology and evolution: An optimal control treatment

There is a consensus among evolutionary microbiologists that the (quasi-)instantaneous specific rate of proliferation is a good measure for fitness. On the other hand, it is well known in evolutionary theory that the appropriate fitness measure is generally dependent on ecotype. We consider two ecotypes: one in which the instantaneous specific growth rate, discounted into the future, is an appropriate measure of fitness, and one in which fitness is measured as “ burst fitness” under intermittently favorable conditions. Our analysis is based on a standard model of microbial growth, the Droop Quota model, which we have extended with a variable balance between assimilation and proliferation, since this balance constitutes an important regulatory choice. We evaluate optimal allocation regimes and contrast these to control regimes based on maximization of the instantaneous specific growth rate.