756 The American Naturalist. [September, 
numerical expansion followed by a more or less abrupt decline. 
Darwin says (Origin of Species Chap. X, 1860). “There is 
reason to believe that the complete extinction of the species of 
a group is generally a slower process than their production ; if 
the appearance and disappearance of a group of species be re- 
presented as before by a vertical line of varying thickness, the 
line is found to taper more gradually at its upper end, which 
marks the progress of extermination, than at its lower end, 
which marks the first appearance and increase in numbers of 
the species.” In the case of favorable environment and high 
vitality the line would probably begin suddenly with a thick- 
ened end, continued and increased for some distance, and slope 
steeply to its termination. Two examples in paleontological 
history illustrate this; the Trilobitic fauna of the Upper Cam- 
brian, the Potsdam of Wisconsin and Minnesota, and the 
successive Ammonitic faunas of the Jura-Lias in Europe. 
Prof. Hall recognized and tentatively separated three hori- 
zons of the trilobitic beds of Wisconsin and Minnesota; the 
earlier trilobites were referable in numbers to the genus Cono- | 
cephalites while Dicelocephalus emerges in the middle beds and 
becomes numerically important through these and the higher 
beds. Prof. Hall was struck with their extreme abundance, 
and records his own impressions in these words; “ the multi- 
tude of individuals of a few species is really wonderful; for in 
some beds the layers may be separated at every inch, or even 
half inch, and yet the entire surface is covered with the dis- 
membered parts of these ancient trilobites.” As to the 
Ammonites of the Jurassic they are celebrated for the sharp- 
ness of lines of demarkation between beds abounding in great 
numbers of the different species. 
Unfavorable Environment and High Vitality—In this case . 
there would result a variable numerical abundance according 
to the equilibrium established between these discordant factors, 
but the average result would be a numerical uniformity ex- 
tended over a considerable length of time. The procreative. 
power would replenish the losses by death, and keep up, at 
least at first, a uniform amplitude of life. The unfavorable 
environment would work a defeating influence upon procrea- 
