The mammalian cochlear map is optimally warped.

The form of the mammalian cochlear frequency-position map has been well described by Greenwood and empirical values found for its coefficients for a number of species. The apical portion of the mammalian map is spatially compressed relative to the base, and this nonuniformity in the representation of frequency is evidently consistent across species. However, an evolutionary reason for this consistency, encompassing critical band behavior with respect to position, is conspicuously missing. Likewise, the length of the cochlea in any mammal, including echolocating species, is related to body size, but attempts to explain the length in terms of frequency limits, range, or resolution have no general explanation. New insight stems from a hypothesis in which the map curvature may be appreciated as an adaptation for optimal frequency resolution over the auditory range. It is demonstrated numerically that the mammalian curve may be considered a member of a family of curves which vary in their degree of warp. The "warp factor" found to be common across mammals is an optimal trade-off between four conflicting constraints: (1) enhancing high-frequency resolution; (2) setting a lower bound on loss of existing low-frequency resolution; (3) minimizing map nonuniformity; and (4) keeping the whole map smooth, thereby avoiding reflections.