CHAPTER V 



EVOLUTION OF THE SKULL AND TEETH OF EOCENE TITANOTHERES 



SECTION 1. GENERAL PRINCIPLES OF THE STUDY OF 

 THE CHARACTERS OF THE SKULL AND TEETH 



PROPORTION CHARACTERS AND TENDENCIES OF EVOLU- 

 TION DISTINGUISHED BY ANALYSIS AND SYNTHESIS 



The key to the evolution of the titanotheres is 

 afforded by the analysis and synthesis of the separate 

 characters of which the individuals in each line of 

 ascent are composed — characters large or small, single 

 or multiple — in correlation with one another and in 

 correlation with the individual as a whole; characters 

 progressing or retrogressing in successive generations; 

 characters evolving rapidly or evolving slowly: such 

 is the composition of each individual titanothere, as 

 well as of each phylum. 



Out of an almost infinite number of characters that 

 are independently evolving we select a few that are 

 visible and measurable. In a few individuals we 

 observe the origin of new characters, but generally 

 we observe the changes of form and of proportion in 

 existing characters, which make up the greater part 

 of the transformation of the individuals composing 

 the family. In heredity each character is a separate 

 unit, completely separable from all others; in adap- 

 tation it is correlated with other characters of the 

 individual, as is fully explained in Chapter IX. 



DISTINCTIONS BETWEEN PROPORTION CHARACTERS AND 

 NEW RECTIGRADATION CHARACTERS 



Methods employed. — The present chapter explains 

 how the characters of titanotheres have been observed, 

 examined, and measured, partly by new methods, 

 largely devised especially to solve the problems that 

 have arisen in the task of working out the genealogy 

 of this family, and partly by old methods, which have 

 been in use by paleontologists and systematists. To 

 distinguish the characters of the teeth, skull, and 

 limbs, which are generally but fragments, necessitates 

 very refined and precise systems of measurement and 

 comparison, because the individual members of differ- 

 ent lines of descent may be very close to each other 

 in certain characters yet readily separable in others. 

 Animals that the zoologist would readily distinguish 

 as species and subspecies by their external coloring, 

 bodily form, or habits of life may be extremely simi- 

 lar in skeletal characters, yet the close methods of 

 measurement and analysis that we have been com- 

 pelled to adopt prove that every character has dis- 

 tinctions that may be revealed by minute and precise 

 observation. 



Researches on proportion characters. — The chief 

 papers on the principles of evolution of the mammaJian 

 skull and teeth which the author has published in the 

 investigation of the titanotheres are the following: 



1896.110. Th • cranial evolution of Titanotherium: Am. Mus. 

 ra . Hist. Bull., vol. 8, art. 9, pp. 157-197, July 

 31, 1896. 



1902.207. Dolichocephaly and brachycephaly in the lower mam- 



mals: Am. Mus. Nat. Hist. Bull., vol. 16, art. 7, 

 pp. 77-89, Feb. 3, 1902. 



1902.208. The four phyla of Oligocene titanotheres: Am. Mus. 



Nat. Hist. Bull., vol. 16, art. 8, pp. 91-109, Feb. 

 18, 1902. 



1907.301. Evolution of mammalian molar teeth to and from 

 the triangular type, 250 pp., New York and Lon- 

 don, Macmillan Co., September, 1907. 



1912.368. Skuh measurements in man and the hoofed mammals: 

 Science, new ser., vol. 35, No. 902, p. 596, Apr. 12, 

 1912. 



1912.372. The continuous origin of certain unit characters as 

 observed by a paleontologist (Harvey lecture) : 

 Am. Naturalist, vol. 46, No. 544, pp. 185-206, 

 April, 1912; No. 545, pp. 249-278, May, 1912; 

 Harvey Soc. Volume, 7th ser., pp. 153-204, No- 

 vember, 1912. 



1912.382. Craniometry of the Equidae: Am. Mus. Nat. Hist. 

 Mem., new ser., vol. 1, pt. 3, pp. 57-100, figs. 1-17, 

 June, 1912. 



1915.416. Origin of single characters as observed in fossil and 

 living animals and plants (Presidential address 

 before the Paleontological Society of America, 

 Dec. 31, 1914) : Am. Naturalist, vol. 49, No. 580, 

 pp. 193-239, AprO, 1915. 



Proportion characters defined hy indices and ratios. — 

 Many specific, generic, and subfamily characters of 

 animals can be best expressed in mathematical ratios 

 and indices, for these figures record most precisely the 

 movements or tendencies of development that lead 

 from species to species. In all ascending series of 

 titanotheres every measurable character is in a state 

 of movement either progressively or retrogressively. 



Significance of tendencies in proportion. — A tendency 

 or trend to evolve in a certain proportional direction 

 is found to be a phyletic distinction of prime im- 

 portance, which leads us through all the stages of 

 mutative, specific, generic, and subfamily characteris- 

 tics. For example, certain titanotheres become more 

 and more broad-headed from lower to higher geologic 

 levels; progressive brachycephaly thus becomes a 

 phyletic character of taxonomic value. One genus 

 may be defined as "progressively brachycephalic," 

 whereas a related genus, in which the tendency to 

 become long-headed prevails, may be defined as 

 " progressively dolichocephalic." 



Taxonomic value oj proportion tendencies.- — Thus the 

 true relations of most of the lines of descent among the 

 Eocene and Oligocene titanotheres have been grad- 

 ually discovered, partly by the old methods of descrip- 

 tive anatomy, used by Leidy, Marsh, and Cope, and 

 partly by the new methods which have been developed 

 since 1900 in the preparation of this monograph. It 



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