(A) Optimal residence time predicted by the population-based model and optimal foraging theory (OFT; Methods). Three scenarios with various particle-wide mortality (mp) and mortality on free-living populations (mF) are simulated with the following rates: (1) particle-wide mortality (mp = 0.05 hr−1, mF = 0.02 hr−1), (2) free-living mortality (mp = 0 hr−1, mF = 0.05 hr−1), and (3) no mortality (mp = 0 hr−1, mF = 0 hr−1). To calculate optimal residence time based on OFT, we used our model and tracked individual cells attaching to a particle. The time-averaged uptake rate of the attached cell and its instantaneous uptake rate were calculated. The residence time with similar instantaneous and time-averaged uptake rates is assumed to be optimal residence time based on OFT (see Method for details). In our population-based model, the optimal residence time is assumed to be a residence time that maximizes the growth return from the particles. (B) The relative abundance of population 1 is shown for competition experiments of two populations with different detachment rates. The relative abundance is measured at the equilibrium, where no changes in the sizes of both populations are observed. The area with white color represents the conditions where either one of the populations is extinct. The mortality on particles is assumed 0.02 hr−1. (inset) Phase diagram of the coexistence as a function of detachment rates for two competing populations. dopt represents the optimal detachment rate that the coexistence range nears zero. (B) The attachment rates are kept constant at 0.0005 hr−1. The number of particles is assumed to be 60 L−1. The carrying capacity of the particle is assumed to be 5e106. Simulations are performed using our population-based mathematical model.