How the brain processes natural sensory input remains an important and poorly understood problem in neuroscience. The efficient coding hypothesis asserts that the brain's coding strategies are adapted to the statistics of natural stimuli in order to efficiently process them, thereby optimizing their perception by the organism. Here we examined whether gymnotiform weakly electric fish displayed behavioral responses that are adapted to the statistics of the natural electrosensory envelopes. Previous studies have shown that the envelopes resulting from movement tend to consist of low (<1 Hz) temporal frequencies and are behaviorally relevant whereas those resulting from social interactions consist of higher (>1 Hz) temporal frequencies that can thus mask more behaviorally relevant signals. We found that the self-generated electric organ discharge frequency follows the detailed time course of the envelope around a mean value that is positively offset with respect to its baseline value for temporal frequencies between 0.001 Hz and 1 Hz. The frequency-following component of this behavioral response decreased in magnitude as a power law as a function of the envelope frequency and was negligible for envelope frequencies above 1 Hz. In contrast, the offset component was relatively constant and somewhat increased for envelope frequencies above 1 Hz. Thus, our results show that weakly electric fish display behavioral responses that track the detailed time course of low but not high frequency envelope stimuli. Furthermore, we found that the magnitude of the frequency-following behavioral response matches, in a one-to-one fashion, the spectral power of natural second-order stimulus attributes observed during movement. Indeed, both decayed as a power law with the same exponent for temporal frequencies spanning three orders of magnitude. Thus, our findings suggest that the neural coding strategies used by weakly electric fish perceive the detailed time course of movement envelopes and are adapted to their statistics as found in the natural environment. They also suggest that weakly electric fish might take advantage of the differential frequency content of movement and social envelopes in order to give appropriate behavioral responses during encounters between two or more conspecifics.