Environmental Engineering Reference
In-Depth Information
Populations can, however, exhibit other kinds of dynamics. For example,
if per individual birth rates were initially slightly higher than in the previ-
ous case but declined more rapidly with population density, then the lag ef-
fect would be larger than in the previous case. Consequently, the pattern
of overshoot and undershoot could be sustained indefinitely causing per-
sistent oscillations as in the case when the population oscillates about the
equilibrium reaching the same maximum density and alternately the same
minimum density within each cycle period (figure 4.3b).This is known as
a stable limit cycle (Edelstein-Keshett 1988).Technically, the population is in
an equilibrium state even though it is oscillating—a stable limit cycle also
represents a type of “balance of nature.”
Stable limit cycles can take on many forms depending on the relative dif-
ference in magnitude between per individual birth and death rates, and the
rate at which birth and mortality rate changes with population density (e.g.,
figures 4.3b and 4.3c).These cycles each are produced by identical intrin-
sic properties.They simply represent different variants of equilibrium.The
implications of this variety of dynamics were used by Caughley (1976a) to
propose some sobering “what if ” questions about proposed management
solutions to a wildlife overabundance issue.
Limit Cycles and the Management of the African “Elephant Problem”
In parts of Africa, there has been considerable attention drawn to the dam-
aging effects of elephants ( Loxodonta Africana ) on forests. Elephants ring bark
or fell mature trees and consume regeneration, which can lead to conver-
sion of woodlands to open savannah or grassland—called the “elephant
problem” (Caughley 1976a).The problem had been attributed to two causes.
First, human-caused habitat loss compressed otherwise widely roaming ele-
phant populations into local areas (the population compression hypothesis).
Second, environmental change had allowed elephants to undergo rapid geo-
metric increase (the population eruption hypothesis). One obvious man-
agement solution would have been to cull elephant population levels to the
point where forests could regenerate.
Caughley critiqued these explanations on two grounds. First, both are
effectively hypotheses that are predicated on the untested assumption that
in the absence of human disturbances elephant populations and forests ex-
ists in a stable ratio of abundances over the long term.That is, they exist at
a fixed-point (nonoscillatory) equilibrium. Second, the time trend under
the two proposed hypotheses indicated that the population increase was re-
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