This paper investigates the consequences, for population dynamics, of the hypothesis that the schooling of fish is an effective means of reducing predation. Since the efficiency of schooling increases with the size of schools (within certain limits), the losses due to predation will be relatively greater at low population levels. This implies “depensation” in the stock-recruitment relationship, which in turn implies a discontinuity in the yield-effort curves, whereby an infinitesimal increase in effort above a certain level switches from a stable state of sustained yield to an unstable state leading to extinction. In case the depensation is “critical”, the path to extinction may be irreversible. A necessary and sufficient condition for the existence of critical depensation is that average fertility is too small to counteract mortality at low population levels where schooling becomes ineffective. The analysis thus suggests that sudden population collapses may be expected in the exploitation of small, schooling species of fish normally subject to heavy predation. Such collapses may result directly from overfishing (this is called the “depensation catastrophe”), or indirectly as the result of environmentally-induced fluctuations operating on an exploited population with significantly reduced resilience.