Skógræktarritið - 15.05.2001, Page 150

Fig. 2 (a). The mean local abundance from the pale-colored center-region in Fig. I is
presented as a traditional time series diagram with density at the ordinate and time
at the abcissa (continuous line). The time units could for example be years. The
density could be for example number of individuals per spatial unit on average in a
sample taken within a grid cell at a given point in time. For comparison, a coarse-
scale view of the mean density for the 12-cell transect as a whole is also shown (stip-
pled line). The coarse scale series is aperiodic, while the finer-scale center-region
series shows an apparent 10-step periodicity for most of the time series
(b). The separate time series for two neighboring center-region grid cell densities
show an approximately 20-year outbreak cycle, with one of the patches lagging
approx. 10 time steps behind the other patch’s peak in abundance. In comparison
to Fig. 2 (a), we see that periodicity is strongly dependent on observational scale in
this example, spanning from period 20 at fine scale (1 grid cell), period 10 at some-
what coarser scale (2-3 grid cells), and aperiodicity at ''regional" scale (12 grid cells).
"outside", i.e. with zero rate of
immigration to the model arena
as a whole. The reason for long-
term survival can be found in the
complex spatio-temporal fluctua-
tions that prevail at finer scales
due to local dispersal. At any
point in time there is always
some local population or anoth-
er increasing in number, and
thus being ready to contribute to
revitalize neighboring localities
through dispersal during a future
local "bust". Contrary to the
mean field scenario where the
model population responds
dynamically as a single unit, the
spatially structured population in
Fig. 1 gives migration as an intrin-
sic process of the system rather
than an extrinsic forcing func-
tion. Thus, the immigration rate
to the total population in Fig. I
is set to zero (only local inter-
patch dispersal takes place) and
the total population still survives
in the long run in spite of fre-
quent local extinctions at fine
scales.
From an empirical point of
view, this kind of effect on spa-
tio-temporal fluctuations on
population viability may be
called "common knowledge"
(e.g., Andrewartha and Birch
1954). However, the point is that
from a theoretical perspective,
the inclusion of space in the
model opens for a huge step for-
ward in terms of realism. There
has been a long tradition in the-
oretical ecological modeling
where this kind of realism has
been more or less ignored, but
present-day modeling has be-
come much more sophisticated
(McGlade 1999).
The "toy" model simulation
insight from formulating the spa-
tial dimension(s) explicitly
instead of "averaging out" local
processes may initiate a cascade
of new investigations involving
real data as well as model refine-
ments. Analysis of the „toy"
model example in Fig. 1, and
similar models from the litera-
ture, predicts that neighborhood
dispersal leads to a pattern of
outbreaks that tend to be damp-
ened due to spatial fluctuation
asynchrony at coarser scales
than the correlation length given
by the typical scale of dispersal
distance. New data used to test
this hypothesis may then lead to
a more coherent theory with a
better predictive power than the
starting point of a too simplistic
non-spatial model.
Another interesting observa-
tion from a specific model output
in Fig. 2 is that one particular
“time series" apparently pro-
duces a -20 temporal unit inter-
val periodicity at the grid cell
scaie, ~10 unit periodicity at spa-
tial scale 2 (two neighbor grid
cells), and aperiodicity at coarser
scales. The new questions that
can be raised from this result are
then (for example): what makes
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