11With increasing antimicrobial resistance, alternatives for treating infections or removing resistant 12 bacteria are urgently needed, such as the bacterial predator Bdellovibrio bacteriovorus or 13 bacteriophage. Therefore, we need to better understand microbial predator-prey dynamics. We 14 developed mass-action mathematical models of predation for chemostats, which capture the low 15 substrate concentration and slow growth typical for intended application areas of the predators such 16 as wastewater treatment, aquaculture or the gut. Our model predicted a minimal prey size required 17 for predator survival, explaining why Bdellovibrio is much smaller than its prey. A too good predator 18 (attack rate too high, mortality too low) overexploited its prey leading to extinction (tragedy of the 19 commons). Surprisingly, a predator taking longer to produce more offspring outcompeted a predator 20 producing fewer offspring more rapidly (rate versus yield trade-off). Predation was only efficient in a 21 narrow region around optimal parameters. Moreover, extreme oscillations under a wide range of 22 conditions led to severe bottlenecks. A bacteriophage outcompeted Bdellovibrio due to its higher 23 burst size and faster life cycle. Together, results suggest that Bdellovibrio would struggle to survive 24 on a single prey, explaining why it must be a generalist predator and suggesting it is better suited to 25 environments with multiple prey than phage. 26 Summers & Kreft Predation strategies of Bdellovibrio 2 157 Since the oscillations generated by our Bdellovibrio model had a much longer period, extremely 158 abrupt rises and falls and a strong asymmetry in wave shapes compared to the typical Lotka-159 Volterra models for animal populations, we compared our model with a protist predator model by 160 Curds and Bazin [27] that generated similarly extreme but shorter period oscillations. The period of 161 the protist model could be increased to that of the Bdellovibrio model just by replacing protist with 162 Bdellovibrio kinetic parameters (SI text on Protist model, Fig. S5).