Evolution of microorganism locomotion induced by starvation

The search strategies of many organisms play a fundamental role in their competition to survive in a given environment. In this context, the propulsion systems of microorganisms have evolved during life history, to optimize the suitable use of energy they take from nutrients. Starting from a model for the motion of Brownian objects with internal energy depot, we show that the propulsion system of microorganisms has an optimal regimen while searching for new sources of food. Bacteria with a too low or too high energy expenditure in propulsion, moving in a nutrient-depleted environment, do not reach remote distances. In this sense, the mean square displacement has a maximum for a finite value of the propulsion rate. Species using the most efficient locomotion system have a considerable advantage for survival in hostile environments, a common situation in the ocean. Moreover, we found the existence of a lower size limit for useful locomotion. This suggests that, for organisms whose linear dimensions are below a certain threshold, it is advantageous not to use any propulsion mechanism at all, a result that is in agreement with what is observed in nature.