The rainfall of this region takes the form of high-amplitude, high-frequency fluctu-
ations (Fig. 12.8). The herb layer, whether grazed or ungrazed, generates a similar
trace of high-amplitude, high-frequency fluctuations as it reacts speedily to rainfall
or the lack thereof. The fluctuations are paralleled by similar but more constrained
fluctuations in the kangaroos’ rate of increase as the population reacts dynamically
to variations in food supply. The trend of kangaroo density differs from the rainfall
regime, comprising fluctuations of high amplitude but low frequency. This result might
have been predictable from first principles: present density is an integration of past
rates of increase, not of present conditions. Initial conditions are not highly influen-
tial: the system remembers previous plant biomass for only 3 years but the memory
of kangaroo density can linger for 10 years. As a consequence of the slow tracking
of resources by kangaroos, there is a substantial time lag in response of kangaroos
to changing climatic conditions. This lag imparts an irregular fluctuation over time,
rather than constancy in abundance, despite the stability of the system under deter-
ministic (constant climatic) conditions. Caughley (1987) has christened systems that
show slow convergence on stochastically shifting equilibria as “centripetal.”206 Chapter 12
25020015010050(^005101520)
Year
Rain / 3-month period (mm)
Fig. 12.8A typical
stochastic series of
rainfall amounts per
3-month period
drawn from a normal
distribution with mean
and variance equivalent
to the Australian data.
(After Caughley 1987.)
0.6
0.4
0.2
0
0 5 10 15 20
Year
Kangaroo density (individuals / ha)
Fig. 12.9A typical
stochastic time series for
kangaroos, using the
model discussed in the
text, for the rainfall
sequence shown in Fig.
12.8.