758 The American Naturalist. [September, 
tain animals though the value of the procreative energy con- 
sidered at the instant of its exercise may be high. Evidently 
for such animals their duration in time will be conditioned 
largely upon favorable circumstances of life and without these 
they must undergo extinction. The numerical representation 
must always be small; it is essentially limited by their intrin- 
sic predisposition to be slow breeders. This assumption seems 
applicable to species which without any apparent change in 
their environment become subject to a progressive failure in 
numbers. The history of invertebrate life on the earth’s sur- 
face emphasizes this. Throughout similar conditions or what, 
from lithological evidence, seem identical conditions, species 
dwindle and disappear. On what hypothesis can this gradual 
vanishment be explained, except that the living momentum 
has run down, a physiological deterioration has set in, which 
must, no matter how auspicious be the physical requirements, 
compass the discomfiture and suppression of the species. Low 
vitality might also reasonably imply a certain functional weak- 
ness which affects the organic intregrity of a species. Under 
either implication, that of low procreative power or functional 
weakness, favorable environment fictitiously prolongs the life 
of the species and gives a deceptive appearance of stability to 
a species internally disintegrating. Its numerical ratio must 
be a reduced one. 
Unfavorable Environment and Low Vitality—This category 
symbolizes the rapid decline of a species, and is symptomatic 
of the final stages in its life-history. Where unfavorable con- 
ditions combine with intrinsic decrepitude the doom of a 
species is quickly sealed, and it vanishes from the scene 
scarcely noticed amidst the on-coming armies of new and 
intense competitors. 
These four categories which we have epitomized, embodying 
the relations of vitality to environment and applied to the 
phenomena of the numerical abundance of a species, may be 
generally regarded as the formal stages of a species’ decline. 
And we observe that the succession of these stages may follow 
one of two directions as divergent lines from an original con- 
dition. That original condition is Favorable Environment and 
