Many physiological traits consist of two hierarchically related levels: physical structures and the emergent functional properties of those structures. Because selection tends to act on the emergent functional traits, the evolution of structural phenotypes will depend on the nature of the form-function relationship. Complex physiological or biomechanical traits are often characterized by many-to-one mapping: numerous structural phenotypes can yield equivalent functions. We suggest that this redundancy can promote the evolution of phenotypic diversity, and we illustrate this effect with a combination of empirical and analytical studies of a complex biomechanical trait, the four-bar linkage found in the jaws of labrid fishes. We show that labrid jaws are subject to many-to-one mapping of form-to-jaw mechanical properties but that some mechanical types have higher levels of morphological redundancy than others. This variation in redundancy has affected the diversity and distribution of labrid jaw shapes: labrid species are disproportionately concentrated around functional traits with higher potential for redundancy. Many-to-one mapping can also mitigate evolutionary constraints imposed by mechanical trade-offs by allowing a species to simultaneously optimize multiple functional properties. Many-to-one mapping may be an important factor in generating the uneven patterns of diversity in physiological traits.