Environmental Engineering Reference
In-Depth Information
Fig. 8.7 Diffusion limited
aggregation, produced with
the fractal generator
FRACTINT. A large number
of mobile cells are started in
the periphery, which attach by
chance to a centrally located
“fixed” cell, bringing up the
typical diffusion-limited
aggregation-pattern
disturbances (i.e. fire), imposed at different spatial extents. Model simulations were
based on data from an experimental community with five grassland species.
A lattice of 200
200 square cells was used, with at most one individual of each
species occupying a cell at a time. Global rules applying at the local scale determine
the state of the system at each time step. The degree of influence of a cell to
neighbouring cells follows a negative exponential decrease. The biological pro-
cesses simulated are seed dispersal and competition. The following main proce-
dures were used:
l
Every individual of each species
i
produces seeds at a given rate
p
i
. We assume
that the distribution of times between individual seed production is exponential,
with a mean of 1/
p
i
.
l
The probability that a seed disperses from one cell to another depends on the
species dispersal type (local, medium or long) and the distance between cells.
l
Displacement of species is modelled in occupied cells depending on the com-
petitive advantage of the invading species. The process of seed dispersal to
neighbouring empty cells is modelled using a probabilistic algorithm.
The model starts with an assignment of seeds to donor cells in a random manner
but with a frequency that is inversely related to donor cell distance. If a cell
receives multiple seeds from different plant species, a random variable linked to
the competition coefficient of the species determines the winner at that cell. All
seeds are then eligible to sprout and will germinate at the next growing season;
dormancy is not considered; the model does not consider environmental variability
between years.
Parameters from an experimental biodiversity study of grasslands in Lesbos,
Greece were used for the model specification. The experimental study was part of
the European-wide research project BIODEPTH (Hector et al. 1999), aiming to
