Natural populations can suffer catastrophic collapse in response to small changes in the environment, and recovery after such a collapse can be difficult. We have used laboratory microcosms to directly measure theoretically proposed early warning signals of impending population collapse. Our experimental yeast populations cooperatively break down the sugar sucrose, meaning that below a critical size the population cannot sustain itself. We find that catastrophic collapse is preceded by a change in the fluctuations of the population, suggesting that this and other indicators may provide advance warning of impending collapse. The cooperative nature of yeast growth on sucrose makes the population susceptible to "cheater" cells, which do not contribute to the public good and reduce the resilience of the population.