Quantifying spectral information about source separation in multisource odour plumes

Odours released by objects in natural environments can contain information about their spatial locations. In particular, the correlation of odour concentration timeseries produced by two spatially separated sources contains information about the distance between the sources. For example, mice are able to distinguish correlated and anti-correlated odour fluctuations at frequencies up to 40 Hz, while insect olfactory receptor neurons can resolve fluctuations exceeding 100 Hz. Can this high-frequency acuity support odour source localization? Here we answer this question by quantifying the spatial information about source separation contained in the spectral constituents of correlations. We used computational fluid dynamics simulations of multisource plumes in two-dimensional chaotic flow environments to generate temporally complex, covarying odour concentration fields. By relating the correlation of these fields to the spectral decompositions of the associated odour concentration timeseries, and making simplifying assumptions about the statistics of these decompositions, we derived analytic expressions for the Fisher information contained in the spectral components of the correlations about source separation. We computed the Fisher information for a broad range of frequencies and source separations for three different source arrangements and found that high frequencies were more informative than low frequencies when sources were close relative to the sizes of the large eddies in the flow. We observed a qualitatively similar effect in an independent set of simulations with different geometry, but not for surrogate data with a similar power spectrum to our simulations but in which all frequencies were a priori equally informative. Our work suggests that the high-frequency acuity of olfactory systems may support high-resolution spatial localization of odour sources. We also provide a model of the distribution of the spectral components of correlations that is accurate over a broad range of frequencies and source separations. More broadly, our work establishes an approach for the quantification of the spatial information in odour concentration timeseries.