408 INTRODUCTION TO EVOLUTION 



Fig. 18.2C shows the increase in horn length when the head length has 

 increased to 50 cm. The length of the horn is calculated using the same 

 constants as before but assigning x a value of 50. We note that y now 

 equals 10 cm. In other words, while the head has doubled in length, the 

 horn has become four times as long as it was at the outset. 



D and E, Fig. 18.2, show the increase in horn length with additional in- 

 crease in length of head. In E the length of the head has increased to four 

 times its original length, but the horn is sixteen times as long as it was at 

 first. 



Our hypothetical example assumes added significance when we note that 

 Fig. 18.2 may be interpreted in one or all of three difl'erent ways. (1 ) The 

 series of heads shown may represent stages in the growth and development 

 of an individual rhinoceroslike animal. In this case A is the head of a 

 young, perhaps newborn, animal, and the succeeding diagrams show 

 stages in the animal's development as it becomes adult. In other words, the 

 diagrams may represent an ontogenetic series (cf. "ontogeny''). (2) On 

 the other hand, the series of heads may represent adult individuals of vary- 

 ing sizes. In this case A would represent an adult of a dwarf species of 

 rhinoceroslike animal, E an adult of a relatively giant species, the inter- 

 vening forms being adults of species of intermediate size. (3) Or again, the 

 series of heads may represent an evolutionary series. In this case A would 

 represent an adult of a prehistoric ancestor, E would be its modern de- 

 scendant, and the intervening forms would be intermediate steps in the 

 sequence of forms leading from A to E. Such series of fossils, marked by 

 increasing size, are frequently encountered; we recall particularly the 

 evolutionary sequences leading to the modern horse and to the modern 

 elephant (pp. 197-216). Thus the series of diagrams in Fig. 18.2 may rep- 

 resent a phylogenetic series (cf. "phylogeny"). 



Let us turn from a hypothetical example to one based on actual data. In 

 our discussion of the evolution of the horse (pp. 197-206) we noted that 

 during evolution the facial or preorbital portion of the skull increased in 

 length disproportionally to the increase in size of the skull as a whole (Fig. 

 10.3, p. 199). The same trend is noted in the ontogeny of modern horses. 

 Line A in Fig. 18.3 shows the increase in length of face as compared to 

 length of brain case (cranium) in modern horses of diff'erent sizes and 

 ages. The lowest point on the line represents a foetal horse; other points 

 represent colts and adults of varying sizes. As the cranium increases in 

 length the face increases in length at a somewhat faster rate {k = about 1 .5) 

 until a cranium length of about 15 cm. is reached (in colts 6 to 8 months 



