or habitat of related species; such differences, if
found, are then cited as the reason competition is
not eliminating all but one of the species. Un
fortunately, however, differences in food and space
requirements are neither always necessary nor al
ways sufficient to prevent competition and permit
coexistence. Actually, to permit coexistence it
seems necessary that each species, when very
abundant, should inhibit its own further increase
more than it inhibits the other's. This is il
lustrated in Figure 1. In this figure, the popula
tions of the two species form the coordinates so
that any point in the plane represents a popula
tion for each species. Each shaded area covers the
points (i.e., the sets of combined populations of
the species) in which the species corresponding to
the shading can increase, within a given environ
ment. Thus, in the doubly-shaded area both
species increase and in the unshaded area both
species decrease. The arrows, representing the
direction of population change, must then be as
shown in the figure for these regions. In order
that a stable equilibrium of the two species should
exist, the arrows in the singly shaded regions
obviously must also be as in the figure; an inter
change of the species represented by the shading
would reverse the directions of these arrows re
sulting in a situation in which o~ly one species
could persist. Thus, for stability, the boundaries
of the shaded zones of increase must have the
relative slope illustrated in the figure with each
species inhibiting its own further increase more
than the other's. The easiest way for this to hap
pen would be to have each species' population
limited by a slightly different factor. It is these
different limiting factors which are the principal
problem in an investigation of multispecific animal
populations regulated by density dependent events.