The evolution of threespine sticklebacks in freshwater lakes constitutes a well-studied example of a phenotypic radiation that has produced numerous instances of parallel evolution, but the exact selective agents that drive these changes are not yet fully understood. We present a comparative study across 74 freshwater populations of threespine stickleback in Norway to test whether evolutionary changes in stickleback morphology are consistent with adaptations to physical parameters such as lake depth, lake area, lake perimeter and shoreline complexity, variables thought to reflect different habitats and feeding niches. Only weak indications of adaptation were found. Instead, populations seem to have diversified in phenotypic directions consistent with allometric scaling relationships. This indicates that evolutionary constraints may have played a role in structuring phenotypic variation across freshwater populations of stickleback. We also tested whether the number of lateral plates evolved in response to lake calcium levels, but found no evidence for this hypothesis.