We show that the aerosol-cloud-precipitation system exhibits characteristics of the predator-prey problem in the field of population dynamics. Both a detailed large eddy simulation of the dynamics and microphysics of a precipitating shallow boundary layer cloud system and a simpler model built upon basic physical principles, reproduce predator-prey behavior with rain acting as the predator and cloud as the prey. The aerosol is shown to modulate the predator-prey response. Steady-state solution to the proposed model shows the known existence of bistability in cloudiness. Three regimes are identified in the time-dependent solutions: (i) the weakly precipitating regime where cloud and rain coexist in a quasi steady state; (ii) the moderately drizzling regime where limit-cycle behavior in the cloud and rain fields is produced; and (iii) the heavily precipitating clouds where collapse of the boundary layer is predicted. The manifestation of predator-prey behavior in the aerosol-cloud-precipitation system is a further example of the self-organizing properties of the system and suggests that exploiting principles of population dynamics may help reduce complex aerosol-cloud-rain interactions to a more tractable problem.