CAUSES OF THE EVOLUTION AND EXTINCTION OF THE TITANOTHERES 



819 



Rectigradations in raonophyletic, dipTiyletic, and triphyletic series, including genera, species, and ascending 



mutations of Waagen 



Geologic level of the Bridger 



Three-branch or triphyletic series (genus A) 



Mutations of Mutations of Mutations of 

 species A^ species A^ species A3 



Two-branch or diphyletic 

 series (genus B) 



Mutations c 

 species B' 



Mutations of 

 species B^ 



Single-branch 



or monophy- 



letic series 



(genus C): 



Mutations of 



species C 



Horizon C le (top) 



Horizon B 2e 



Horizon B 1, 1 



Horizon A 3 



Horizon A 2, 2. 



Horizon A 1, 1 (bottoni) 



Ale 

 41 d 



Ale 

 Alb 



Ala 



A' 



A2b 



A2. 



A3d 



ASd 



A3c 

 A3b 

 A3 a 

 A3 



Ble 



Bid 

 Bu 

 Bib 



B2d 

 B2C 

 B2b 

 B2a 



b2 



0= 



Cid 

 Ci-^ 



Qlb 



CI" 

 CI 



The table begins with three "Linnaean genera," 

 A, B, C, each genus corresponding to one to three 

 phyla, and each genus persisting throughout a long 

 geologic period, namely, from horizon A 1, 1 to horizon 

 C le. The table represents thirty-four "ascending 

 mutations " of Waagen, distinguished by the successive 

 addition of new rectigradations (1, 2, 3, etc.) and by 

 changes of proportion (allometrons) (a, b, c, d, etc.). 



Tracing each phylum from the lowest to the highest 

 geologic level through ascending mutations we observe 

 that 



Mutation A'*^ may exhibit four new rectigradation 

 cusps and final allometrons. 



Mutation A^ "^ may exhibit three new rectigradation 

 cusps and subfinal allometrons. 



Mutation A'" may exhibit two new rectigradation 

 cusps and intermediate allometrons. 



Mutation A'" may exhibit one new rectigradation 

 cusp and incipient allometrons. 



Mutation A'" may exhibit no rectigradations and 

 no changes of proportion. 



"mutations" and "species" 



Reading horizontally on any given geologic level, 

 say horizon A, level 2, 2, we may discover six "ascend- 

 ing mutations" of Waagen, namely, A'*, a^, A^*, B'"', 

 b^ C", as shown in the table above. 



This- entire geologic section of the Eocene theoreti- 

 cally shows, among the 34 ascending mutations of 

 Waagen, 6 Linnaean species: A'"'^, A^"^", A^""*, B'"'*, 



Thus, through the contemporaneous evolution at 

 different phylogenetic velocities of "homologous" 

 (more strictly "homomorphous") rectigradations and 

 allometrons new rectigradations and proportions at 

 their first appearance correspond with the least or 

 minimal systematic divisions of the zoologic system- 

 atist. When a number of these biocharacters continue 

 101959— 29— VOL 2 9 



to progress they constitute the "ascending mutations" 

 of Waagen; when a number of these ascending muta- 

 tions are similarly grouped they become the "species" 

 of Linnaeus. Therefore the simultaneous evolution of 

 a large number of biocharacters at different rates 

 of evolution constitutes the divergence of chai'acter 

 that underlies both the old zoologic and the new 

 paleontologic classification. 



These terms and distinctions, which are very diffi- 

 cult to express or to understand in descriptive text, 

 are readily comprehended when members of five or 

 six independently evolving phyla are compared in the 

 museum, character by character, or as shown in the 

 plates and synthetic diagrams. 



This mode of dental evolution through rectigrada- 

 tion and allometry is precisely what we observe in 

 other families of mammals, such as the Equidae, the 

 Rhinocerotidae, the Canidae. 



HERITAGE SEPARABILITY OF RECTIGRADATION DENTAL 

 CUSPS AND FOLDS 



The different rates of development of the premolar 

 cusps indicate that they are true biocharacters, be- 

 cause they display germinal (that is heritage) separ- 

 ability. Exactly similar homomorphous biocharacters 

 appear in the grinding teeth of the horse and of the 

 ass, accompanied by a number of secondary recti- 

 gradation enamel foldings and plications. In the 

 hybrid mule, offspring of the male ass and female 

 horse, it is found that these rectigradation folds are 

 completely separated as shown in Figure 736. 



RECTIGRADATION CUSPS ON TITANOTHERE TEETH ARE 

 UNLIKE SALTATIONS 



In all the hundreds of stages of titanothere dental 

 evolution studied not a single instance has been 

 observed in which a rectigradation cusp and fold 

 appear suddenly, wholly formed; in every instance 



