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|Abstract: We explore the evidential relationships that connect two standard claims of modern evolutionary biology. The hypothesis of common ancestry (which says that all organisms now on earth trace back to a single progenitor) and the hypothesis of natural selection (which says that natural selection has been an important influence on the traits exhibited by organisms) are logically independent; however, this leaves open whether testing one requires assumptions about the status of the other. Darwin noted that an extreme version of adaptationism would undercut the possibility of making inferences about common ancestry. Here we develop a converse claim—hypotheses that assert that natural selection has been an important influence on trait values are untestable unless supplemented by suitable background assumptions. The fact of common ancestry and a claim about quantitative genetics together suffice to render such hypotheses testable. Furthermore, we see no plausible alternative to these assumptions; we hypothesize that they are necessary as well as sufficient for adaptive hypotheses to be tested. This point has important implications for biological practice, since biologists standardly assume that adaptive hypotheses predict trait associations among tip species. Another consequence is that adaptive hypotheses cannot be confirmed or disconfirmed by a trait value that is universal within a single species, if that trait value deviates even slightly from the optimum.|