408 The Use of Graphs in Paleontology. 
not always possible to state what are the precise anatomical or 
histological constituents which make up the “structural unit” 
under consideration. A term seems to be needed which will stand 
for the phenomenon referred to in this paper under such phrases 
as a “unit series of changes ’’, “ flow-line of change ”’, “ direction of 
change’. Even a clearly defined structural unit may be the subject 
of several different but definite directions of change in less closely 
related lineages, cf. the ambulacral areas of paleeozoic and modern 
echinoids, or the feet of perissodactyles and artiodactyles. 
Tallness and dwarfness in peas have become classical subjects 
for experimentation. These two features in peas seem to belong 
to the same order of phenomena as narrowness and broadness of 
skull in Titanotheres. These types of skull have been proved to 
arise gradually from skulls of median proportions.’ Judging by the 
fact that peas of all statures between tall and short exist to-day 
it seems not improbable that the tall and short races must likewise 
have arisen gradually, during the passage of time, from a race of 
median stature. Be this as it may, the tall and short peas, with which 
the experiments were performed, are to-day distinct races; that 
is to say, they belong to different lineages which breed true and 
which for a period of time have been pursuing divergent lines of 
evolution in respect of stature. The experimenter crosses the 
races and transposes the tallness of one line to the other line, and 
by so doing produces a new race having the usual characters of the 
dwarf pea except as regards stature. The fact that he is able to do 
this suggests that a similar exchange, likewise resulting in the 
sudden appearance of a new race, could and did take place in nature, 
for during the early history of allied lineages it is reasonable to infer 
that they would be as mutually fertile as these two races of peas. 
Thus, in Fig. 10 it is conceivable that mutation y was produced by 
a cross between a form similar to K and one in which there were 
few minor and many major septa. If that has been the case then v, 
like the experimenter’s new race of peas, had a dual ancestry. 
This is, of course, purely hypothetical, nevertheless, it illustrates one 
type of problem that the use of graphic methods in paleontology 
may hope to solve. Meanwhile, the results of Mendelian 
experimentation produce the uncomfortable feeling that a 
paleontologist tracing lineages of species, or even in some cases, of 
genera to common ancestors 1s pursuing a “ will-o’-th’-wisp ”, that 
converging lines of descent run back, not into a point, but into a net- 
work of incipient lineages, in which structural elements as they 
change are shuffled across, like strands, from one thread to another, 
until several combinations of developmental stages have been hit 
upon which are both stable and mutually sterile. 
My thanks are due to my colleagues, Mr. H. 8. Holden and 
Mr. A. W. Richardson, for much free discussion of the subject matter 
of this paper and for many helpful criticisms and suggestions. 
? Osborn, Bull. Amer. Mus. Nat. Hist., 1902, pp. 77-89. 
