252 



TITANOTHEEES OF ANCIENT WYOMING, DAKOTA, AND NEBRASKA 



has been found that the changing proportions of the 

 various parts of the slvull, of the individual grinding 

 teeth, of every part of the skeleton, especially the 

 limbs, are highly distinctive systematic and phyletic 

 characters. 



Five distinctions of 'phyla. — Each line of descent is 

 distinguished by five different methods: First, by the 

 presence or absence of certain characters; second, by 

 the new proportions of certain characters; third, by 

 the tendencies or directions in which proportions are 

 being changed; fourth, by the rates of change in 

 proportion characters, whether retarded or acceler- 

 ated; fifth, by the appearance of new rectigradation 

 characters. 



Numerous extinct iranclies or phyla. — The distinc- 

 tions in characters multiply with the multiplication of 

 the phyla. In 1914 no less than 20 branches of the 

 titanothere famdy were known, and probably many 

 more existed that had not yet been discovered. 

 Throughout Eocene time titanotheres continued to 

 migrate into the mountain region of the Bridger and 

 Washakie Basins of Wyoming. Allowing for certain 

 branches that drop out, we find that the number of 

 their known branches constantly increases from lower 

 to higher levels, as shown below. 



Oligocene : White River group 7-8 



Summit of upper Eocene: Lower part of Uinta C (true 



Uinta formation), Uinta Basin, Utah 4 



Upper Eocene: Uinta B 2 of Uinta Basin, Utah; Washakie 



B 2 of Washakie Basin, Wyo 6 



Upper Eocene: Washakie B 1 of Washakie Basin, Wyo.; 



and Uinta B 1 of Uinta Basin, Utah 8 



Middle Eocene: Bridger C and D of Bridger Basin, Wyo.; 



Wasliakie A of Washakie Basin, Wyo 5 



Middle Eocene: Bridger A and B of Bridger Basin, Wyo.; 



Huerfano B, Huerfano Park, Colo 2 



Lower Eocene: Wind River formation, Wind River Basin, 



Wyo.; Huerfano A, Huerfano Park, Colo 2 



Universal change oj form. — No characters in any 

 genus or phylum are stationary. During the long 

 intervals of geologic time the members of each of these 

 branches were constantly diverging in some characters 

 and converging in others and becoming more and 

 more unlike one another both as a whole and, so far as 

 we can observe, in each one of their single characters. 



ATLometrons and rectigradations. — The term allome- 

 trons (Osborn, 1912.372, pp. 249-278) designates 

 characters that arise through continuous changes of 

 size or proportion in old features — that is, purely 

 quantitative changes — such as may be expressed in 

 differences of measurement as well as in indices and 

 ratios. Rectigradations are new characters that tend 

 to evolve in a definite direction — the earliest "rudi- 

 ments" or discernible stages of absolutely new forms. 

 In 1889 Osborn called such characters "definite vari- 

 ations" (Osborn, 1907.301, p. 239). 



Six points in the distinction between allometrons 

 and rectigradations may be readily grasped: (1) 

 When the shadowy beginning of a new cusp on the 



grinding teeth or the rudiment of a horn is first dis- 

 cernible as a new character it appears as a "rectigrada- 

 tion"; (2) when this same rudiment of a cusp or horn 

 takes on a new shape the change of form appears as 

 an " allometron " ; (3) in the hard parts of a titano- 

 there, as of any other mammal, the rectigradations — 

 the numerically new characters of any kind — are com- 

 paratively few and uncommon, but the allometrons — 

 the transformations of existing characters — comprise 

 the larger number of changes; (4) both allometrons and 

 rectigradations are distinctly heritable characters; (5) 

 in the genesis of rudiments (rectigradations) of new 

 cusps or of horns all the branches or phyla of titano- 

 theres sooner or later tend to resemble one another — 

 that is, to develop the same cusps and the same horn 

 swellings — and thus to become convergent; (6) on the 

 other hand, in changes in the proportions (allometrons) 

 of the skull, the different phyla may differ widely from 

 one another and through dissimilar allometrons may 

 become divergent. (See fig. 210.) 



STEPS IN TRANSFORMATION OF CHARACTERS 



So far as we have observed, all absolutely new char- 

 acters that we have traced to their very beginnings in 

 titanotheres arise gradually and continuously; there is 

 no evidence of sudden leaps from mutation to muta- 

 tion or from species to species. This continuous mode 

 of evolution is more fully considered in Chapter IX. 



The addition (rectigradation) or the modification 

 (allometron) of a single character is theoretically the 

 first step in transformation, but as a matter of fact 

 all characters are being simultaneously more or less 

 modified, and in the individual as a whole new char- 

 acters are constantly being added. Only when fully 

 developed after the lapse of many generations does a 

 rectigradation or an allometron become of sufficient 

 systematic value to define the mutation or the species. 

 None the less each of these changes forms one in a 

 series of steps in the transformation of species. 



One by one the characters, either rectigradations or 

 allometrons, in many parts of the titanothere are inde- 

 pendently changed until the changes build up what 

 paleontologists call an "ascending mutation" in the 

 sense in which the German invertebrate paleontologist 

 Waagen defined this term in 1869. An ascending mu- 

 tation is a stage in a continuous evolutional ascent in 

 one or more characters from one species to another; 

 there is no evidence that it is a saltation or "mutation" 

 in the sense of that word as used by De Vries. 



Finally these rectigradations and allometrons attain 

 by accumulation sufficient importance to enable us to 

 call a stage a "species" in the Linnaean sense or a 

 "subspecies" in the modern sense. 



The divergence between the several branches of the 

 titanothere family therefore actually consists of the 

 sum total of changes in an almost infinite number of 

 single characters, only a few of which are measurable. 

 These changes are of the following principal lands: 



