Geoscience Reference
In-Depth Information
A
B
Figure 6.3
Graphic detection of delayed density dependence wherein points representing con-
secutive generations are connected. (A) Percentage mortality caused by the parasitoid Encarsia for-
mosa on the greenhouse white fly (Trialeuroides vaporarorium). (Redrawn from Varley et al. 1973,
Fig. 4.5; data from Burnett 1958). (B) Change in density on a log scale (R) vs. density of the Cana-
dian lynx (redrawn from Royama 1977; data from Elton and Nicholson 1942).
the best known time series in ecology, the snowshoe hare and lynx oscillation
in Canada based on pelts delivered to the Hudson Bay Company over a time
period exceeding 100 years (Elton and Nicholson 1942). These data have been
analyzed by Royama (1992). Figure 6.4 shows fluctuations in density of the
lynx populations, along with the autocorrelation function (
ACF
) and the partial
autocorrelation function (
PACF
). The
ACF
expresses the correlation between each
measure of density and the densities 1, 2, . . .
n
generations back (the lag time).
For time series that display pronounced cycles, as in figure 6.4, the
ACF
reaches
a peak value at a lag time corresponding to cycle period.
The
ACF
can be used to determine whether time series are truly cyclic.
Although the cycles are obvious in figure 6.4, in many time series the fluctua-
tions are more irregular and detecting the difference between cyclic behavior
and random fluctuations is not at all obvious. Delayed density dependence can
be detected by looking at the
PACF
. The
PACF
represents the correlation that
remains at each lag time (between
X
t
and
X
t-n
), with the correlations due to
smaller lag times removed. For example, in most population time series there
is a fairly high correlation between
X
t
and
X
t
-1
(figure 6.4). For the same rea-
son
X
t
-1
is correlated with
X
t
-2
, and, consequently, a positive correlation exists
