When non-canonical olfaction is optimal

The early olfactory system is canonically described by a "one-receptor-to-one-neuron" model: each olfactory sensory neuron (OSN) expresses a single type of olfactory receptor. Although the olfactory systems of many model organisms approximately follow this canonical organization, a number of exceptions are known. In particular, Aedes aegypti mosquitoes co-express multiple types of olfactory receptors in many OSNs. Why do some olfactory systems follow the canonical organization while others violate it? We approach this question from the normative perspective of efficient coding. We find that the canonical and non-canonical organizations optimally encode odor signals in different types of olfactory environment. Non-canonical olfaction is beneficial when relevant sources emit correlated odorants and the environment contains odorants from ethologically irrelevant odor sources. Our theory explains previous observations of receptor co-expression and provides a framework from which to understand the structure of early olfactory systems.