48
RICHARD S. MILLER
indirect exploitation of the resources contained within the intersection
subset of their niches, and would not usually apply in the case of competitive interference with access to the resource. Chance oscillations in
the environmental variables controlling the values of tc and / I might
pass back and forth through the equilibrium point for the two species,
continually reversing the direction of competition and the probability
of survival of one or the other of the competitors (Hutchinson, 1948).
The theoretical possibility of a stable equilibrium is instructive, even
though it could not be sustained in a naturally changing environment.
Its principal value lies in the fact that it allows us to recognize conditions which would permit the coexistence of two species and to examine
these criteria with respect to events in natural ecosystems. Thus, these
analyses support Hutchinson’s (1948) observation that the rule of competitive exclusion need-not apply when (1) external factors act to rarefy
the mixed-species population so that the required resources are not
heavily exploited, or ( 2 ) when the values for tc and @ are under environmental control and chance oscillations prevent the establishment of a
permanent equilibrium.
VI. CONDITIONS OF COMPETITIVE EXCLUSION
The conditions of temperature and moisture in Park’s experiments
with Tribolium confusum and T . castaneum may be viewed as a set of
points in the intersection subset between two fundamental niches (Fig.
2, Case 2). It is evident from the data for control replicates that all
points in the fundamental niche spaces N, or N, do not have equal
survival value for the species, which in turn implies that the outcome
of competition between two species with intersecting niches will not
be the same at all points in their intersection subset N,.N,. This will
be the case especially in interactions where the dominant form of competition is exploitation and the outcome of the interaction depends on
(1) the ability of each species to survive, in the absence of interspecies
competition, a t different points in the niche space of the intersection
subset, and (2) their different exploitation and survival rates during
interspecies competition. Park’s experiments provide an especially good
illustration of the change in interaction values occurring at different
points in the intersection subset, and of the fact that an indeterminate
zone exists where the outcome of competition cannot be predicted with
certainty. Rather than the strict system of fundamental and realized
niches referred to earlier with reference to Case 1 and Case 2 (Fig. 2),
the indeterminate zone is an area of probabilities in which both species
may occur with changing frequency.
However, when competition is chiefly through interference, there
tends to be a more definite exclusion point corresponding to the
RICHARD S. MILLER
indirect exploitation of the resources contained within the intersection
subset of their niches, and would not usually apply in the case of competitive interference with access to the resource. Chance oscillations in
the environmental variables controlling the values of tc and / I might
pass back and forth through the equilibrium point for the two species,
continually reversing the direction of competition and the probability
of survival of one or the other of the competitors (Hutchinson, 1948).
The theoretical possibility of a stable equilibrium is instructive, even
though it could not be sustained in a naturally changing environment.
Its principal value lies in the fact that it allows us to recognize conditions which would permit the coexistence of two species and to examine
these criteria with respect to events in natural ecosystems. Thus, these
analyses support Hutchinson’s (1948) observation that the rule of competitive exclusion need-not apply when (1) external factors act to rarefy
the mixed-species population so that the required resources are not
heavily exploited, or ( 2 ) when the values for tc and @ are under environmental control and chance oscillations prevent the establishment of a
permanent equilibrium.
VI. CONDITIONS OF COMPETITIVE EXCLUSION
The conditions of temperature and moisture in Park’s experiments
with Tribolium confusum and T . castaneum may be viewed as a set of
points in the intersection subset between two fundamental niches (Fig.
2, Case 2). It is evident from the data for control replicates that all
points in the fundamental niche spaces N, or N, do not have equal
survival value for the species, which in turn implies that the outcome
of competition between two species with intersecting niches will not
be the same at all points in their intersection subset N,.N,. This will
be the case especially in interactions where the dominant form of competition is exploitation and the outcome of the interaction depends on
(1) the ability of each species to survive, in the absence of interspecies
competition, a t different points in the niche space of the intersection
subset, and (2) their different exploitation and survival rates during
interspecies competition. Park’s experiments provide an especially good
illustration of the change in interaction values occurring at different
points in the intersection subset, and of the fact that an indeterminate
zone exists where the outcome of competition cannot be predicted with
certainty. Rather than the strict system of fundamental and realized
niches referred to earlier with reference to Case 1 and Case 2 (Fig. 2),
the indeterminate zone is an area of probabilities in which both species
may occur with changing frequency.
However, when competition is chiefly through interference, there
tends to be a more definite exclusion point corresponding to the