Determinants of species diversity in microbial ecosystems remain poorly understood. Bacteriophages are believed to increase the diversity by the virtue of Kill-the-Winner infection bias preventing the fastest growing organism from taking over the community. Phage-bacterial ecosystems are traditionally described in terms of the static equilibrium state of Lotka-Volterra equations in which bacterial growth is exactly balanced by losses due to phage predation. Here we consider a more dynamic scenario in which phage infections give rise to abrupt and severe collapses of bacterial populations whenever they become sufficiently large. As a consequence, each bacterial population in our model follows cyclic dynamics of exponential growth interrupted by sudden declines. The total population of all species fluctuates around the carrying capacity of the environment, making these cycles cryptic. While a subset of the slowest growing species in our model is always driven towards extinction, in general the overall ecosystem diversity remains high. The number of surviving species is inversely proportional to the variation in their growth rates but increases with the frequency and severity of phage-induced collapses. Thus counter-intuitively we predict that microbial communities exposed to more violent perturbations should have higher diversity.An important and largely unsolved question in microbial ecology is what determines the diversity of microbial ecosystems. Indeed, unbridled competition between microbes sharing common resources would eventually limit species diversity not to exceed the number of different nutrient types 1 . Predation by bacteriophages introduces the negative frequency-dependent selection 2-5 which offers the possibility for a dramatically larger species diversity 5 . In the classical Kill-the-Winner (KtW) model of Thingstad 5 virulent phages reduce populations of their susceptible hosts to a low steady state level, which is independent of hosts' growth rate thus allowing multiple species per nutrient type. The number of co-existing bacterial species in the resulting ecosystem is determined exclusively by the parameters of phage predation 5 , the topology of the phage-bacterial infection network [6][7][8] , and the carrying capacity of the environment 4,[7][8][9] . Microbial populations are routinely exposed to more dynamics than assumed in the traditional steady state KtW model and its variants. Extended Lotka-Volterra equations for two layer ecosystems of phages and bacteria could predict persistently varying populations 10 , even without considering mutations. In addition, microbial systems are typically exposed to changes in interaction rules and new invading species. For example, in the lab experiments 11 E. coli population suffered a dramatic collapse by a factor ~10 4 -10 5 caused by a T7 phage infection. Collapse-driven dynamics is common in both natural 12 and man-made 13-16 ecosystems in which bacteria are engaged in the continuous arms race with phages [17][18][19][20][21] . Here we propose and ...