Skógræktarritið - 15.05.2001, Side 149

ecological conditions and scales
of observation. If validated
against proper real historic data,
it will represent an additional
contribution to already per-
formed modeling efforts for this
system (e.g., Virtanen et al. 1998)
if the HIBECO model predicts
with confidence not only the
actual outbreak- based on a
given a set of conditions (model
input) - but also its expected
severity and dispersion on a local
and regional scale.
The present modeling program
will unfortunately not have re-
sources to actually make such a
detailed forecast for a given
locality, due to the substantial
magnitude of data that would be
necessary for this kind of fore-
cast. However, the key point is
that the model - whether it
regards insect outbreaks or other
important aspects of the moun-
tain birch forest system - can be
expected to create forecasts with
a reasonable confidence level for
such a complex system even for
specific localities - given the neces-
sary and a priori specified quality
and quantity of model input.
Revealine results of a different
kind is the strongest kind of
model assessment. In this case
the model predicts something
not expected and when searched
forthrough more research, is
found to occur. Even if the avail-
able resources for modeling work
always are limited, revealing new
and unexpected results that can
be vaiidated against real data is
will always be a modeler’s dream
and ultimate goal. This level of
model assessment will be illus-
trated in more detail below.
Exploring scaling complexity
Scaling complexity is one of the
potential arenas where the
HIBECO model may bring in new
hypotheses and reveal new re-
sults, in addition to offering a
tool for simulation and valida-
tion against data for relation-
ships that are formulated a priori.
For example, consider the
hypothetical local population
dynamics of a virtual animal
species, which shows exponential
growth until it overshoots the en-
vironment's carrying capacity, and
then goes extinct. This example is
by no way realistic enough to sim-
ulate actual insect outbreaks in
the mountain birch forest ecosys-
tem, but it will be used below to
illustrate the kind of process com-
plexity that may appear in any
spatially extended system.
In a non-spatial, "mean field",
modeling context the kind of out-
break scenario described above
is not viable without the inclu-
sion of some kind of an immigra-
tion term (forcing function).
Without "rescue" from immigra-
tion, a model population which
goes extinct from intrinsic "boom
and bust" dynamics will obvious-
ly not be able to reappear and
increase again after extinction.
Modeled in a spatial arena
with a regional extent, however,
population dynamics that are
unstable iocally may still show a
viable regional population at
coarser scales within a given spa-
tial arena for the model. As illus-
trated in Fig. I, this may happen
even without including any simu-
lated "rescue effect" (Brown and
Kodric-Brown 1977) from the
Fig. 1. Local population density fluctuations are simulated in a spatial grid system
consisting of 12 local grid cells. Each vertical column in the grid consists of 12 cells
which represent a transect of 12 local "patches" in the virtual landscape at a given
point in time. The successive columns from left to right in the Figure shows the
transect at successive points in time, for example years, in a series of 101 time
intervals. The color codes for each grid cell represent local population densities,
ranging from low and medium (blue| to high (brown) and extremely high (yellow)
(the latter is only represented with one "peak" at time 14 from the left and located
at cell 11 from the bottom). Thus, a single vertical column of 12 cells shows local
population density variations overthis spatial transect at the chosen point in time,
while a specific horizontal row consisting of 101 cells shows how the local density in
this cell varies over time over 101 time intervals. 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. A specific center-region of the transect is marked with
pale colors. For this specific center-region of between two and three grid cells,
temporal outbreaks are marked along the time axis with the vertical arrows along
the top of the grid. A close inspection of this center-region shows that sometimes
the outbreak appear at one end of this center-region, and sometimes at the other
end, or somewhere in the middle. The complex spatio-temporal fluctuations in
abundance - which appears by reading the grid columns from left to right in the
Figure - are due to the specific set of model rules in this simulation: A percentage
of the individuals in a "booming" patch is defined to migrate to neighboring patch-
es during the following "bust” event of local extinction. ln this manner, this migra-
tion process may either re-populate a previously extinct local population, or the
new immigrants simply add more density to the local population at that time.
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