Similarities as Evidence for Common Ancestry -- A Likelihood Epistemology

Darwin claims in the {\em Origin} that similarity is evidence for common ancestry, but that adaptive similarities are "almost valueless" as evidence. This 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.