Many-to-one form-to-function mapping weakens parallel morphological evolution.

Evolutionary ecologists aim to explain and predict evolutionary change under different selective regimes. Theory suggests that such evolutionary prediction should be more difficult for biomechanical systems in which different trait combinations generate the same functional output: "many-to-one mapping." Many-to-one mapping of phenotype to function enables multiple morphological solutions to meet the same adaptive challenges. Therefore, many-to-one mapping should undermine parallel morphological evolution, and hence evolutionary predictability, even when selection pressures are shared among populations. Studying 16 replicate pairs of lake- and stream-adapted threespine stickleback (Gasterosteus aculeatus), we quantified three parts of the teleost feeding apparatus and used biomechanical models to calculate their expected functional outputs. The three feeding structures differed in their form-to-function relationship from one-to-one (lower jaw lever ratio) to increasingly many-to-one (buccal suction index, opercular 4-bar linkage). We tested for (1) weaker linear correlations between phenotype and calculated function, and (2) less parallel evolution across lake-stream pairs, in the many-to-one systems relative to the one-to-one system. We confirm both predictions, thus supporting the theoretical expectation that increasing many-to-one mapping undermines parallel evolution. Therefore, sole consideration of morphological variation within and among populations might not serve as a proxy for functional variation when multiple adaptive trait combinations exist.