CAUSES OF THE EVOLUTION AND EXTINCTION OF THE TITANOTHERES 



813 



RESEMBLANCES BETWEEN KECTIGRADATIONS AND 

 ALLOMETRONS AS BIOCHARACTERS 



Rectigradations and allometrons have certain points 

 of resemblance: (1) Both are orthogenetic, continuous, 

 or gradual in origin, rather than discontinuous, 

 saltatory, or tychogenetic (tLxv, chance, fortuity; 

 ykveai-s, genesis); (2) both appear in increasing inten- 

 sity in successive "ascending mutations" of the same 

 phyla, a new dental cusp, for example, becoming more 

 distinct, the brachycephaly becoming more pronounced; 

 (3) both are subject to similar laws of cellular growth, 

 the rectigradations more localized, the allometrons 

 more diffused; (i) both display differences in phylo- 

 genetic velocity; similar rectigradations and allo- 

 metrons arise in different geologic stages; (5) both 



display differences in ontogenetic velocity; horn 

 rudiments and skull proportions, for example, may be 

 accelerated or retarded in development; (6) both are 

 subject to the law of correlation, compensation, and 

 coordination with other parts; (7) both may or may 

 not be correlated with sex; (8) after rectigradations 

 such as rudiments of horns have first appeared, they 

 are subject to changes of proportion — that is, to 

 allometrons. 



CONTRASTS BETWEEN RECTIGRADATIONS AND 

 ALLOMETRONS AS BIOCHARACTERS 



The contrasts between the features of rectigrada- 

 tions and allometrons are shown in the accompanying 

 table. 



Contrasts between rectigradations and allometrons 



Features of rectigradations 



Features of allometrons 



1. Rectigradations are strictly new biocharacters — local out- 



growths — such as dental cuspules or horn rudiments. 



2. Rectigradations give rise to so-called "homologies," more 



strictly "homomorphs"; the mesostyle of Mesohippus and 

 that of Palaeosyops are said to be homologous, although 

 one animal is not descended from the other, but both are 

 descended from a very remote common ancestor that had 

 no mesostyle. 



3. Rectigradations are neomorphs, new outgrowths, numeri- 



cally new biocharacters — for example, a tooth having 

 three cusps develops five or six cusps. 



4. Rectigradations appear chiefly in near or remote descendants 



of common ancestors; the mammals of the order Peris- 

 sodactyla, for example, evolve many similar rectigrada- 

 tions in their grinding teeth which do not appear in the 

 teeth of the Artiodactyla or the Amblj'poda. 



5. Rectigradations apparently have little or no observable 



adaptive value at their origin, little or no selection sur- 

 vival value. 



6. The origin of similar rectigradations in independent phyla of 



mammals and families of mammals always gives rise to 

 parallelism, convergence — for example, the molar teeth of 

 Eohippus, a horse, converge toward those of Notharctus, a 

 lemur, in the independent origin of similar cuspules. 



7. Rectigradations are not known to be produced experimentally 



in ontogeny. So far as observed they are from the begin- 

 ning germinal biocharacters. 



8. Rectigradations as neomorphs are relatively rare or infre- 



quent in mammals; see Miller's definitions of the species 

 of European mammals (1912.1). 



9. Rectigradations may be measured by indices and ratios only 



after they have developed to a sufficient size — for example, 

 changes of proportion in horns and cu^ps (allometrons). 



10. Rectigradations characteristic of a phylum in one geologic 



period may appear in rudimentary form at a later period 

 in another phylum as "homomorphs" — such as the 

 enamel folds known as crista, crochet, antecrochet in 

 horses, titanotheres, rhinoceroses. 



1. Allometrons are generally changes of old proportions not 



localized — for example, dolichocephaly, brachycephaly, 

 hypsodonty. 



2. Allometrons give rise to analogies, never to homologies in 



any sense; dolichocephaly, for example, is an analogous 

 change of the cranium in Homo and in Menodus. 



3. Allometrons are allomorphs, or heteromorphs, or changes of 



proportion — they are quantitative; a narrow tooth, for 

 example, becomes a broad tooth. 



4. Allometrons are totally independent of remote ancestral 



affinity — for example, Perissodactyla, Artiodactyla, Am- 

 blypoda may alike become dolichocephalic. They are 

 partly independent of near ancestral afiinity; nearly re- 

 lated races of men of the same species (Homo sapiens) 

 become dolichocephahc or brachycephalic. 



5. Allometrons may have adaptive or mechanical significance 



throughout; they may consist of changes of limb propor- 

 tion, which appear to be adaptable or inadaptable through- 

 out their evolution. 



6. The origin of allometrons in animals of the same ancestry 



or of nearly allied strain may give rise either to conver- 

 gence or to divergence; a dolichocephalic phylum, for 

 example, may diverge from a brachycephalic phylum. 



7. Allometrons may be produced experimentally in ontogeny; 



new limb proportions, for example, may arise from new or 

 modified habits. All allometrons are not certainly known 

 to be germinal at the beginning. 



8. Allometrons are universal phenomena, constantly appearing 



in specific definition; see Miller, op. cit. 



9. Allometrons constantly afford changing indices and ratios in 



all stages of ontogeny and of phylogeny. 



10. Similar or dissimilar allometrons may arise in related phyla 



at different periods of geologic time. 



