Naturalistic animal behavior can now be efficiently collected and annotated, but understanding brain function in natural settings remains challenging. It is difficult to record neural activity in freely moving animals, and complex statistics and lack of stimulus repeats preclude traditional analyses. While a popular approach is to first identify reduced, data-driven behavioral variables prior to seeking neural correlates, we propose a complementary approach: comparing a suite of mechanistic models, directly fit to behavior, that embody competing hypotheses about single-cell or population neural codes. Using recordings from a large set of fly auditory neurons to design several such models, we in turn fit these to a separate, naturalistic fly courtship dataset. In doing so we find that female locomotion is best predicted by a distributed population representation of the male’s complex and hallmark courtship song. This best-fit population code requires multiplicative adaptation and heterogeneous timescales across the population, predicting female motor output far better than the best single-neuron code. Moreover, we find the behaviorally predictive axis to be nearly orthogonal to the dominant axes of neural variability, suggesting behavior may be modulated largely by deviations around larger ongoing neural fluctuations. This work establishes invertebrate brains as a potentially rich system for studying distributed processing of temporally complex communication signals and illuminates a viable approach for gaining insight into neural population codes from pure natural behavior data.