Geoscience Reference
In-Depth Information
populations is important because it depends not only on
internal properties of the ecosystems (intrinsic factors)
but also on the nature and frequency of the perturbations
(extrinsic factors). Populations vary more in climatically
unpredictable ecosystems like the arctic, subarctic, arid
and semi-arid regions than in predictable ones like the
tropical rain forests, suggesting that extrinsic factors may
govern variability more than intrinsic ones.
C
Stability
domain
K
Equilibrium
A
D
B
Time
Figure 22.6
Ecological systems with different stability
boreal coniferous forest, less stable than A; D dynamic
stability with population cycles.
Examples of stability
Information concerning the stability of biological
populations (mammals, birds, insects) is notoriously
difficult to obtain. It requires long-term studies to monitor
long-term effects; long runs of population data are needed
because short-term studies can be poor indicators of long-
term trends. Charles Elton analysed data from the
Hudson's Bay Company in Canada to record population
trends for the chief fur-bearing animals (see
Chapter 24).
He argued that, as hunting and trapping effort is not
likely to change much from year to year, company records
of furs and skins bought would be good indices of
population numbers.
Overall population trends have long been of interest to
ecologists, who wonder whether they reflect long-term
environmental changes or human impact. Steele has
argued that there are two basic trends - 'red noise' and
'white noise'. 'Red noise' is the stability situation where the
variability of populations increases with time; 'white noise'
is the stability situation where variability does not increase
with time. In the former case the amplitudes of variability
increase with time; in the latter case, the amplitudes are
constant.
Figure 22.8
plots the standard deviations of the
logarithms (SDL) against the period over which the
calculation was made. SDL increases with time for the 'red'
but not for the 'white' population. Steele put forward the
Measures of stability
Two approaches to defining stability quantitatively are
possible. The first, favoured by the ecologist MacArthur,
uses information theory, in a similar manner to its use in
the definition of diversity (pp. 538-9). Arguing that more
ecosystem linkages and a more even flow of energy along
them will give greater stability, one arrives at:
u
S =
P
i
log P
i
i=1
where
S
= stability,
Pi
= proportions of energy passing
through the
i
th species. Two different stability situations
are shown in
Figure 22.7
.
The killer whale receives energy
equally from five separate sources. This is a system with
maximum choice, low information content and
maximum uncertainty. In contrast the wolf subsists
mainly on caribou, whose migration paths it follows, with
lesser amounts of energy from a range of small mammals.
This is a system of little choice, high information content
and little uncertainty. The differences are reflected in the
stability values of 0·70 and 0·47. MacArthur hypothesized
that any failure of one energy pathway would be less
severe the greater the number of pathways and the more
even the distribution of energy between the pathways.
A second index of stability is the degree to which a
biological population fluctuates, i.e. the variability of
population density over time. This can be measured by the
standard statistical measures of variance (
s = 0.70
.LOOHU:KDOH
0.2
0.2
0.2
0.2
0.2
Seal
Penguin
Fish
Birds
Krill
n
8
s =
-
P
i
log P
i
:ROI
s = 0.47
i = 1
2
), standard
deviation (
) or coefficient of variation (cv) where:
0.6
0.1
0.1
0.1
0.1
Caribou
Vole
Hare
Rabbit
Lemming
cv =
/
¯
wolf is overdependent on one prey, whereas the killer whale
receives food from a range of equally energetic sources.
where cv = coefficient of variation,
= standard deviation
and
¯
= mean density. The variability of biological
