Hyperbolic odorant mixtures as a basis for more efficient signaling between flowering plants and bees

Abstract

Animals use odors in many natural contexts, for example, for finding mates or food, or signaling danger. Analyses of natural odors search for either the most meaningful components of a natural odor mixture, or they use linear metrics to analyze the mixture compositions. Both analyses assume that the odor space itself is Euclidian, like visual and auditory spaces. However, we have recently shown that the physical space for complex mixtures is 'hyperbolic' -curved -because of the correlations that arise in biosynthetic pathways. Here we shown that the shape of the space for flowers (Brassica rapa) using an existing data set can also be better described with a hyperbolic rather than a linear shape, and that components in the space correlate to the nectar and pollen resource sought by bee pollinators. We also show that honey bee and bumble bee antennae can detect most components of the B. rapa odor space. We argue that further investigation of the implications of hyperbolic space can have important implications for how sensory systems have evolved to encode the space.

Restructuring of olfactory representations in the fly brain around odor relationships in natural sources

“…We found that the natural odor abundance data was best described by a threedimensional hyperbolic space with a negative curvature of -5.12. These results echo previous results using a more limited dataset of natural fruit or flower odor sources where hyperbolic geometry also provided a significantly better fit than the standard Euclidean geometry 12,45 . The intuitive explanation for these findings is that hyperbolic spaces provide good descriptions of the structure of natural odor spaces because they arise as continuous approximations to tree-like hierarchical networks.…”

“…This space was also found to be hyperbolic, but with much smaller curvature (0.05) and higher dimensionality (dim=6). Since odor distances in the hyperbolic embedding better captured the correlational structure of abundances of odors across natural sources that stem from hierarchical odor as compared to equivalent distances computed from a Euclidean embedding 12,45 , we used hyperbolic distances as a metric of odor relationships in natural source space.…”

“…Recently, we showed that the use of hyperbolic coordinates to embed the concentrations of individual monomolecular odorants as they occur in natural odor sources better captures odor relationships in the space of natural sources, compared to embeddings that use Euclidean metrics 12,45 . Thus, to describe the similarity in distribution across natural odor sources for a given pair of odors, we started with a normalized correlation coefficient computed between odor abundances across different natural sources.…”

“…Odors from natural sources are typically complex mixtures of dozens to hundreds of monomolecular odorants, the composition of which is controlled by the conserved biochemical and metabolic processes in the source 10,11 . The relative abundance or ratios of volatiles in natural odor profiles can provide information about the value or state of the odor source 12,13 , for instance, if microbes that promote fermentation or spoilage are dominant. Thus, the odor space of the natural world is highly structured, and this structure often contains information about the identity or ethological value of the odor source.…”