We analyse population dynamics in Barro Colorado Island (Panama) using census data of a 50 ha forest plot spanning 35 years, and address the question whether this community is in a stationary state. Individual species abundances show large fluctuations, but assessing stationariety requires discriminating random fluctuations from actual trends. This requires evaluating mean quantities as well as the structure (i.e. the correlations) of the fluctuations around this mean. We argue that a species average is the best surrogate for the theoretically required but unfeasible history average. We define the overlap, a species-averaged measure of composition similarity, which reveals that the BCI population dynamics is stationary but not static, displaying fluctuations with a characteristic time of around 15 years, two orders of magnitude less than previously estimated.