Phages and bacteria coexist under widely different conditions, ranging from liquid cultures to oceans, soil, and the human gut. However, our models are typically limited to well-mixed liquid cultures governed by mass-action kinetics. Here, we suggest a modification to the Lotka-Volterra dynamics by including the formation of microcolonies. By analyzing the model in an open system with a steady influx of bacteria, we predict that the colony size distribution is power-low distributed with steeper exponents for the stronger external influx. In the realistic case where the phage attack rate to individual colonies is proportional to their radius, we obtain self-organization to a steady state where the maximal colony size is smaller for stronger external driving.
