Environmental Engineering Reference
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a problematic principle because often the niche is not defined precisely enough to
give the principle content. Indeed, there are many and various definitions of the niche
[ 29 ], but perhaps the one most usefully behind the principle is the Eltonian niche
which is about how an organism uses the environment [ 29 ]. However, when natural
enemies are considered, the niche must include not just how a species uses the
environment, but also how other organisms in the environment use that species.
Thus, the niche needs to be defined as how an organism relates to the environment
[ 15 , 29 ]. Regardless of whether this idea can be measured in an absolute sense, the
quantity r provides a relative sense in which two species relate to the environment.
This definition specifically removes the overall level of adaptedness to the environ-
ment from the comparison between species, focusing on how they relate to it. This
way of comparing niches differs markedly from what would be concluded from
comparing niches according to the recent niche definition of Chase and Leibold [ 29 ].
Under their definition, the conditions in the environment defining zero per capita
growth rates are the niche. That means species would only overlap completely if their
growth rates were zero under exactly the same conditions. Species with r = 1 would
overlap completely according to the approach here, but would not have zero growth
under the same conditions unless their k values were the same too.
The sense in which the competitive exclusion principle is correct is that no two
species can coexist stably if their niches overlap completely, i.e., r = 1. The
Lotka-Volterra approach defines this idea here, and makes it precise, but it is
important to realize that it in fact emerges from a broad array of models, as will be
discussed further below, without evidently any contrary models. More important,
these ideas allow a quantitative approach to the competitive exclusion principle.
A niche overlap value of r =1 is an unlikely occurrence in nature, but a value near 1
is not unreasonable. Here condition ( Eq. 13.6 ) shows that when species have high
niche overlap, their fitnesses are very closely constrained to be more nearly equal.
Thus, there is a more quantitative exclusion principle that relates not just to compe-
tition, but to apparent competition too, and states that species with high niche
overlap must have correspondingly high similarity in average fitness if they
are to coexist. This principle then replaces a statement with limited application to
a more significant one about the difficulty of coexistence for species with strongly
overlapping niches. That degree of difficulty is measured by how similar in average
fitness the species must be to allow coexistence with that degree of overlap.
Stabilizing and Equalizing Mechanisms
The expanded exclusion principle defined here is broadened with the realization
that there are two general but not equivalent ways in which species coexistence can
be favored. First is low overlap in niches, and second is similarity in average fitness.
Mechanisms that lead to low niche overlap are called stabilizing mechanisms, and
those that lead to similar average fitnesses are termed equalizing mechanisms. The
issue that distinguishes these two ways of achieving coexistence is the role of
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