28
RICHARD S. MILLER
What these analyses do not, and cannot, show is any actual relationship between fundamental and realized niches, and therefore empirical
evidence of either competitive exclusion or coexistence at the level of
species interactions. In order to verify or deny the possibility that
competition affects community composition, we must first know how
many species are geographically and ecologically available to the community and whether there is intersection in their fundamental niches.
As Elton and Miller (1954) have noted, there is very little empirical
evidence that gives satisfactory proof of interspecific competition in
natural communities, “most of that adduced being equally explicable
by selective processes acting through other density-dependent population pressures.” This distinction was not clearly realized by Elton (1 946)
in his analysis. We have not, therefore, answered the question of whether
competition is a daily occurrence in the lives of many animals, or
whether it has occurred in their evolutionary histories, even though
laboratory evidence and some competition theory “is so strong and
persuasive that it must be taken into account in theories about community ecology” (Elton and Miller, 1954).
c. SPECIES-ABUNDANCE
When the MacArthur (1957) model of species-abundance is used to
demonstrate competitive exclusion, it suffers from the same inadequacies as other inferences predicated on the a priori assumption that
mutually exclusive distributions are invariably the product of competition. Of the three alternative situations considered in this model,
the one based on non-overlapping niches most nearly fits the conditions
of competitive exclusion. This case assumes that the Gause hypothesis
is universally valid and that all species in the community are mutually
exclusive, i.e. that each species in the community “utilizes the environment in some way so as to make it completely unavailable to the other
species in the community” (Slobodkin, 1961).
If we consider the total community environment to be a line of
finite length, we may divide it into n random parts by throwing (n - 1)
random points onto the line. The abundance of each species in the
community will have the same distribution as the length of parts of
the line. Under these conditions the expected distribution of the rth
rarest species is given by:
in which there are S species and N individuals. There is a limitation
on this theory such that the ratio of total numbers of individuals to
RICHARD S. MILLER
What these analyses do not, and cannot, show is any actual relationship between fundamental and realized niches, and therefore empirical
evidence of either competitive exclusion or coexistence at the level of
species interactions. In order to verify or deny the possibility that
competition affects community composition, we must first know how
many species are geographically and ecologically available to the community and whether there is intersection in their fundamental niches.
As Elton and Miller (1954) have noted, there is very little empirical
evidence that gives satisfactory proof of interspecific competition in
natural communities, “most of that adduced being equally explicable
by selective processes acting through other density-dependent population pressures.” This distinction was not clearly realized by Elton (1 946)
in his analysis. We have not, therefore, answered the question of whether
competition is a daily occurrence in the lives of many animals, or
whether it has occurred in their evolutionary histories, even though
laboratory evidence and some competition theory “is so strong and
persuasive that it must be taken into account in theories about community ecology” (Elton and Miller, 1954).
c. SPECIES-ABUNDANCE
When the MacArthur (1957) model of species-abundance is used to
demonstrate competitive exclusion, it suffers from the same inadequacies as other inferences predicated on the a priori assumption that
mutually exclusive distributions are invariably the product of competition. Of the three alternative situations considered in this model,
the one based on non-overlapping niches most nearly fits the conditions
of competitive exclusion. This case assumes that the Gause hypothesis
is universally valid and that all species in the community are mutually
exclusive, i.e. that each species in the community “utilizes the environment in some way so as to make it completely unavailable to the other
species in the community” (Slobodkin, 1961).
If we consider the total community environment to be a line of
finite length, we may divide it into n random parts by throwing (n - 1)
random points onto the line. The abundance of each species in the
community will have the same distribution as the length of parts of
the line. Under these conditions the expected distribution of the rth
rarest species is given by:
in which there are S species and N individuals. There is a limitation
on this theory such that the ratio of total numbers of individuals to