Inferring the causes for change in the fossil record has been a persistent problem in evolutionary biology. Three independent lines of evidence indicate that a lineage of the fossil stickleback fish Gasterosteus doryssus experienced directional natural selection for reduction of armor. Nonetheless, application to this lineage of three methods to infer natural selection in the fossil record could not exclude random process as the cause for armor change. Excluding stabilizing selection and genetic drift as the mechanisms for biostratigraphic patterns in the fossil record when directional natural selection was the actual cause is very difficult. Biostratigraphic sequences with extremely fine temporal resolution among samples and other favorable properties must be used to infer directional selection in the fossil record.