820 



TIT.^NOTHERES OF ANCIENT WYOMING, DAKOTA, AND NEBRASKA 



the origin of these new cuspules is so contionnus and 

 gradual that they become discernible only after the 

 passage of long periods of geologic time. They are 

 also invariabty orthogenetic, evolving in a uniform 

 direction. This mode of evolution recalls the ob- 

 servation of Waagen as to the mode of origin of his 

 mutations. In any large series of titanothere or 

 other mammalian teeth one occasionally finds also 

 major and minor saltations, smaller or larger cuspules, 

 which are usually duplications of the rectigradation 

 cusps, or reversions of former rectigradation cusps, 

 such as the hypocone on the last superior molar. 



RECTIGRADATIONS INFLUENCED BY DEGREE OF 

 ZOOLOGIC AFFINITY 



The addition of new dental cusps on the teeth and 

 of horn swellinais on the skuU as rectigradations is 



PRINCIPLES OF PROPORTION 

 PROPORTION BIOCHARACTERS (ALLOMETRONS) 



Changes in proportion common. — Allometrons play a 

 larger part in the evolution of the titanotheres than 

 rectigradations. All the bones of the skull and the 

 skeleton are continuously undergoing a change of 

 proportion — in other words, developing allometrons. 

 Continuous change of proportion is a dominant mode 

 of titanothere evolution; the addition of new parts 

 and the loss of old parts have been second iu impor- 

 tance. It is demonstrated throughout this monograph 

 and summarized in the comparative measurements 

 and various tables that all changes of proportion, as 

 a whole, represent the sum of changes of separable 

 parts, biocharacters, each of which has its own rate of 

 evolution. For example, if the top parts of a titano- 



FiGUKE 736. — Separabilit}- of rectigradation biocharacters in the grinding teeth of the hybrid offspring of a 

 male ass {Equus asinus) and female horse {E. caballus) 



Section through the crown of the fourth superior premolar tooth (p') showing that the mule inherits most of the enamel fold rectigradations 

 of the ass but few of those of the horse. After Osborn, 1912.3. The following is a summary of the rectigradation biocharacters in the 

 grinding tooth of the mule: 



Distinctly asslike.-. - ^jii peculiar to ass. 



Less distinctly asslike 6] 



Common to horse and ass 5=5 common to both. 



Distinctly horselike - 2\ 



Less distinctly horselikc 4J" 



6 peculiar to horse. 



influenced by nearness or remoteness of ancestral 

 zoologic afhnity. (See predeterminate rectigradation 

 under "Theoretic causes of evolution," p. 834.) De- 

 grees of resemblance in the origia of these new bio- 

 characters always increase with closeness and intensity 

 of kinship. Thus the kinds of rectigradations (whether 

 cuspules or hornlets), as well as the rates of change 

 (phylogenetic velocities), are strongest in phyletic 

 members of the same species; they are somewhat less 

 strong in phyletic members of the same genera; they 

 become increasingly dissimilar as we compare phyletic 

 members of the same subfamilies, orders, etc. Never- 

 theless the most striking principle in the mode of 

 origin of rectigradations is that similar rectigradations 

 sooner or later tend to appear in descendants of 

 common ancestral forms. This is in striking contrast 

 to the mode of evolution of allometrons; for both dis- 

 similar and similar proportions tend to appear in the 

 descendants of common ancestors. 



there skull (DolicJiorJiinus, see below) evolve more 

 rapidly than the bottom parts, the axis of the skull 

 must be bent downward, and the skull as a whole in 

 consequence becomes cyptocephalic; if all the com- 

 ponent bones broaden more rapidly than they lengthen 

 the skull becomes brachycephalic. 



The causes of changes in the proportions of the 

 skull are. probably the same in all other mammals as 

 in man. The processes and results are distinguished 

 as follows: 



