The theory of punctuated equilibria promoted by Niles Eldredge and Stephen Jay Gould in 1972 re-ignited the long-standing conflict between traditionalists who believe that species are fixed in form and Lamarck-Darwin progressivists who envision species changing through time. The history of Poecilozonites developed by Gould is slightly complicated, but there was no special ‘punctuation’ in the speciation nor any static ‘equilibrium’ in Gould’s original interpretation. The history of Phacops developed by Eldredge is similarly slightly complicated, but there was no special ‘punctuation’ in the speciation, nor any statistically-justified ‘equilibrium’ in Eldredge’s interpretation. The Metrabdotos species lineages described by Cheetham et al. in 2007 are lineages in stasis. Species pairs diverged rapidly, yielding punctuated patterns, but the divergences can all be explained by directional selection at the median step rate for field studies documented here in Chapter 8. Empirical step rates are high and change by natural selection is much faster than many paleontologists appreciate.