CAUSES OF THE EVOLUTION AND EXTINCTION OP THE TITANOTHERES 



833 



have broadened out, especially the magnum and 

 astragalus, into the broad foot of Brontotherium. 



4. These examples, for which detailed evidence is 

 given elsewhere, thus illustrate the supposed inter- 

 mingling and alternate triumph of tendencies toward 

 lengthening and broadening of the parts in the various 

 phyla of titanotheres. 



IRREVERSIBLE AND REVERSIBLE EVOLUTION OF 

 ALLOMETHONS 



The marked trend in certain directions which we 

 have termed "progressive brachycephaly, " "progres- 

 sive dolichocephaly, " and "cyptocephaly" in some 

 cases runs to an extreme, so that the skull reaches a 

 limit of broadening, of lengthening, or of bending that 

 is apparently an inadaptive extreme — an assertion as 

 to adaptation, however, which may be a matter of 

 opinion or of theory rather than a statement of 

 established fact. The broadening and lengthening 

 tendency seems certainly to be cumulative in succes- 

 sive generations, affecting the skull as a whole. 



Such a tendency, however, does not apply to parts 

 of skulls in which reversible allometry is observed. 

 On comparing the skull of Brontotherium leidyi with 

 those of all lower Eocene Perissodactyla we see at 

 once that there has been a marked lengthening of 

 the cranium proper. On comparing the skull of 

 this form with that of its late successor B. platyceras 

 we see that the progressive lengthening has either 

 ceased or has been overshadowed by a marked broad- 

 ening. Here, then, is an example of lengthening that 

 has been superseded by broadening. A similar proc- 

 ess is seen in Brontops. Although Brontops hrachy- 

 cepJialus has a I'elatively longer cranium proper than 

 the primitive Perissodactyla, the lengthening was later 

 overshadowed by the broadening, both of the skull 

 top and of the zygomata, that culminates in B. rohustus 

 and " Diploclonus" amplus. 



The observation that broadening of the skull or 

 certain of its parts sometimes succeeds lengthening is 

 paralleled in the evolution of the feet, where gravi- 

 portal (weight-bearing) proportions often succeed 

 subcursorial (slender) proportions. This reversible 

 mode of evolution in proportions is of very wide appli- 

 cation in the descent of the perissodactyls and other 

 ungulates. Once admitted as a working hypothesis it 

 clears up many hitherto confused problems — the 

 structurally ancestral position of the light-limbed 

 HyracJiyus to the heavy-limbed amynodonts and 

 rhinoceroses, of the narrow-skulled, light-footed Eoti- 

 tanops to Palaeosyops and perhaps to Teltnatherium, of 

 the light-footed MesatirJiinus to the relatively broad- 

 footed DolichorJiinus . If the principle is valid that 

 in graviportal types broadening succeeds lengthening, 

 then there is less difficulty in deriving the broad-footed 

 Oligocene titanotheres with their very broad magnum 



from the more narrow-footed Eocene types with a 

 narrow (that is, primitive perissodactyl) magnum. 

 (See Gregory, 1910.1, pp. 386, 392-394, 450.) 



SEPAEABIIITY AND CORRELATION OF BIOCHARACTERS 



SEPARABILITY OF ALLOMETRONS IN HEREDITY 



The above-described differential modes of evolution 

 in the titanotheres furnish presumptive evidence of 

 the germinal separability of allometrons in their 

 velocities of change as biocharacters. The fact that 

 every allometron, like every rectigradation, has a 

 more or less distinctive time of appearance and velocity 

 of change shows that it is also connected with separable 

 germinal genes. This conclusion is confirmed by 

 hybridization in recent mammals. 



The central idea of Mendel's discovery is that when 

 two contrasting tendencies (such as dolichocephaly 

 and brachycephaly) enter a hybrid, one from each 

 parent, they separate in the germ cells of the hybrid, 

 so that some of the germ cells are purely dolichocephalic 

 and others are purely brachycephalic, like those of the 

 original parents. Chance meetings of these germ cells 

 give rise to ratios characteristic of Mendelian heredity. 



The very important question whether the "broad 

 heads" and the "long heads" as allometric biochar- 

 acters have a germinal separability like that of the 

 "tallness" or the "shortness" observed by Mendel 

 in his classic experiments on the pea plant can not 

 be determined in the titanotheres but can be inferred 

 from crosses between "long heads" and "medium 

 heads" in the related horse family, the Equidae. 

 Here, as pointed out by Osborn (1912.372, pp. 

 177-190), the dolichocephalic skull of Equus caballus, 

 when crossed with the relatively mesaticephalic skull 

 of E. asinus, gives in the mule a dolichocephalic skull 

 and not an intermediate, blended form. 



In crossing the female horse with the male ass 

 it is seen that the skull of the resulting mule has the 

 dominant dolichocephalic proportions of the horse, 

 with slight blending or intermediate proportions of 

 certain bones (like the lacrimal) between the forms 

 observed in the horse and ass. 



Careful comparison of the proportion indices in the 

 hybrid mule proves that it inherits from its mother, 

 the horse, very closely the following: 



1 . Its cephalic index ; a long, narrow skull as a whole. 



2. Its diastema index; a long diastema, or space for, 

 the bit. 



3. Its craniofacial index; a relatively short cranium 

 and a very long face. 



4. Its orbital index; a long, oval orbit. 



5. Its molar index; a relatively long and narrow set 

 of grinding teeth. 



6. Its occiput-vertex angle index; a vertically placed 

 occiput. The ass has a much more ancient type of 

 skull than the horse. 



