142 VERTEBRATE PALAEONTOLOGY 



another matter. Thus we don't know the time or the source of 

 origin of the vertebrates. We do not know the relationship 

 between the Agnatha and the Placoderms. We do not know the 

 ancestry of the Osteichthyes or Chondrichthyes. We do not know 

 if the Amphibia are monophyletic or diphyletic. We do not know 

 if the mammals are monophyletic or polyphyletic. 



In spite of the ignorance on these basic points certain changes 

 have been taking place. Thus in older classifications one could 

 read about a group called " Pisces." This group is no longer 

 considered a suitable classiflcatory unit and it has been broken 

 down into the groups Agnatha, Placoderms, Osteichthyes and so 

 on. In other words the group " Pisces " was a complex grade of 

 organisation, a grade corresponding to the " fish level of com- 

 plexity." Further studies may show that the Amphibia, reptiles 

 and mammals are all grades of organisation and not necessarily 

 very closely related groups of animals. 



Rates of Evolution 



Within recent years the study of genera and species in the 

 various geological strata has been put on a quantitative basis. 

 Thus if one studies a group of animals and examines the number of 

 genera present, say, in the Ordovician and then examines how 

 many of these genera are present in more recent strata one can 

 make a calculation of the time over which each genus existed and 

 from this one mav come to certain tentative conclusions about the 



J 



evolution of the groups as a whole. 



This technique, together with various others, has been applied 

 with considerable success by G. G. Simpson in his books Tempo 

 and Mode in Evolution (1944) and The Major Features of Evolution 

 (1953). These works satisfy two desires in the reader: the first 

 is for an intelligent approach to fossil animals and the realisation 

 that they once were living animals; the second is for a treatment of 

 evolution and palaeontology in a mathematical and symbolic 

 manner. 



Simpson takes two groups, the Lamellibranches and the 

 Carnivores (excluding the Pinnipedia) and for each draws up a 

 table showing the number of genera present in the Ordovician, 

 Silurian, Devonian and so on, and also the level at which each 



