We apply a method of analyzing species abundance through time that may have great potential for describing extinction dynamics across ecological and geologic scales. We examine abundance fluctuations of populations of foraminifera in an upper Eocene-lower Oligocene stratigraphic section. Populations with greater abundance fluctuations apparently become locally extinct sooner. This earlier extinction may apply not only to local populations but to the species itself. These tentative results also give insight into the dynamics of fluctuations: populations with less density-dependent control show greater amplitudes in the abundance time series. It is the resulting "higher highs" and "lower lows" that seem to lead to the early extinction. Because the method is fractal based, it is a very robust approach to problems of gaps in and dating of the record, as illustrated with computer simulations.