ABSTRACT Darwin claims in the Origin that similarity is evidence for common ancestry, but that adaptive similarities are ‘almost valueless’ as evidence. This second claim seems reasonable for some adaptive similarities but not for others. Here we clarify and evaluate these and related matters by using the law of likelihood as an analytic tool and by considering mathematical models of three evolutionary processes: directional selection, stabilizing selection, and drift. Our results apply both to Darwin’s theory of evolution and to modern (...) evolutionary biology. _1_ Introduction _2_ The Likelihood Framework _3_ A Sufficient Condition for a Similarity to Favour Common Ancestry over Separate Ancestry _4_ The 1/p Criterion and Its Limitations _5_ Directional Selection versus Drift _6_ Stabilizing Selection versus Drift _7_ Going beyond Two Taxa _8_ Conclusions Appendix. (shrink)