Biology Reference
In-Depth Information
(2) deterministic equations are sufficient to model population growth,
and environmental fluctuations need not be considered;
(3) the environment is spatially homogeneous and migration is unimportant;
(4) competition is the only important biological interaction; and
(5) coexistence requires a stable equilibrium point.
They further summarize the consequences of these assumptions, i.e., that
n species can coexist only if there are no fewer than n limiting resources,
and that there is a limiting similarity between species: species evolved in
response to interspecific competition. Assumption 4 (above) is relaxed
when predators are present, i.e., n species may coexist when fewer than n
resources are present. If the environment favours different species in
different patches, n species may coexist in at least n patches, even if the
species use the same limiting resource.
The authors then contrast these assumptions with those of nonequili-
brium situations. Nonequilibrium is seen as ''any situation where species
densities do not remain constant over time in each spatial location.'' Even
if fluctuations occur at small spatial scales that level each other out at larger
scales, an explanation would still be a nonequilibrium explanation if the
fluctuations are an essential part of the explanation. Chesson and Case
(
1986
) discuss the following four points that deviate from classical equili-
brium assumptions:
(1) populations are not at a point equilibrium but competition still
occurs continuously and is important; this may permit more than
n species to coexist on n resources (e.g., Armstrong and McGee
1980
);
(2) fluctuations in population density or environmental variables are
dominant, population dynamics may be density-independent;
(3) means and variances of environmental fluctuations are not constant
over time; and
(4) populations are random-walking, but time to extinction is so long that
species persist over a long time (''slow competitive displacement'').
Concerning nonequilibrium, Cappucino (
1995
) argues that only ran-
domly walking populations are unambiguously nonequilibrial. All other
usages are misplaced. Thus, the most commonly used meaning of non-
equilibrium in populations refers to situations where local populations do
not trend towards a point equilibrium (density-vagueness of Strong [
1984
];
stochastic boundedness of Chesson [
1978
]). However, according to
Cappucino, fluctuations in such populations are bounded and therefore
