Many attempts have been made at supporting either one of the allegedly complementary divergence models Phyletic Gradualism and Punctuated Equilibria by patterns found in specific fossil sequences. However, assessing each model's connection with reality via such “individual case histories” appears not to constitute a relevant approach. Instead, in order to correctly establish the possible merits of both concepts, the claims of each have to be verified against general evolutionary theory. This is being pointed out herein by analyzing cladogenesis at the (...) specific level as an example. [Phyletic Gradualism; Punctuated Equilibria; evolutionary theory; divergence models; case histories; additive speciation.]. (shrink)